Daily Papers

Large Language Models (LLMs) have made significant strides in natural language generation but often face challenges in tasks requiring precise calculations and structural analysis. This paper investigates the performance of state-of-the-art LLMs on language complexity measurement tasks, through the computation of the LIX readability metric and Average Dependency Distance (ADD). Using Swedish high school and university-level essays, we evaluate the models' abilities to compute LIX scores and perform dependency parsing, comparing their results to established ground truths. Our findings reveal that while all models demonstrate some capacity for these tasks, ChatGPT-o1-mini performs most consistently, achieving the highest accuracy in both LIX computation and dependency parsing. Additionally, we observe a strong significant correlation -0.875 p 0.026 (N=6) between the models' accuracy in computing LIX and their overall performance on the Massive Multitask Language Understanding (MMLU) benchmark. These results suggest that language complexity measurement abilities can serve as a noisy zero-shot proxies for assessing the general capabilities of LLMs, providing a practical method for model evaluation without the need for extensive benchmarking datasets.

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the double descent curve, achieving a maximum at the interpolation regime. We study this phenomenon in the context of image classification and ask whether fragmentation could be predictive of generalization performance. Using a fragmentation-based complexity measure, we show this to be possible by achieving good performance on the PGDL (Predicting Generalization in Deep Learning) benchmark. In addition, we report on new observations related to fragmentation, namely (i) fragmentation is not limited to the input space but occurs in the hidden representations as well, (ii) fragmentation follows the trends in the validation error throughout training, and (iii) fragmentation is not a direct result of increased weight norms. Together, this indicates that fragmentation is a phenomenon worth investigating further when studying the generalization ability of deep neural networks.

A common approach for sequence tagging tasks based on contextual word representations is to train a machine learning classifier directly on these embedding vectors. This approach has two shortcomings. First, such methods consider single input sequences in isolation and are unable to put an individual embedding vector in relation to vectors outside the current local context of use. Second, the high performance of these models relies on fine-tuning the embedding model in conjunction with the classifier, which may not always be feasible due to the size or inaccessibility of the underlying feature-generation model. It is thus desirable, given a collection of embedding vectors of a corpus, i.e., a datastore, to find features of each vector that describe its relation to other, similar vectors in the datastore. With this in mind, we introduce complexity measures of the local topology of the latent space of a contextual language model with respect to a given datastore. The effectiveness of our features is demonstrated through their application to dialogue term extraction. Our work continues a line of research that explores the manifold hypothesis for word embeddings, demonstrating that local structure in the space carved out by word embeddings can be exploited to infer semantic properties.

Theory of Mind (ToM) can be used to assess the capabilities of Large Language Models (LLMs) in complex scenarios where social reasoning is required. While the research community has proposed many ToM benchmarks, their hardness varies greatly, and their complexity is not well defined. This work proposes a framework inspired by cognitive load theory to measure the complexity of ToM tasks. We quantify a problem's complexity as the number of states necessary to solve it correctly. Our complexity measure also accounts for spurious states of a ToM problem designed to make it apparently harder. We use our method to assess the complexity of five widely adopted ToM benchmarks. On top of this framework, we design a prompting technique that augments the information available to a model with a description of how the environment changes with the agents' interactions. We name this technique Discrete World Models (DWM) and show how it elicits superior performance on ToM tasks.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

In this paper, we propose a new measure to gauge the complexity of image classification problems. Given an annotated image dataset, our method computes a complexity measure called the cumulative spectral gradient (CSG) which strongly correlates with the test accuracy of convolutional neural networks (CNN). The CSG measure is derived from the probabilistic divergence between classes in a spectral clustering framework. We show that this metric correlates with the overall separability of the dataset and thus its inherent complexity. As will be shown, our metric can be used for dataset reduction, to assess which classes are more difficult to disentangle, and approximate the accuracy one could expect to get with a CNN. Results obtained on 11 datasets and three CNN models reveal that our method is more accurate and faster than previous complexity measures.

Utilizing massive web-scale datasets has led to unprecedented performance gains in machine learning models, but also imposes outlandish compute requirements for their training. In order to improve training and data efficiency, we here push the limits of pruning large-scale multimodal datasets for training CLIP-style models. Today's most effective pruning method on ImageNet clusters data samples into separate concepts according to their embedding and prunes away the most prototypical samples. We scale this approach to LAION and improve it by noting that the pruning rate should be concept-specific and adapted to the complexity of the concept. Using a simple and intuitive complexity measure, we are able to reduce the training cost to a quarter of regular training. By filtering from the LAION dataset, we find that training on a smaller set of high-quality data can lead to higher performance with significantly lower training costs. More specifically, we are able to outperform the LAION-trained OpenCLIP-ViT-B32 model on ImageNet zero-shot accuracy by 1.1p.p. while only using 27.7% of the data and training compute. Despite a strong reduction in training cost, we also see improvements on ImageNet dist. shifts, retrieval tasks and VTAB. On the DataComp Medium benchmark, we achieve a new state-of-the-art ImageNet zero-shot accuracy and a competitive average zero-shot accuracy on 38 evaluation tasks.

Self-attention is at the heart of the popular Transformer architecture, yet suffers from quadratic time and memory complexity. The breakthrough FlashAttention algorithm revealed I/O complexity as the true bottleneck in scaling Transformers. Given two levels of memory hierarchy, a fast cache (e.g. GPU on-chip SRAM) and a slow memory (e.g. GPU high-bandwidth memory), the I/O complexity measures the number of accesses to memory. FlashAttention computes attention using N^2d^2{M} I/O operations where N is the dimension of the attention matrix, d the head-dimension and M the cache size. However, is this I/O complexity optimal? The known lower bound only rules out an I/O complexity of o(Nd) when M=Theta(Nd), since the output that needs to be written to slow memory is Omega(Nd). This leads to the main question of our work: Is FlashAttention I/O optimal for all values of M? We resolve the above question in its full generality by showing an I/O complexity lower bound that matches the upper bound provided by FlashAttention for any values of M geq d^2 within any constant factors. Further, we give a better algorithm with lower I/O complexity for M < d^2, and show that it is optimal as well. Moreover, our lower bounds do not rely on using combinatorial matrix multiplication for computing the attention matrix. We show even if one uses fast matrix multiplication, the above I/O complexity bounds cannot be improved. We do so by introducing a new communication complexity protocol for matrix compression, and connecting communication complexity to I/O complexity. To the best of our knowledge, this is the first work to establish a connection between communication complexity and I/O complexity, and we believe this connection could be of independent interest and will find many more applications in proving I/O complexity lower bounds in the future.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.

Large Language Models (LLMs) have shown strong in-context learning (ICL) abilities with a few demonstrations. However, one critical challenge is how to select demonstrations to elicit the full potential of LLMs. In this paper, we propose Curriculum Demonstration Selection (CDS), a novel demonstration selection method for ICL. Instead of merely using similarity, CDS additionally partitions samples by their complexity measurements. Following curriculum learning, CDS then selects demonstrations from easy to difficult. Thus the selected demonstrations cover a wide range of difficulty levels, enabling LLMs to learn from varied complexities within the training set. Experiments demonstrate that our CDS consistently outperforms baseline methods, achieving notable improvements across nine LLMs on three benchmarks. Moreover, CDS proves especially effective in enhancing LLM performance in solving challenging problems.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

Large Language Models (LLMs) suffer from reliability issues on complex tasks, as existing decomposition methods are heuristic and rely on agent or manual decomposition. This work introduces a novel, systematic decomposition framework that we call Analysis of CONstraint-Induced Complexity (ACONIC), which models the task as a constraint problem and leveraging formal complexity measures to guide decomposition. On combinatorial (SATBench) and LLM database querying tasks (Spider), we find that by decomposing the tasks following the measure of complexity, agent can perform considerably better (10-40 percentage point).

