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Jan 12

Fairy2i: Training Complex LLMs from Real LLMs with All Parameters in $\{\pm 1, \pm i\}$

Large language models (LLMs) have revolutionized artificial intelligence, yet their massive memory and computational demands necessitate aggressive quantization, increasingly pushing representations toward the theoretical limit of a single bit. While complex-valued LLMs, such as iFairy, offer a superior chance for low-bit representation compared to real-valued counterparts, they require training from scratch, preventing the utilization of the vast ecosystem of pre-trained real-valued foundation models. Here we present Fairy2i, a universal framework that transforms pre-trained real-valued layers into an equivalent widely-linear complex form, enabling extremely low-bit quantization while reusing existing checkpoints. By proving a lossless mathematical equivalence between real and widely-linear maps, we convert standard Transformers into the complex domain and employ a phase-aware quantization scheme with a highly efficient codebook of fourth roots of unity. Furthermore, we introduce a recursive residual quantization mechanism that iteratively minimizes quantization error, allowing inference to proceed via efficient multiplication-free accumulation. We demonstrate that Fairy2i restores the performance of LLaMA-2 7B at an effective 2-bit precision to levels nearly comparable with full-precision baselines, significantly outperforming state-of-the-art real-valued binary and ternary quantization methods. This work bridges the gap between the representational efficiency of complex-valued arithmetic and the practical utility of pre-trained models, paving a new way for efficient inference on commodity hardware.

PKU-DS-LAB PKU-DS-LAB
·
Dec 2, 2025 2

BiPer: Binary Neural Networks using a Periodic Function

Quantized neural networks employ reduced precision representations for both weights and activations. This quantization process significantly reduces the memory requirements and computational complexity of the network. Binary Neural Networks (BNNs) are the extreme quantization case, representing values with just one bit. Since the sign function is typically used to map real values to binary values, smooth approximations are introduced to mimic the gradients during error backpropagation. Thus, the mismatch between the forward and backward models corrupts the direction of the gradient, causing training inconsistency problems and performance degradation. In contrast to current BNN approaches, we propose to employ a binary periodic (BiPer) function during binarization. Specifically, we use a square wave for the forward pass to obtain the binary values and employ the trigonometric sine function with the same period of the square wave as a differentiable surrogate during the backward pass. We demonstrate that this approach can control the quantization error by using the frequency of the periodic function and improves network performance. Extensive experiments validate the effectiveness of BiPer in benchmark datasets and network architectures, with improvements of up to 1% and 0.69% with respect to state-of-the-art methods in the classification task over CIFAR-10 and ImageNet, respectively. Our code is publicly available at https://github.com/edmav4/BiPer.

  • 4 authors
·
Apr 1, 2024

Binary and Ternary Natural Language Generation

Ternary and binary neural networks enable multiplication-free computation and promise multiple orders of magnitude efficiency gains over full-precision networks if implemented on specialized hardware. However, since both the parameter and the output space are highly discretized, such networks have proven very difficult to optimize. The difficulties are compounded for the class of transformer text generation models due to the sensitivity of the attention operation to quantization and the noise-compounding effects of autoregressive decoding in the high-cardinality output space. We approach the problem with a mix of statistics-based quantization for the weights and elastic quantization of the activations and demonstrate the first ternary and binary transformer models on the downstream tasks of summarization and machine translation. Our ternary BART base achieves an R1 score of 41 on the CNN/DailyMail benchmark, which is merely 3.9 points behind the full model while being 16x more efficient. Our binary model, while less accurate, achieves a highly non-trivial score of 35.6. For machine translation, we achieved BLEU scores of 21.7 and 17.6 on the WMT16 En-Ro benchmark, compared with a full precision mBART model score of 26.8. We also compare our approach in the 8-bit activation setting, where our ternary and even binary weight models can match or outperform the best existing 8-bit weight models in the literature. Our code and models are available at: https://github.com/facebookresearch/Ternary_Binary_Transformer

  • 5 authors
·
Jun 2, 2023

Trainable Fixed-Point Quantization for Deep Learning Acceleration on FPGAs

Quantization is a crucial technique for deploying deep learning models on resource-constrained devices, such as embedded FPGAs. Prior efforts mostly focus on quantizing matrix multiplications, leaving other layers like BatchNorm or shortcuts in floating-point form, even though fixed-point arithmetic is more efficient on FPGAs. A common practice is to fine-tune a pre-trained model to fixed-point for FPGA deployment, but potentially degrading accuracy. This work presents QFX, a novel trainable fixed-point quantization approach that automatically learns the binary-point position during model training. Additionally, we introduce a multiplier-free quantization strategy within QFX to minimize DSP usage. QFX is implemented as a PyTorch-based library that efficiently emulates fixed-point arithmetic, supported by FPGA HLS, in a differentiable manner during backpropagation. With minimal effort, models trained with QFX can readily be deployed through HLS, producing the same numerical results as their software counterparts. Our evaluation shows that compared to post-training quantization, QFX can quantize models trained with element-wise layers quantized to fewer bits and achieve higher accuracy on both CIFAR-10 and ImageNet datasets. We further demonstrate the efficacy of multiplier-free quantization using a state-of-the-art binarized neural network accelerator designed for an embedded FPGA (AMD Xilinx Ultra96 v2). We plan to release QFX in open-source format.

  • 7 authors
·
Jan 30, 2024

PTQTP: Post-Training Quantization to Trit-Planes for Large Language Models

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

  • 9 authors
·
Sep 21, 2025

Binary Latent Diffusion

In this paper, we show that a binary latent space can be explored for compact yet expressive image representations. We model the bi-directional mappings between an image and the corresponding latent binary representation by training an auto-encoder with a Bernoulli encoding distribution. On the one hand, the binary latent space provides a compact discrete image representation of which the distribution can be modeled more efficiently than pixels or continuous latent representations. On the other hand, we now represent each image patch as a binary vector instead of an index of a learned cookbook as in discrete image representations with vector quantization. In this way, we obtain binary latent representations that allow for better image quality and high-resolution image representations without any multi-stage hierarchy in the latent space. In this binary latent space, images can now be generated effectively using a binary latent diffusion model tailored specifically for modeling the prior over the binary image representations. We present both conditional and unconditional image generation experiments with multiple datasets, and show that the proposed method performs comparably to state-of-the-art methods while dramatically improving the sampling efficiency to as few as 16 steps without using any test-time acceleration. The proposed framework can also be seamlessly scaled to 1024 times 1024 high-resolution image generation without resorting to latent hierarchy or multi-stage refinements.

  • 4 authors
·
Apr 10, 2023

FlexQ: Efficient Post-training INT6 Quantization for LLM Serving via Algorithm-System Co-Design

Large Language Models (LLMs) demonstrate exceptional performance but entail significant memory and computational costs, restricting their practical deployment. While existing INT4/INT8 quantization reduces these costs, they often degrade accuracy or lack optimal efficiency. INT6 quantization offers a superior trade-off between model accuracy and inference efficiency, but lacks hardware support in modern GPUs, forcing emulation via higher-precision arithmetic units that limit acceleration. In this paper, we propose FlexQ, a novel post-training INT6 quantization framework combining algorithmic innovation with system-level optimizations. FlexQ employs uniform 6-bit weight quantization across all layers, with adaptive retention of 8-bit activations in layers identified through layer-wise sensitivity analysis. To maximize hardware efficiency, we develop a specialized high-performance GPU kernel supporting matrix multiplication for W6A6 and W6A8 representations via Binary Tensor Core (BTC) equivalents, effectively bypassing the lack of native INT6 tensor cores. Evaluations on LLaMA models show FlexQ maintains near-FP16 accuracy, with perplexity increases of no more than 0.05. The proposed kernel achieves an average 1.39times speedup over ABQ-LLM on LLaMA-2-70B linear layers. End-to-end, FlexQ delivers 1.33times inference acceleration and 1.21times memory savings over SmoothQuant. Code is released at https://github.com/FlyFoxPlayer/FlexQ.