Interactively learning from observation and language feedback is an increasingly studied area driven by the emergence of large language model (LLM) agents. While impressive empirical demonstrations have been shown, so far a principled framing of these decision problems remains lacking. In this paper, we formalize the Learning from Language Feedback (LLF) problem, assert sufficient assumptions to enable learning despite latent rewards, and introduce transfer eluder dimension as a complexity measure to characterize the hardness of LLF problems. We show that transfer eluder dimension captures the intuition that information in the feedback changes the learning complexity of the LLF problem. We demonstrate cases where learning from rich language feedback can be exponentially faster than learning from reward. We develop a no-regret algorithm, called HELiX, that provably solves LLF problems through sequential interactions, with performance guarantees that scale with the transfer eluder dimension of the problem. Across several empirical domains, we show that HELiX performs well even when repeatedly prompting LLMs does not work reliably. Our contributions mark a first step towards designing principled interactive learning algorithms from generic language feedback.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

This work introduces the first toolkit around path-norms that fully encompasses general DAG ReLU networks with biases, skip connections and any operation based on the extraction of order statistics: max pooling, GroupSort etc. This toolkit notably allows us to establish generalization bounds for modern neural networks that are not only the most widely applicable path-norm based ones, but also recover or beat the sharpest known bounds of this type. These extended path-norms further enjoy the usual benefits of path-norms: ease of computation, invariance under the symmetries of the network, and improved sharpness on layered fully-connected networks compared to the product of operator norms, another complexity measure most commonly used. The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

We explore a new class of diffusion models based on the transformer architecture. We train latent diffusion models of images, replacing the commonly-used U-Net backbone with a transformer that operates on latent patches. We analyze the scalability of our Diffusion Transformers (DiTs) through the lens of forward pass complexity as measured by Gflops. We find that DiTs with higher Gflops -- through increased transformer depth/width or increased number of input tokens -- consistently have lower FID. In addition to possessing good scalability properties, our largest DiT-XL/2 models outperform all prior diffusion models on the class-conditional ImageNet 512x512 and 256x256 benchmarks, achieving a state-of-the-art FID of 2.27 on the latter.

In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets.

This study introduces a novel approach by replacing the traditional perceptron neuron model with a biologically inspired probabilistic meta neuron, where the internal neuron parameters are jointly learned, leading to improved classification accuracy of spiking neural networks (SNNs). To validate this innovation, we implement and compare two SNN architectures: one based on standard leaky integrate-and-fire (LIF) neurons and another utilizing the proposed probabilistic meta neuron model. As a second key contribution, we present a new biologically inspired classification framework that uniquely integrates SNNs with Lempel-Ziv complexity (LZC) a measure closely related to entropy rate. By combining the temporal precision and biological plausibility of SNNs with the capacity of LZC to capture structural regularity, the proposed approach enables efficient and interpretable classification of spatiotemporal neural data, an aspect not addressed in existing works. We consider learning algorithms such as backpropagation, spike-timing-dependent plasticity (STDP), and the Tempotron learning rule. To explore neural dynamics, we use Poisson processes to model neuronal spike trains, a well-established method for simulating the stochastic firing behavior of biological neurons. Our results reveal that depending on the training method, the classifier's efficiency can improve by up to 11.00%, highlighting the advantage of learning additional neuron parameters beyond the traditional focus on weighted inputs alone.

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.

The rapid progress of image generative AI has blurred the boundary between synthetic and real images, fueling an arms race between generators and discriminators. This paper investigates the conditions under which discriminators are most disadvantaged in this competition. We analyze two key factors: data dimensionality and data complexity. While increased dimensionality often strengthens the discriminators ability to detect subtle inconsistencies, complexity introduces a more nuanced effect. Using Kolmogorov complexity as a measure of intrinsic dataset structure, we show that both very simple and highly complex datasets reduce the detectability of synthetic images; generators can learn simple datasets almost perfectly, whereas extreme diversity masks imperfections. In contrast, intermediate-complexity datasets create the most favorable conditions for detection, as generators fail to fully capture the distribution and their errors remain visible.

EHR audit logs are a highly granular stream of events that capture clinician activities, and is a significant area of interest for research in characterizing clinician workflow on the electronic health record (EHR). Existing techniques to measure the complexity of workflow through EHR audit logs (audit logs) involve time- or frequency-based cross-sectional aggregations that are unable to capture the full complexity of a EHR session. We briefly evaluate the usage of transformer-based tabular language model (tabular LM) in measuring the entropy or disorderedness of action sequences within workflow and release the evaluated models publicly.

This paper presents ``Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the {\em inverse} of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Free-text rationales justify model decisions in natural language and thus become likable and accessible among approaches to explanation across many tasks. However, their effectiveness can be hindered by misinterpretation and hallucination. As a perturbation test, we investigate how large language models (LLMs) perform rationale generation under the effects of readability level control, i.e., being prompted for an explanation targeting a specific expertise level, such as sixth grade or college. We find that explanations are adaptable to such instruction, though the requested readability is often misaligned with the measured text complexity according to traditional readability metrics. Furthermore, the generated rationales tend to feature medium level complexity, which correlates with the measured quality using automatic metrics. Finally, our human annotators confirm a generally satisfactory impression on rationales at all readability levels, with high-school-level readability being most commonly perceived and favored.

We investigate whether Alfv\'enic fluctuations (AFs) can affect the structure of magnetic ejecta (MEs) within interplanetary coronal mass ejections (ICMEs). We study an ICME observed on 2001 December 29 at 1 au by ACE and Wind, at a total angular separation of sim0.8^circ (sim0.014~au). We focus on the correlation and complexity of its magnetic structure measured between two spacecraft in association with large-amplitude AFs. The Alfv\'enicity of the ME is investigated in terms of the residual energy and cross helicity of fluctuations. We find that as for the event of interest, large-amplitude AFs occur in the rear region of the ME at both Wind and ACE with a duration of about six hours. We compare the correlation of the magnetic field strength and vector components measured between Wind and ACE, and investigate complexity in terms of the magnetic hodograms. The region showing AFs is found to be associated with a decreased correlation of the magnetic field components and an increased complexity of the ME magnetic configuration detected at ACE and Wind, which may be due to the fact that the two spacecraft crossing the same ME along different trajectories likely sampled AFs in different oscillation phases. Combining multi-point in-situ measurements and remote-sensing observations of the ICME source region, we further discuss different potential sources of the AFs.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

The complexity of laboratory environments requires solutions that simplify instrument interaction and enhance measurement automation. Traditional tools often require configuration, software, and programming skills, creating barriers to productivity. Previous approaches, including dedicated software suites and custom scripts, frequently fall short in providing user-friendly solutions that align with programming practices. We present LABIIUM, an AI-enhanced, zero-configuration measurement automation system designed to streamline experimental workflows and improve user productivity. LABIIUM integrates an AI assistant powered by Large Language Models (LLMs) to generate code. LABIIUM's Lab-Automation-Measurement Bridges (LAMBs) enable seamless instrument connectivity using standard tools such as VSCode and Python, eliminating setup overhead. To demonstrate its capabilities, we conducted experiments involving the measurement of the parametric transfer curve of a simple two-transistor inverting amplifier with a current source load. The AI assistant was evaluated using different prompt scenarios and compared with multiple models, including Claude Sonnet 3.5, Gemini Pro 1.5, and GPT-4o. An expert solution implementing the Gradient-Weighted Adaptive Stochastic Sampling (GWASS) method was used as a baseline. The solutions generated by the AI assistant were compared with the expert solution and a uniform linear sweep baseline with 10,000 points. The graph results show that the LLMs were able to successfully complete the most basic uniform sweep, but LLMs were unable to develop adaptive sweeping algorithms to compete with GWASS. The evaluation underscores LABIIUM's ability to enhance laboratory productivity and support digital transformation in research and industry, and emphasizes the future work required to improve LLM performance in Electronic Measurement Science Tasks.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

In the field of psychology, traditional assessment methods, such as standardized scales, are frequently critiqued for their static nature, lack of personalization, and reduced participant engagement, while comprehensive counseling evaluations are often inaccessible. The complexity of quantifying psychological traits further limits these methods. Despite advances with large language models (LLMs), many still depend on single-round Question-and-Answer interactions. To bridge this gap, we introduce PsyDI, a personalized and progressively in-depth chatbot designed for psychological measurements, exemplified by its application in the Myers-Briggs Type Indicator (MBTI) framework. PsyDI leverages user-related multi-modal information and engages in customized, multi-turn interactions to provide personalized, easily accessible measurements, while ensuring precise MBTI type determination. To address the challenge of unquantifiable psychological traits, we introduce a novel training paradigm that involves learning the ranking of proxy variables associated with these traits, culminating in a robust score model for MBTI measurements. The score model enables PsyDI to conduct comprehensive and precise measurements through multi-turn interactions within a unified estimation context. Through various experiments, we validate the efficacy of both the score model and the PsyDI pipeline, demonstrating its potential to serve as a general framework for psychological measurements. Furthermore, the online deployment of PsyDI has garnered substantial user engagement, with over 3,000 visits, resulting in the collection of numerous multi-turn dialogues annotated with MBTI types, which facilitates further research.