  • 7 authors
·
Aug 6, 2025

Optimization of embeddings storage for RAG systems using quantization and dimensionality reduction techniques

Retrieval-Augmented Generation enhances language models by retrieving relevant information from external knowledge bases, relying on high-dimensional vector embeddings typically stored in float32 precision. However, storing these embeddings at scale presents significant memory challenges. To address this issue, we systematically investigate on MTEB benchmark two complementary optimization strategies: quantization, evaluating standard formats (float16, int8, binary) and low-bit floating-point types (float8), and dimensionality reduction, assessing methods like PCA, Kernel PCA, UMAP, Random Projections and Autoencoders. Our results show that float8 quantization achieves a 4x storage reduction with minimal performance degradation (<0.3%), significantly outperforming int8 quantization at the same compression level, being simpler to implement. PCA emerges as the most effective dimensionality reduction technique. Crucially, combining moderate PCA (e.g., retaining 50% dimensions) with float8 quantization offers an excellent trade-off, achieving 8x total compression with less performance impact than using int8 alone (which provides only 4x compression). To facilitate practical application, we propose a methodology based on visualizing the performance-storage trade-off space to identify the optimal configuration that maximizes performance within their specific memory constraints.

  • 5 authors
·
Apr 30, 2025 1

Hierarchical Patch Compression for ColPali: Efficient Multi-Vector Document Retrieval with Dynamic Pruning and Quantization

Multi-vector document retrieval systems, such as ColPali, excel in fine-grained matching for complex queries but incur significant storage and computational costs due to their reliance on high-dimensional patch embeddings and late-interaction scoring. To address these challenges, we propose HPC-ColPali, a Hierarchical Patch Compression framework that enhances the efficiency of ColPali while preserving its retrieval accuracy. Our approach integrates three innovative techniques: (1) K-Means quantization, which compresses patch embeddings into 1-byte centroid indices, achieving up to 32times storage reduction; (2) attention-guided dynamic pruning, utilizing Vision-Language Model attention weights to retain only the top-p% most salient patches, reducing late-interaction computation by up to 60\% with less than 2\% nDCG@10 loss; and (3) optional binary encoding of centroid indices into b-bit strings (b=lceillog_2 Krceil), enabling rapid Hamming distance-based similarity search for resource-constrained environments. Evaluated on the ViDoRe and SEC-Filings datasets, HPC-ColPali achieves 30--50\% lower query latency under HNSW indexing while maintaining high retrieval precision. When integrated into a Retrieval-Augmented Generation pipeline for legal summarization, it reduces hallucination rates by 30\% and halves end-to-end latency. These advancements establish HPC-ColPali as a scalable and efficient solution for multi-vector document retrieval across diverse applications. Code is available at https://github.com/DngBack/HPC-ColPali.

  • 1 authors
·
Jun 19, 2025

ABQ-LLM: Arbitrary-Bit Quantized Inference Acceleration for Large Language Models

Large Language Models (LLMs) have revolutionized natural language processing tasks. However, their practical application is constrained by substantial memory and computational demands. Post-training quantization (PTQ) is considered an effective method to accelerate LLM inference. Despite its growing popularity in LLM model compression, PTQ deployment faces two major challenges. First, low-bit quantization leads to performance degradation. Second, restricted by the limited integer computing unit type on GPUs, quantized matrix operations with different precisions cannot be effectively accelerated. To address these issues, we introduce a novel arbitrary-bit quantization algorithm and inference framework, ABQ-LLM. It achieves superior performance across various quantization settings and enables efficient arbitrary-precision quantized inference on the GPU. ABQ-LLM introduces several key innovations: (1) a distribution correction method for transformer blocks to mitigate distribution differences caused by full quantization of weights and activations, improving performance at low bit-widths. (2) the bit balance strategy to counteract performance degradation from asymmetric distribution issues at very low bit-widths (e.g., 2-bit). (3) an innovative quantization acceleration framework that reconstructs the quantization matrix multiplication of arbitrary precision combinations based on BTC (Binary TensorCore) equivalents, gets rid of the limitations of INT4/INT8 computing units. ABQ-LLM can convert each component bit width gain into actual acceleration gain, maximizing performance under mixed precision(e.g., W6A6, W2A8). Based on W2*A8 quantization configuration on LLaMA-7B model, it achieved a WikiText2 perplexity of 7.59 (2.17downarrow vs 9.76 in AffineQuant). Compared to SmoothQuant, we realized 1.6times acceleration improvement and 2.7times memory compression gain.

  • 9 authors
·
Aug 16, 2024