We extend our previous work on Inductive Conformal Prediction (ICP) for multi-label text classification and present a novel approach for addressing the computational inefficiency of the Label Powerset (LP) ICP, arrising when dealing with a high number of unique labels. We present experimental results using the original and the proposed efficient LP-ICP on two English and one Czech language data-sets. Specifically, we apply the LP-ICP on three deep Artificial Neural Network (ANN) classifiers of two types: one based on contextualised (bert) and two on non-contextualised (word2vec) word-embeddings. In the LP-ICP setting we assign nonconformity scores to label-sets from which the corresponding p-values and prediction-sets are determined. Our approach deals with the increased computational burden of LP by eliminating from consideration a significant number of label-sets that will surely have p-values below the specified significance level. This reduces dramatically the computational complexity of the approach while fully respecting the standard CP guarantees. Our experimental results show that the contextualised-based classifier surpasses the non-contextualised-based ones and obtains state-of-the-art performance for all data-sets examined. The good performance of the underlying classifiers is carried on to their ICP counterparts without any significant accuracy loss, but with the added benefits of ICP, i.e. the confidence information encapsulated in the prediction sets. We experimentally demonstrate that the resulting prediction sets can be tight enough to be practically useful even though the set of all possible label-sets contains more than 1e+16 combinations. Additionally, the empirical error rates of the obtained prediction-sets confirm that our outputs are well-calibrated.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

Permutation Entropy and statistiCal Complexity Analysis for astRophYsics (PECCARY) is a computationally inexpensive, statistical method by which any time-series can be characterized as predominantly regular, complex, or stochastic. Elements of the PECCARY method have been used in a variety of physical, biological, economic, and mathematical scenarios, but have not yet gained traction in the astrophysical community. This study introduces the PECCARY technique with the specific aims to motivate its use in and optimize it for the analysis of astrophysical orbital systems. PECCARY works by decomposing a time-dependent measure, such as the x-coordinate or orbital angular momentum time-series, into ordinal patterns. Due to its unique approach and statistical nature, PECCARY is well-suited for detecting preferred and forbidden patterns (a signature of chaos), even when the chaotic behavior is short-lived or when working with a relatively short duration time-series or small sets of time-series data. A variety of examples are used to demonstrate the capabilities of PECCARY. These include mathematical examples (sine waves, varieties of noise, sums of sine waves, well-known chaotic functions), a double pendulum system, and astrophysical tracer particle simulations with potentials of varying intricacies. Since the adopted timescale used to diagnose a given time-series can affect the outcome, a method is presented to identify an ideal sampling scheme, constrained by the overall duration and the natural timescale of the system. The accompanying PECCARY Python package and its usage are discussed.

Understanding how humans perceive visual complexity is a key area of study in visual cognition. Previous approaches to modeling visual complexity assessments have often resulted in intricate, difficult-to-interpret algorithms that employ numerous features or sophisticated deep learning architectures. While these complex models achieve high performance on specific datasets, they often sacrifice interpretability, making it challenging to understand the factors driving human perception of complexity. Recently (Shen, et al. 2024) proposed an interpretable segmentation-based model that accurately predicted complexity across various datasets, supporting the idea that complexity can be explained simply. In this work, we investigate the failure of their model to capture structural, color and surprisal contributions to complexity. To this end, we propose Multi-Scale Sobel Gradient (MSG) which measures spatial intensity variations, Multi-Scale Unique Color (MUC) which quantifies colorfulness across multiple scales, and surprise scores generated using a Large Language Model. We test our features on existing benchmarks and a novel dataset (Surprising Visual Genome) containing surprising images from Visual Genome. Our experiments demonstrate that modeling complexity accurately is not as simple as previously thought, requiring additional perceptual and semantic factors to address dataset biases. Our model improves predictive performance while maintaining interpretability, offering deeper insights into how visual complexity is perceived and assessed. Our code, analysis and data are available at https://github.com/Complexity-Project/Complexity-in-Complexity.

Recent progress has pushed AI frontiers from pattern recognition tasks toward problems that require step by step, System2 style reasoning, especially with large language models. Yet, unlike learning, where generalization and out of distribution (OoD) evaluation concepts are well formalized, there is no clear, consistent definition or metric for reasoning ability. We propose Complexity Out of Distribution (Complexity OoD) generalization as a framework and problem setting to define and measure reasoning. A model exhibits Complexity OoD generalization when it maintains performance on test instances whose minimal required solution complexity, either representational (richer solution structure) or computational (more reasoning steps/program length), exceeds that of all training examples. We formalize complexity via solution description Kolmogorov complexity and operational proxies (e.g., object/relation counts; reasoning step counts), clarifying how Complexity OoD differs from length and compositional OoD. This lens unifies learning and reasoning: many cases solvable with System1 like processing at low complexity become System2 like under complexity pressure, while System2 can be viewed as generalization over solution structures. We translate this perspective into practice with recommendations for operationalizing Complexity OoD across the stack: incorporating complexity into benchmark and evaluation metric design, rethinking supervision to target solution traces, seeking and designing inductive biases for Complexity OoD generalization, addressing learning to reason spillovers such as spurious shortcuts, semantic robustness, catastrophic forgetting, and step wise calibration. Because Complexity OoD cannot be solved by scaling data alone, progress toward robust reasoning will require architectures and training regimes that explicitly model and allocate computation with respect to complexity.

Recent research interest in the learning-based processing of garments, from virtual fitting to generation and reconstruction, stumbles on a scarcity of high-quality public data in the domain. We contribute to resolving this need by presenting the first large-scale synthetic dataset of 3D made-to-measure garments with sewing patterns, as well as its generation pipeline. GarmentCodeData contains 115,000 data points that cover a variety of designs in many common garment categories: tops, shirts, dresses, jumpsuits, skirts, pants, etc., fitted to a variety of body shapes sampled from a custom statistical body model based on CAESAR, as well as a standard reference body shape, applying three different textile materials. To enable the creation of datasets of such complexity, we introduce a set of algorithms for automatically taking tailor's measures on sampled body shapes, sampling strategies for sewing pattern design, and propose an automatic, open-source 3D garment draping pipeline based on a fast XPBD simulator, while contributing several solutions for collision resolution and drape correctness to enable scalability. Project Page: https://igl.ethz.ch/projects/GarmentCodeData/

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

The quadratic complexity of the attention mechanism represents one of the biggest hurdles for processing long sequences using Transformers. Current methods, relying on sparse representations or stateful recurrence, sacrifice token-to-token interactions, which ultimately leads to compromises in performance. This paper introduces TaylorShift, a novel reformulation of the Taylor softmax that enables computing full token-to-token interactions in linear time and space. We analytically determine the crossover points where employing TaylorShift becomes more efficient than traditional attention, aligning closely with empirical measurements. Specifically, our findings demonstrate that TaylorShift enhances memory efficiency for sequences as short as 800 tokens and accelerates inference for inputs of approximately 1700 tokens and beyond. For shorter sequences, TaylorShift scales comparably with the vanilla attention. Furthermore, a classification benchmark across five tasks involving long sequences reveals no degradation in accuracy when employing Transformers equipped with TaylorShift. For reproducibility, we provide access to our code under https://github.com/tobna/TaylorShift.

We introduce BigO(Bench), a novel coding benchmark designed to evaluate the capabilities of generative language models in understanding and generating code with specified time and space complexities. This benchmark addresses the gap in current evaluations that often overlook the ability of models to comprehend and produce code constrained by computational complexity. BigO(Bench) includes tooling to infer the algorithmic complexity of any Python function from profiling measurements, including human- or LLM-generated solutions. BigO(Bench) also includes of set of 3,105 coding problems and 1,190,250 solutions from Code Contests annotated with inferred (synthetic) time and space complexity labels from the complexity framework, as well as corresponding runtime and memory footprint values for a large set of input sizes. We present results from evaluating multiple state-of-the-art language models on this benchmark, highlighting their strengths and weaknesses in handling complexity requirements. In particular, token-space reasoning models are unrivaled in code generation but not in complexity understanding, hinting that they may not generalize well to tasks for which no reward was given at training time.

Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in computational efficiency. Thus, this paper stems from data-driven learning to advance states of dynamical systems utilizing a structured neural network (StNN). The proposed learning technique also seeks to identify an optimal, low-complexity operator to solve dynamical systems, the so-called Hankel operator, derived from time-delay measurements. Thus, we utilize the StNN based on the Hankel operator to solve dynamical systems as an alternative to existing data-driven techniques. We show that the proposed StNN reduces the number of parameters and computational complexity compared with the conventional neural networks and also with the classical data-driven techniques, such as Sparse Identification of Nonlinear Dynamics (SINDy) and Hankel Alternative view of Koopman (HAVOK), which is commonly known as delay-Dynamic Mode Decomposition(DMD) or Hankel-DMD. More specifically, we present numerical simulations to solve dynamical systems utilizing the StNN based on the Hankel operator beginning from the fundamental Lotka-Volterra model, where we compare the StNN with the LEarning Across Dynamical Systems (LEADS), and extend our analysis to highly nonlinear and chaotic Lorenz systems, comparing the StNN with conventional neural networks, SINDy, and HAVOK. Hence, we show that the proposed StNN paves the way for realizing state-space dynamical systems with a low-complexity learning algorithm, enabling prediction and understanding of future states.

Tokenization is fundamental to Natural Language Processing (NLP), directly impacting model efficiency and linguistic fidelity. While Byte Pair Encoding (BPE) is widely used in Large Language Models (LLMs), it often disregards morpheme boundaries, leading to suboptimal segmentation, particularly in morphologically rich languages. We introduce MorphBPE, a morphology-aware extension of BPE that integrates linguistic structure into subword tokenization while preserving statistical efficiency. Additionally, we propose two morphology-based evaluation metrics: (i) Morphological Consistency F1-Score, which quantifies the consistency between morpheme sharing and token sharing, contributing to LLM training convergence, and (ii) Morphological Edit Distance, which measures alignment between morphemes and tokens concerning interpretability. Experiments on English, Russian, Hungarian, and Arabic across 300M and 1B parameter LLMs demonstrate that MorphBPE consistently reduces cross-entropy loss, accelerates convergence, and improves morphological alignment scores. Fully compatible with existing LLM pipelines, MorphBPE requires minimal modifications for integration. The MorphBPE codebase and tokenizer playground will be available at: https://github.com/llm-lab-org/MorphBPE and https://tokenizer.llm-lab.org

Robust Markov Decision Processes (MDPs) and risk-sensitive MDPs are both powerful tools for making decisions in the presence of uncertainties. Previous efforts have aimed to establish their connections, revealing equivalences in specific formulations. This paper introduces a new formulation for risk-sensitive MDPs, which assesses risk in a slightly different manner compared to the classical Markov risk measure (Ruszczy\'nski 2010), and establishes its equivalence with a class of regularized robust MDP (RMDP) problems, including the standard RMDP as a special case. Leveraging this equivalence, we further derive the policy gradient theorem for both problems, proving gradient domination and global convergence of the exact policy gradient method under the tabular setting with direct parameterization. This forms a sharp contrast to the Markov risk measure, known to be potentially non-gradient-dominant (Huang et al. 2021). We also propose a sample-based offline learning algorithm, namely the robust fitted-Z iteration (RFZI), for a specific regularized RMDP problem with a KL-divergence regularization term (or equivalently the risk-sensitive MDP with an entropy risk measure). We showcase its streamlined design and less stringent assumptions due to the equivalence and analyze its sample complexity.

Pruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters. However, relatively little work has gone into characterising the small pruned networks obtained, beyond a measure of their accuracy. In this paper, we use the sparse double descent approach to identify univocally and characterise pruned models associated with classification tasks. We observe empirically that, for a given task, iterative magnitude pruning (IMP) tends to converge to networks of comparable sizes even when starting from full networks with sizes ranging over orders of magnitude. We analyse the best pruned models in a controlled experimental setup and show that their number of parameters reflects task difficulty and that they are much better than full networks at capturing the true conditional probability distribution of the labels. On real data, we similarly observe that pruned models are less prone to overconfident predictions. Our results suggest that pruned models obtained via IMP not only have advantageous computational properties but also provide a better representation of uncertainty in learning.

In this paper, we study the problem of unsupervised object segmentation from single images. We do not introduce a new algorithm, but systematically investigate the effectiveness of existing unsupervised models on challenging real-world images. We firstly introduce four complexity factors to quantitatively measure the distributions of object- and scene-level biases in appearance and geometry for datasets with human annotations. With the aid of these factors, we empirically find that, not surprisingly, existing unsupervised models catastrophically fail to segment generic objects in real-world images, although they can easily achieve excellent performance on numerous simple synthetic datasets, due to the vast gap in objectness biases between synthetic and real images. By conducting extensive experiments on multiple groups of ablated real-world datasets, we ultimately find that the key factors underlying the colossal failure of existing unsupervised models on real-world images are the challenging distributions of object- and scene-level biases in appearance and geometry. Because of this, the inductive biases introduced in existing unsupervised models can hardly capture the diverse object distributions. Our research results suggest that future work should exploit more explicit objectness biases in the network design.

Instruction tuning is a standard technique employed to align large language models to end tasks and user preferences after the initial pretraining phase. Recent research indicates the critical role of data engineering in instruction tuning -- when appropriately selected, only limited data is necessary to achieve superior performance. However, we still lack a principled understanding of what makes good instruction tuning data for alignment, and how we should select data automatically and effectively. In this work, we delve deeply into automatic data selection strategies for alignment. We start with controlled studies to measure data across three dimensions: complexity, quality, and diversity, along which we examine existing methods and introduce novel techniques for enhanced data measurement. Subsequently, we propose a simple strategy to select data samples based on the measurement. We present deita (short for Data-Efficient Instruction Tuning for Alignment), a series of models fine-tuned from LLaMA and Mistral models using data samples automatically selected with our proposed approach. Empirically, deita performs better or on par with the state-of-the-art open-source alignment models with only 6K SFT training data samples -- over 10x less than the data used in the baselines. When further trained with direct preference optimization (DPO), deita-Mistral-7B + DPO trained with 6K SFT and 10K DPO samples achieve 7.55 MT-Bench and 90.06% AlpacaEval scores. We anticipate this work to provide tools on automatic data selection, facilitating data-efficient alignment. We release our models as well as the selected datasets for future researches to effectively align models more efficiently.

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias. After suggesting algebraic topology as a measure for data complexity, we show that the power of a network to express the topological complexity of a dataset in its decision region is a strictly limiting factor in its ability to generalize. We then provide the first empirical characterization of the topological capacity of neural networks. Our empirical analysis shows that at every level of dataset complexity, neural networks exhibit topological phase transitions. This observation allowed us to connect existing theory to empirically driven conjectures on the choice of architectures for fully-connected neural networks.

The multifaceted challenge of accurately measuring gender stereotypical bias in language models is akin to discerning different segments of a broader, unseen entity. This short paper primarily focuses on intrinsic bias mitigation and measurement strategies for language models, building on prior research that demonstrates a lack of correlation between intrinsic and extrinsic approaches. We delve deeper into intrinsic measurements, identifying inconsistencies and suggesting that these benchmarks may reflect different facets of gender stereotype. Our methodology involves analyzing data distributions across datasets and integrating gender stereotype components informed by social psychology. By adjusting the distribution of two datasets, we achieve a better alignment of outcomes. Our findings underscore the complexity of gender stereotyping in language models and point to new directions for developing more refined techniques to detect and reduce bias.

In this paper, we propose Text-based Open Molecule Generation Benchmark (TOMG-Bench), the first benchmark to evaluate the open-domain molecule generation capability of LLMs. TOMG-Bench encompasses a dataset of three major tasks: molecule editing (MolEdit), molecule optimization (MolOpt), and customized molecule generation (MolCustom). Each task further contains three subtasks, with each subtask comprising 5,000 test samples. Given the inherent complexity of open molecule generation, we have also developed an automated evaluation system that helps measure both the quality and the accuracy of the generated molecules. Our comprehensive benchmarking of 25 LLMs reveals the current limitations and potential areas for improvement in text-guided molecule discovery. Furthermore, with the assistance of OpenMolIns, a specialized instruction tuning dataset proposed for solving challenges raised by TOMG-Bench, Llama3.1-8B could outperform all the open-source general LLMs, even surpassing GPT-3.5-turbo by 46.5\% on TOMG-Bench. Our codes and datasets are available through https://github.com/phenixace/TOMG-Bench.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent approach in current deep learning is the set-based approach which measures the discrepancy between two surfaces by comparing two randomly sampled point-clouds from the two meshes with Chamfer pseudo-distance. Nevertheless, the set-based approach still has limitations such as lacking a theoretical guarantee for choosing the number of points in sampled point-clouds, and the pseudo-metricity and the quadratic complexity of the Chamfer divergence. To address these issues, we propose a novel metric for learning mesh deformation. The metric is defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach. By leveraging probability measure space, we gain flexibility in encoding meshes using diverse forms of probability measures, such as continuous, empirical, and discrete measures via varifold representation. After having encoded probability measures, we can compare meshes by using the sliced Wasserstein distance which is an effective optimal transport distance with linear computational complexity and can provide a fast statistical rate for approximating the surface of meshes. To the end, we employ a neural ordinary differential equation (ODE) to deform the input surface into the target shape by modeling the trajectories of the points on the surface. Our experiments on cortical surface reconstruction demonstrate that our approach surpasses other competing methods in multiple datasets and metrics.

Diffusion models have shown superior performance in real-world video super-resolution (VSR). However, the slow processing speeds and heavy resource consumption of diffusion models hinder their practical application and deployment. Quantization offers a potential solution for compressing the VSR model. Nevertheless, quantizing VSR models is challenging due to their temporal characteristics and high fidelity requirements. To address these issues, we propose QuantVSR, a low-bit quantization model for real-world VSR. We propose a spatio-temporal complexity aware (STCA) mechanism, where we first utilize the calibration dataset to measure both spatial and temporal complexities for each layer. Based on these statistics, we allocate layer-specific ranks to the low-rank full-precision (FP) auxiliary branch. Subsequently, we jointly refine the FP and low-bit branches to achieve simultaneous optimization. In addition, we propose a learnable bias alignment (LBA) module to reduce the biased quantization errors. Extensive experiments on synthetic and real-world datasets demonstrate that our method obtains comparable performance with the FP model and significantly outperforms recent leading low-bit quantization methods. Code is available at: https://github.com/bowenchai/QuantVSR.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it remains unclear in particular how the irregularity of the time series affects their predictions. By merging the rich theory of controlled differential equations (CDE) and Lipschitz-based measures of the complexity of deep neural nets, we take a first step towards the theoretical understanding of NCDE. Our first result is a generalization bound for this class of predictors that depends on the regularity of the time series data. In a second time, we leverage the continuity of the flow of CDEs to provide a detailed analysis of both the sampling-induced bias and the approximation bias. Regarding this last result, we show how classical approximation results on neural nets may transfer to NCDEs. Our theoretical results are validated through a series of experiments.

In the realm of embodied artificial intelligence, the reasoning capabilities of Large Language Models (LLMs) play a pivotal role. Although there are effective methods like program-of-thought prompting for LLMs which uses programming language to tackle complex reasoning tasks, the specific impact of code data on the improvement of reasoning capabilities remains under-explored. To address this gap, we propose complexity-impacted reasoning score (CIRS), which combines structural and logical attributes, to measure the correlation between code and reasoning abilities. Specifically, we use the abstract syntax tree to encode the structural information and calculate logical complexity by considering the difficulty and the cyclomatic complexity. Through an empirical analysis, we find not all code data of complexity can be learned or understood by LLMs. Optimal level of complexity is critical to the improvement of reasoning abilities by program-aided prompting. Then we design an auto-synthesizing and stratifying algorithm, and apply it to instruction generation for mathematical reasoning and code data filtering for code generation tasks. Extensive results demonstrates the effectiveness of our proposed approach. Code will be integrated into the EasyInstruct framework at https://github.com/zjunlp/EasyInstruct.

This study investigates the reasoning robustness of large language models (LLMs) on mathematical problem-solving tasks under systematically introduced input perturbations. Using the GSM8K dataset as a controlled testbed, we evaluate how well state-of-the-art models maintain logical consistency and correctness when confronted with four categories of prompt perturbations: irrelevant context, pathological instructions, factually relevant but non-essential context, and a combination of the latter two. Our experiments, conducted on thirteen open-source and closed-source LLMs, reveal that introducing irrelevant context within the model's context window significantly degrades performance, suggesting that distinguishing essential from extraneous details remains a pressing challenge. Surprisingly, performance regressions are relatively insensitive to the complexity of the reasoning task, as measured by the number of steps required, and are not strictly correlated with model size. Moreover, we observe that certain perturbations inadvertently trigger chain-of-thought-like reasoning behaviors, even without explicit prompting. Our findings highlight critical vulnerabilities in current LLMs and underscore the need for improved robustness against noisy, misleading, and contextually dense inputs, paving the way for more resilient and reliable reasoning in real-world applications.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

To pursue the goal of creating an open-ended agent in Minecraft, an open-ended game environment with unlimited possibilities, this paper introduces a task-centric framework named MCU for Minecraft agent evaluation. The MCU framework leverages the concept of atom tasks as fundamental building blocks, enabling the generation of diverse or even arbitrary tasks. Within the MCU framework, each task is measured with six distinct difficulty scores (time consumption, operational effort, planning complexity, intricacy, creativity, novelty). These scores offer a multi-dimensional assessment of a task from different angles, and thus can reveal an agent's capability on specific facets. The difficulty scores also serve as the feature of each task, which creates a meaningful task space and unveils the relationship between tasks. For efficient evaluation of Minecraft agents employing the MCU framework, we maintain a unified benchmark, namely SkillForge, which comprises representative tasks with diverse categories and difficulty distribution. We also provide convenient filters for users to select tasks to assess specific capabilities of agents. We show that MCU has the high expressivity to cover all tasks used in recent literature on Minecraft agent, and underscores the need for advancements in areas such as creativity, precise control, and out-of-distribution generalization under the goal of open-ended Minecraft agent development.

Developing large-scale foundational datasets is a critical milestone in advancing artificial intelligence (AI)-driven scientific innovation. However, unlike AI-mature fields such as natural language processing, materials science, particularly polymer research, has significantly lagged in developing extensive open datasets. This lag is primarily due to the high costs of polymer synthesis and property measurements, along with the vastness and complexity of the chemical space. This study presents PolyOmics, an omics-scale computational database generated through fully automated molecular dynamics simulation pipelines that provide diverse physical properties for over 10^5 polymeric materials. The PolyOmics database is collaboratively developed by approximately 260 researchers from 48 institutions to bridge the gap between academia and industry. Machine learning models pretrained on PolyOmics can be efficiently fine-tuned for a wide range of real-world downstream tasks, even when only limited experimental data are available. Notably, the generalisation capability of these simulation-to-real transfer models improve significantly as the size of the PolyOmics database increases, exhibiting power-law scaling. The emergence of scaling laws supports the "more is better" principle, highlighting the significance of ultralarge-scale computational materials data for improving real-world prediction performance. This unprecedented omics-scale database reveals vast unexplored regions of polymer materials, providing a foundation for AI-driven polymer science.

Embedding models play a crucial role in representing and retrieving information across various NLP applications. Recent advancements in Large Language Models (LLMs) have further enhanced the performance of embedding models, which are trained on massive amounts of text covering almost every domain. These models are often benchmarked on general-purpose datasets like Massive Text Embedding Benchmark (MTEB), where they demonstrate superior performance. However, a critical question arises: Is the development of domain-specific embedding models necessary when general-purpose models are trained on vast corpora that already include specialized domain texts? In this paper, we empirically investigate this question, choosing the finance domain as an example. We introduce the Finance Massive Text Embedding Benchmark (FinMTEB), a counterpart to MTEB that consists of financial domain-specific text datasets. We evaluate the performance of seven state-of-the-art embedding models on FinMTEB and observe a significant performance drop compared to their performance on MTEB. To account for the possibility that this drop is driven by FinMTEB's higher complexity, we propose four measures to quantify dataset complexity and control for this factor in our analysis. Our analysis provides compelling evidence that state-of-the-art embedding models struggle to capture domain-specific linguistic and semantic patterns, even when trained on large general-purpose corpora. This study sheds light on the necessity of developing domain-specific embedding models in the LLM era, offering valuable insights for researchers and practitioners.

Similar case retrieval (SCR) is a representative legal AI application that plays a pivotal role in promoting judicial fairness. However, existing SCR datasets only focus on the fact description section when judging the similarity between cases, ignoring other valuable sections (e.g., the court's opinion) that can provide insightful reasoning process behind. Furthermore, the case similarities are typically measured solely by the textual semantics of the fact descriptions, which may fail to capture the full complexity of legal cases from the perspective of legal knowledge. In this work, we present MUSER, a similar case retrieval dataset based on multi-view similarity measurement and comprehensive legal element with sentence-level legal element annotations. Specifically, we select three perspectives (legal fact, dispute focus, and law statutory) and build a comprehensive and structured label schema of legal elements for each of them, to enable accurate and knowledgeable evaluation of case similarities. The constructed dataset originates from Chinese civil cases and contains 100 query cases and 4,024 candidate cases. We implement several text classification algorithms for legal element prediction and various retrieval methods for retrieving similar cases on MUSER. The experimental results indicate that incorporating legal elements can benefit the performance of SCR models, but further efforts are still required to address the remaining challenges posed by MUSER. The source code and dataset are released at https://github.com/THUlawtech/MUSER.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

Previous results have shown that a two time-scale update rule (TTUR) using different learning rates, such as different constant rates or different decaying rates, is useful for training generative adversarial networks (GANs) in theory and in practice. Moreover, not only the learning rate but also the batch size is important for training GANs with TTURs and they both affect the number of steps needed for training. This paper studies the relationship between batch size and the number of steps needed for training GANs with TTURs based on constant learning rates. We theoretically show that, for a TTUR with constant learning rates, the number of steps needed to find stationary points of the loss functions of both the discriminator and generator decreases as the batch size increases and that there exists a critical batch size minimizing the stochastic first-order oracle (SFO) complexity. Then, we use the Fr'echet inception distance (FID) as the performance measure for training and provide numerical results indicating that the number of steps needed to achieve a low FID score decreases as the batch size increases and that the SFO complexity increases once the batch size exceeds the measured critical batch size. Moreover, we show that measured critical batch sizes are close to the sizes estimated from our theoretical results.

It is widely accepted that information derived from analyzing speech (the acoustic signal) and language production (words and sentences) serves as a useful window into the health of an individual's cognitive ability. In fact, most neuropsychological testing batteries have a component related to speech and language where clinicians elicit speech from patients for subjective evaluation across a broad set of dimensions. With advances in speech signal processing and natural language processing, there has been recent interest in developing tools to detect more subtle changes in cognitive-linguistic function. This work relies on extracting a set of features from recorded and transcribed speech for objective assessments of speech and language, early diagnosis of neurological disease, and tracking of disease after diagnosis. With an emphasis on cognitive and thought disorders, in this paper we provide a review of existing speech and language features used in this domain, discuss their clinical application, and highlight their advantages and disadvantages. Broadly speaking, the review is split into two categories: language features based on natural language processing and speech features based on speech signal processing. Within each category, we consider features that aim to measure complementary dimensions of cognitive-linguistics, including language diversity, syntactic complexity, semantic coherence, and timing. We conclude the review with a proposal of new research directions to further advance the field.

Although large language models (LLMs) have become transformative, they still make mistakes and can explore unproductive reasoning paths. Self-correction is an important capability for a trustworthy LLM, particularly an autoregressive LLM. While LLMs can identify error in user input, they exhibit a systematic 'Self-Correction Blind Spot' - failing to correct identical error in their own outputs. To systematically study this phenomenon, we introduce Self-Correction Bench, a systematic framework to measure this phenomenon through controlled error injection at three complexity levels. Testing 14 models, we find an average 64.5% blind spot rate. We find multiple evidences that this limitation relates to training data composition: human training demonstrations predominantly show error-free responses rather than error-correction sequences, unlike RL-trained models that learn error correction through outcome feedback. Remarkably, simply appending "Wait" reduces blind spots by 89.3%, suggesting that the capability exists but requires activation. Our work highlights a critical limitation in current LLMs and offers potential avenues for improving their reliability and trustworthiness.

Large Language Models (LLMs) have become an indispensable part of natural language processing tasks. However, autoregressive sampling has become an efficiency bottleneck. Multi-Draft Speculative Decoding (MDSD) is a recent approach where, when generating each token, a small draft model generates multiple drafts, and the target LLM verifies them in parallel, ensuring that the final output conforms to the target model distribution. The two main design choices in MDSD are the draft sampling method and the verification algorithm. For a fixed draft sampling method, the optimal acceptance rate is a solution to an optimal transport problem, but the complexity of this problem makes it difficult to solve for the optimal acceptance rate and measure the gap between existing verification algorithms and the theoretical upper bound. This paper discusses the dual of the optimal transport problem, providing a way to efficiently compute the optimal acceptance rate. For the first time, we measure the theoretical upper bound of MDSD efficiency for vocabulary sizes in the thousands and quantify the gap between existing verification algorithms and this bound. We also compare different draft sampling methods based on their optimal acceptance rates. Our results show that the draft sampling method strongly influences the optimal acceptance rate, with sampling without replacement outperforming sampling with replacement. Additionally, existing verification algorithms do not reach the theoretical upper bound for both without replacement and with replacement sampling. Our findings suggest that carefully designed draft sampling methods can potentially improve the optimal acceptance rate and enable the development of verification algorithms that closely match the theoretical upper bound.

Assessing the effectiveness of large language models (LLMs) in addressing diverse tasks is essential for comprehending their strengths and weaknesses. Conventional evaluation techniques typically apply a single prompting strategy uniformly across datasets, not considering the varying degrees of task complexity. We introduce the Hierarchical Prompting Taxonomy (HPT), a taxonomy that employs a Hierarchical Prompt Framework (HPF) composed of five unique prompting strategies, arranged from the simplest to the most complex, to assess LLMs more precisely and to offer a clearer perspective. This taxonomy assigns a score, called the Hierarchical Prompting Score (HP-Score), to datasets as well as LLMs based on the rules of the taxonomy, providing a nuanced understanding of their ability to solve diverse tasks and offering a universal measure of task complexity. Additionally, we introduce the Adaptive Hierarchical Prompt framework, which automates the selection of appropriate prompting strategies for each task. This study compares manual and adaptive hierarchical prompt frameworks using four instruction-tuned LLMs, namely Llama 3 8B, Phi 3 3.8B, Mistral 7B, and Gemma 7B, across four datasets: BoolQ, CommonSenseQA (CSQA), IWSLT-2017 en-fr (IWSLT), and SamSum. Experiments demonstrate the effectiveness of HPT, providing a reliable way to compare different tasks and LLM capabilities. This paper leads to the development of a universal evaluation metric that can be used to evaluate both the complexity of the datasets and the capabilities of LLMs. The implementation of both manual HPF and adaptive HPF is publicly available.

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

Despite extensive safety enhancements in large language models (LLMs), multi-turn "jailbreak" conversations crafted by skilled human adversaries can still breach even the most sophisticated guardrails. However, these multi-turn attacks demand considerable manual effort, limiting their scalability. In this work, we introduce a novel approach called Multi-turn-to-Single-turn (M2S) that systematically converts multi-turn jailbreak prompts into single-turn attacks. Specifically, we propose three conversion strategies - Hyphenize, Numberize, and Pythonize - each preserving sequential context yet packaging it in a single query. Our experiments on the Multi-turn Human Jailbreak (MHJ) dataset show that M2S often increases or maintains high Attack Success Rates (ASRs) compared to original multi-turn conversations. Notably, using a StrongREJECT-based evaluation of harmfulness, M2S achieves up to 95.9% ASR on Mistral-7B and outperforms original multi-turn prompts by as much as 17.5% in absolute improvement on GPT-4o. Further analysis reveals that certain adversarial tactics, when consolidated into a single prompt, exploit structural formatting cues to evade standard policy checks. These findings underscore that single-turn attacks - despite being simpler and cheaper to conduct - can be just as potent, if not more, than their multi-turn counterparts. Our findings underscore the urgent need to reevaluate and reinforce LLM safety strategies, given how adversarial queries can be compacted into a single prompt while still retaining sufficient complexity to bypass existing safety measures.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

Automatically estimating the complexity of texts for readers has a variety of applications, such as recommending texts with an appropriate complexity level to language learners or supporting the evaluation of text simplification approaches. In this paper, we present our submission to the Text Complexity DE Challenge 2022, a regression task where the goal is to predict the complexity of a German sentence for German learners at level B. Our approach relies on more than 220,000 pseudo-labels created from the German Wikipedia and other corpora to train Transformer-based models, and refrains from any feature engineering or any additional, labeled data. We find that the pseudo-label-based approach gives impressive results yet requires little to no adjustment to the specific task and therefore could be easily adapted to other domains and tasks.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

This paper presents TextComplexityDE, a dataset consisting of 1000 sentences in German language taken from 23 Wikipedia articles in 3 different article-genres to be used for developing text-complexity predictor models and automatic text simplification in German language. The dataset includes subjective assessment of different text-complexity aspects provided by German learners in level A and B. In addition, it contains manual simplification of 250 of those sentences provided by native speakers and subjective assessment of the simplified sentences by participants from the target group. The subjective ratings were collected using both laboratory studies and crowdsourcing approach.

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of Dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero Time complexity, zero Space complexity, and an infinite Dimensional complexity. This algorithm is used to generate the number line.

We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular automata (ECA), simple yet powerful one-dimensional systems that generate behaviors ranging from trivial to highly complex. By training distinct Large Language Models (LLMs) on different ECAs, we evaluated the relationship between the complexity of the rules' behavior and the intelligence exhibited by the LLMs, as reflected in their performance on downstream tasks. Our findings reveal that rules with higher complexity lead to models exhibiting greater intelligence, as demonstrated by their performance on reasoning and chess move prediction tasks. Both uniform and periodic systems, and often also highly chaotic systems, resulted in poorer downstream performance, highlighting a sweet spot of complexity conducive to intelligence. We conjecture that intelligence arises from the ability to predict complexity and that creating intelligence may require only exposure to complexity.

We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of widetilde O(|S||A|t_{mix}^2 epsilon^{-2}) and a lower bound of Omega(|S||A|t_{mix} epsilon^{-2}). In these expressions, |S| and |A| denote the cardinalities of the state and action spaces respectively, t_{mix} serves as a uniform upper limit for the total variation mixing times, and epsilon signifies the error tolerance. Therefore, a notable gap of t_{mix} still remains to be bridged. Our primary contribution is the development of an estimator for the optimal policy of average reward MDPs with a sample complexity of widetilde O(|S||A|t_{mix}epsilon^{-2}). This marks the first algorithm and analysis to reach the literature's lower bound. Our new algorithm draws inspiration from ideas in Li et al. (2020), Jin and Sidford (2021), and Wang et al. (2023). Additionally, we conduct numerical experiments to validate our theoretical findings.

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory -- the field that studies the resources (such as time, space, and randomness) needed to solve computational problems -- leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.

Code based Language Models (LMs) have shown very promising results in the field of software engineering with applications such as code refinement, code completion and generation. However, the task of time and space complexity classification from code has not been extensively explored due to a lack of datasets, with prior endeavors being limited to Java. In this project, we aim to address these gaps by creating a labelled dataset of code snippets spanning multiple languages (Python and C++ datasets currently, with C, C#, and JavaScript datasets being released shortly). We find that existing time complexity calculation libraries and tools only apply to a limited number of use-cases. The lack of a well-defined rule based system motivates the application of several recently proposed code-based LMs. We demonstrate the effectiveness of dead code elimination and increasing the maximum sequence length of LMs. In addition to time complexity, we propose to use LMs to find space complexities from code, and to the best of our knowledge, this is the first attempt to do so. Furthermore, we introduce a novel code comprehension task, called cross-language transfer, where we fine-tune the LM on one language and run inference on another. Finally, we visualize the activation of the attention fed classification head of our LMs using Non-negative Matrix Factorization (NMF) to interpret our results.

Intrinsic dimension (ID) is an important tool in modern LLM analysis, informing studies of training dynamics, scaling behavior, and dataset structure, yet its textual determinants remain underexplored. We provide the first comprehensive study grounding ID in interpretable text properties through cross-encoder analysis, linguistic features, and sparse autoencoders (SAEs). In this work, we establish three key findings. First, ID is complementary to entropy-based metrics: after controlling for length, the two are uncorrelated, with ID capturing geometric complexity orthogonal to prediction quality. Second, ID exhibits robust genre stratification: scientific prose shows low ID (~8), encyclopedic content medium ID (~9), and creative/opinion writing high ID (~10.5) across all models tested. This reveals that contemporary LLMs find scientific text "representationally simple" while fiction requires additional degrees of freedom. Third, using SAEs, we identify causal features: scientific signals (formal tone, report templates, statistics) reduce ID; humanized signals (personalization, emotion, narrative) increase it. Steering experiments confirm these effects are causal. Thus, for contemporary models, scientific writing appears comparatively "easy", whereas fiction, opinion, and affect add representational degrees of freedom. Our multi-faceted analysis provides practical guidance for the proper use of ID and the sound interpretation of ID-based results.

We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and reward functions can be represented by constant depth circuits with polynomial size, while the optimal Q-function suffers an exponential circuit complexity in constant-depth circuits. By drawing attention to the approximation errors and building connections to complexity theory, our theory provides unique insights into why model-based algorithms usually enjoy better sample complexity than model-free algorithms from a novel representation complexity perspective: in some cases, the ground-truth rule (model) of the environment is simple to represent, while other quantities, such as Q-function, appear complex. We empirically corroborate our theory by comparing the approximation error of the transition kernel, reward function, and optimal Q-function in various Mujoco environments, which demonstrates that the approximation errors of the transition kernel and reward function are consistently lower than those of the optimal Q-function. To the best of our knowledge, this work is the first to study the circuit complexity of RL, which also provides a rigorous framework for future research.

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

Large language models (LLMs) have shown promising results in a wide array of generative NLP tasks, such as summarization and machine translation. In the context of narrative generation, however, existing models still do not capture factors that contribute to producing consistent text. For instance, it is logical that a piece of text or a story should be uniformly readable throughout and that this form of complexity should be controllable. As such, if the complexity of an input text prompt is rated first-grade reading level in the Flesch Reading Ease test, then the generated text continuing the plot should also be within this range of complexity. With this in mind, we introduce Uniform Complexity for Text Generation (UCTG), a new benchmark test which raises the challenge of making generative models observe uniform linguistic properties with respect to prompts. We experiment with over 150+ linguistically and cognitively motivated features for evaluating text complexity in humans and generative models. From our results, we find that models such as GPT-2 struggle to preserve the complexity of input prompts used in its generations, even if finetuned with professionally written texts.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

While machine learning has advanced through massive parallelization, we identify a critical blind spot: some problems are fundamentally sequential. These "inherently serial" problems-from mathematical reasoning to physical simulations to sequential decision-making-require dependent computational steps that cannot be parallelized. Drawing from complexity theory, we formalize this distinction and demonstrate that current parallel-centric architectures face fundamental limitations on such tasks. We argue that recognizing the serial nature of computation holds profound implications on machine learning, model design, hardware development. As AI tackles increasingly complex reasoning, deliberately scaling serial computation-not just parallel computation-is essential for continued progress.

We introduce a high-quality dataset that contains 3,397 samples comprising (i) multiple choice questions, (ii) answers (including distractors), and (iii) their source documents, from the educational domain. Each question is phrased in two forms, normal and close. Correct answers are linked to source documents with sentence-level annotations. Thus, our versatile dataset can be used for both question and distractor generation, as well as to explore new challenges such as question format conversion. Furthermore, 903 questions are accompanied by their cognitive complexity level as per Bloom's taxonomy. All questions have been generated by educational experts rather than crowd workers to ensure they are maintaining educational and learning standards. Our analysis and experiments suggest distinguishable differences between our dataset and commonly used ones for question generation for educational purposes. We believe this new dataset can serve as a valuable resource for research and evaluation in the educational domain. The dataset and baselines will be released to support further research in question generation.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

This paper describes the performance of the team cs60075_team2 at SemEval 2021 Task 1 - Lexical Complexity Prediction. The main contribution of this paper is to fine-tune transformer-based language models pre-trained on several text corpora, some being general (E.g., Wikipedia, BooksCorpus), some being the corpora from which the CompLex Dataset was extracted, and others being from other specific domains such as Finance, Law, etc. We perform ablation studies on selecting the transformer models and how their individual complexity scores are aggregated to get the resulting complexity scores. Our method achieves a best Pearson Correlation of 0.784 in sub-task 1 (single word) and 0.836 in sub-task 2 (multiple word expressions).

Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than computability in philosophical and AI problems. Second, to rephrase the notion of computability in terms of solvability, i.e. treating computability as non-sufficient for establishing intelligence. The Church-Turing thesis is therefore revisited and rephrased in order to capture the ontological background of spatial and temporal complexity. Third, to emphasize ontological differences between different time complexities, which seem to provide a solid base towards better understanding of artificial intelligence in general.

Large Language Models (LLMs) are increasingly used for tasks involving Knowledge Graphs (KGs), whose evaluation typically focuses on accuracy and output correctness. We propose a complementary task characterization approach using three complexity frameworks from cognitive psychology. Applying this to the LLM-KG-Bench framework, we highlight value distributions, identify underrepresented demands and motivate richer interpretation and diversity for benchmark evaluation tasks.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Characterizing samples that are difficult to learn from is crucial to developing highly performant ML models. This has led to numerous Hardness Characterization Methods (HCMs) that aim to identify "hard" samples. However, there is a lack of consensus regarding the definition and evaluation of "hardness". Unfortunately, current HCMs have only been evaluated on specific types of hardness and often only qualitatively or with respect to downstream performance, overlooking the fundamental quantitative identification task. We address this gap by presenting a fine-grained taxonomy of hardness types. Additionally, we propose the Hardness Characterization Analysis Toolkit (H-CAT), which supports comprehensive and quantitative benchmarking of HCMs across the hardness taxonomy and can easily be extended to new HCMs, hardness types, and datasets. We use H-CAT to evaluate 13 different HCMs across 8 hardness types. This comprehensive evaluation encompassing over 14K setups uncovers strengths and weaknesses of different HCMs, leading to practical tips to guide HCM selection and future development. Our findings highlight the need for more comprehensive HCM evaluation, while we hope our hardness taxonomy and toolkit will advance the principled evaluation and uptake of data-centric AI methods.

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr's three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the Moral Tractability Thesis (MTT).

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward g(gamma, v) depends on the proposed threshold gamma and latent value v and it can be only achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most epsilon smaller than the optimum and prove that the number of queries needed can be infinitely large even when g(gamma, v) is monotone with respect to both gamma and v. On the positive side, we provide a tight query complexity Theta(1/epsilon^3) when g is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight Theta(1/epsilon^3) query complexity can be achieved as long as g satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight Theta(T^{2/3}) regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

The increasing complexity of Artificial Intelligence models poses challenges to interpretability, particularly in the healthcare sector. This study investigates the impact of deep learning model complexity and Explainable AI (XAI) efficacy, utilizing four ResNet architectures (ResNet-18, 34, 50, 101). Through methodical experimentation on 4,369 lung X-ray images of COVID-19-infected and healthy patients, the research evaluates models' classification performance and the relevance of corresponding XAI explanations with respect to the ground-truth disease masks. Results indicate that the increase in model complexity is associated with a decrease in classification accuracy and AUC-ROC scores (ResNet-18: 98.4%, 0.997; ResNet-101: 95.9%, 0.988). Notably, in eleven out of twelve statistical tests performed, no statistically significant differences occurred between XAI quantitative metrics - Relevance Rank Accuracy and the proposed Positive Attribution Ratio - across trained models. These results suggest that increased model complexity does not consistently lead to higher performance or relevance of explanations for models' decision-making processes.

Measuring diversity accurately is important for many scientific fields, including machine learning (ML), ecology, and chemistry. The Vendi Score was introduced as a generic similarity-based diversity metric that extends the Hill number of order q=1 by leveraging ideas from quantum statistical mechanics. Contrary to many diversity metrics in ecology, the Vendi Score accounts for similarity and does not require knowledge of the prevalence of the categories in the collection to be evaluated for diversity. However, the Vendi Score treats each item in a given collection with a level of sensitivity proportional to the item's prevalence. This is undesirable in settings where there is a significant imbalance in item prevalence. In this paper, we extend the other Hill numbers using similarity to provide flexibility in allocating sensitivity to rare or common items. This leads to a family of diversity metrics -- Vendi scores with different levels of sensitivity -- that can be used in a variety of applications. We study the properties of the scores in a synthetic controlled setting where the ground truth diversity is known. We then test their utility in improving molecular simulations via Vendi Sampling. Finally, we use the Vendi scores to better understand the behavior of image generative models in terms of memorization, duplication, diversity, and sample quality.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by mannor2011 and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order alpha T, where alpha is the independence number of the graph, and T is the time horizon. However, this is proven only when the number of rounds T is larger than alpha^3, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity R^*, called the problem complexity, and prove that the minimax regret is proportional to R^* for any graph and time horizon T. Introducing an intricate exploration strategy, we define the \mainAlgorithm algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if T is smaller than alpha^3.

To make AI systems broadly useful for challenging real-world tasks, we need them to learn complex human goals and preferences. One approach to specifying complex goals asks humans to judge during training which agent behaviors are safe and useful, but this approach can fail if the task is too complicated for a human to directly judge. To help address this concern, we propose training agents via self play on a zero sum debate game. Given a question or proposed action, two agents take turns making short statements up to a limit, then a human judges which of the agents gave the most true, useful information. In an analogy to complexity theory, debate with optimal play can answer any question in PSPACE given polynomial time judges (direct judging answers only NP questions). In practice, whether debate works involves empirical questions about humans and the tasks we want AIs to perform, plus theoretical questions about the meaning of AI alignment. We report results on an initial MNIST experiment where agents compete to convince a sparse classifier, boosting the classifier's accuracy from 59.4% to 88.9% given 6 pixels and from 48.2% to 85.2% given 4 pixels. Finally, we discuss theoretical and practical aspects of the debate model, focusing on potential weaknesses as the model scales up, and we propose future human and computer experiments to test these properties.

Recent work has sought to quantify large language model uncertainty to facilitate model control and modulate user trust. Previous works focus on measures of uncertainty that are theoretically grounded or reflect the average overt behavior of the model. In this work, we investigate a variety of uncertainty measures, in order to identify measures that correlate with human group-level uncertainty. We find that Bayesian measures and a variation on entropy measures, top-k entropy, tend to agree with human behavior as a function of model size. We find that some strong measures decrease in human-similarity with model size, but, by multiple linear regression, we find that combining multiple uncertainty measures provide comparable human-alignment with reduced size-dependency.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations (PDEs). The main novelty of the proposed dataset is that we consider discontinuous coefficients with high contrast. These coefficient functions are sampled from a selected set of distributions. This class of problems is not only of great academic interest, but is also the basis for describing various environmental and industrial problems. In this way, ConDiff shortens the gap with real-world problems while remaining fully synthetic and easy to use. ConDiff consists of a diverse set of diffusion equations with coefficients covering a wide range of contrast levels and heterogeneity with a measurable complexity metric for clearer comparison between different coefficient functions. We baseline ConDiff on standard deep learning models in the field of scientific machine learning. By providing a large number of problem instances, each with its own coefficient function and right-hand side, we hope to encourage the development of novel physics-based deep learning approaches, such as neural operators, ultimately driving progress towards more accurate and efficient solutions of complex PDE problems.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.