Large Language Models (LLMs) have significantly advanced natural language processing with exceptional task generalization capabilities. Low-Rank Adaption (LoRA) offers a cost-effective fine-tuning solution, freezing the original model parameters and training only lightweight, low-rank adapter matrices. However, the memory footprint of LoRA is largely dominated by the original model parameters. To mitigate this, we propose LoRAM, a memory-efficient LoRA training scheme founded on the intuition that many neurons in over-parameterized LLMs have low training utility but are essential for inference. LoRAM presents a unique twist: it trains on a pruned (small) model to obtain pruned low-rank matrices, which are then recovered and utilized with the original (large) model for inference. Additionally, minimal-cost continual pre-training, performed by the model publishers in advance, aligns the knowledge discrepancy between pruned and original models. Our extensive experiments demonstrate the efficacy of LoRAM across various pruning strategies and downstream tasks. For a model with 70 billion parameters, LoRAM enables training on a GPU with only 20G HBM, replacing an A100-80G GPU for LoRA training and 15 GPUs for full fine-tuning. Specifically, QLoRAM implemented by structured pruning combined with 4-bit quantization, for LLaMA-3.1-70B (LLaMA-2-70B), reduces the parameter storage cost that dominates the memory usage in low-rank matrix training by 15.81$\times$ (16.95$\times$), while achieving dominant performance gains over both the original LLaMA-3.1-70B (LLaMA-2-70B) and LoRA-trained LLaMA-3.1-8B (LLaMA-2-13B).
Large Language Models (LLMs) suffer severe performance degradation when facing extremely low-bit (sub 2-bit) quantization. Several existing sub 2-bit post-training quantization (PTQ) methods utilize a mix-precision scheme by leveraging an unstructured fine-grained mask to explicitly distinguish salient weights, while which introduces an extra 1-bit or more per weight. To explore the real limit of PTQ, we propose an extremely low-bit PTQ method called PTQ1.61, which enables weight quantization to 1.61-bit for the first time. Specifically, we first introduce a one-dimensional structured mask with negligibly additional 0.0002-bit per weight based on input activations from the perspective of reducing the upper bound of quantization error to allocate corresponding salient weight channels to 4-bit. For non-salient channels binarization, an efficient block-wise scaling factors optimization framework is then presented to take implicit row-wise correlations and angular biases into account. Different from prior works that concentrate on adjusting quantization methodologies, we further propose a novel paradigm called quantization preprocessing, where we argue that transforming the weight distribution of the pretrained model before quantization can alleviate the difficulty in per-channel extremely low-bit PTQ. Extensive experiments indicate our PTQ1.61 achieves state-of-the-art performance in extremely low-bit quantization. Codes are available at https://github.com/zjq0455/PTQ1.61.
Post-training Quantization (PTQ) technique has been extensively adopted for large language models (LLMs) compression owing to its efficiency and low resource requirement. However, current research lacks a in-depth analysis of the superior and applicable scenarios of each PTQ strategy. In addition, existing algorithms focus primarily on performance, overlooking the trade-off among model size, performance, and quantization bitwidth. To mitigate these confusions, we provide a novel benchmark for LLMs PTQ in this paper. Firstly, in order to support our benchmark, we propose a comprehensive taxonomy for existing mainstream methods by scrutinizing their computational strategies (e.g., optimization-based, compensation-based, etc.). Then, we conduct extensive experiments with the baseline within each class, covering models with various sizes (7B-70B), bitwidths, training levels (LLaMA1/2/3/3.1), architectures (Mixtral, DeepSeekMoE and Mamba) and modality (LLaVA1.5 and VILA1.5) on a wide range of evaluation metrics.Through comparative analysis on the results, we summarize the superior of each PTQ strategy and modelsize-bitwidth trade-off considering the performance. For example, our benchmark reveals that compensation-based technique demonstrates outstanding cross-architecture robustness and extremely low-bit PTQ for ultra large models should be reexamined. Finally, we further accordingly claim that a practical combination of compensation and other PTQ strategy can achieve SOTA various robustness. We believe that our benchmark will provide valuable recommendations for the deployment of LLMs and future research on PTQ approaches.We conduct an repository for our benchmark at https://github.com/zjq0455/PTQ_Benchmark.
Post-training quantization (PTQ) has emerged as a critical technique for efficient deployment of large language models (LLMs). This work proposes NestQuant, a novel PTQ scheme for weights and activations that is based on self-similar nested lattices. Recent works have mathematically shown such quantizers to be information-theoretically optimal for low-precision matrix multiplication. We implement a practical low-complexity version of NestQuant based on Gosset lattice, making it a drop-in quantizer for any matrix multiplication step (e.g., in self-attention, MLP etc). For example, NestQuant quantizes weights, KV-cache, and activations of Llama-3-8B to 4 bits, achieving perplexity of 6.6 on wikitext2. This represents more than 55% reduction in perplexity gap with respect to unquantized model (perplexity of 6.14) compared to state-of-the-art Metas SpinQuant (perplexity 7.3), OstQuant (7.3) and QuaRot (8.2). Comparisons on bigger models (up to 70B) and on various LLM evaluation benchmarks confirm uniform superiority of NestQuant.
Vision Large Language Models (VLMs) combine visual understanding with natural language processing, enabling tasks like image captioning, visual question answering, and video analysis. While VLMs show impressive capabilities across domains such as autonomous vehicles, smart surveillance, and healthcare, their deployment on resource-constrained edge devices remains challenging due to processing power, memory, and energy limitations. This survey explores recent advancements in optimizing VLMs for edge environments, focusing on model compression techniques, including pruning, quantization, knowledge distillation, and specialized hardware solutions that enhance efficiency. We provide a detailed discussion of efficient training and fine-tuning methods, edge deployment challenges, and privacy considerations. Additionally, we discuss the diverse applications of lightweight VLMs across healthcare, environmental monitoring, and autonomous systems, illustrating their growing impact. By highlighting key design strategies, current challenges, and offering recommendations for future directions, this survey aims to inspire further research into the practical deployment of VLMs, ultimately making advanced AI accessible in resource-limited settings.
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. Previous approaches address the signal recovery problem as an optimization problem. We focus on a regime with low blur and suggest that the operations of blur, sampling, and quantization are not unlike the operation of a computer program and have an abstraction that can be studied with a type of logic. When the minimum distance between discontinuity points is between $1.5$ and 2 times the sampling interval, we can encounter the simplest form of a type of interference between discontinuity points that we call ``commingling.'' We describe a way to reason about two sets of samples of the same signal that will often result in the correct recovery of signal amplitudes. We also discuss ways to estimate bounds on the distances between discontinuity points.
Large language models (LLMs) require immense resources for training and inference. Quantization, a technique that reduces the precision of model parameters, offers a promising solution for improving LLM efficiency and sustainability. While post-training quantization methods typically achieve 4-8 bits per parameter, recent research suggests that training LLMs with 1.58 bits per weight parameter from scratch can maintain model accuracy while greatly reducing memory requirements and energy consumption at inference time. Here, we investigate a training strategy for quantization-aware pre-training, where the models are first trained with 16-bit precision and then transition into 1.58-bit quantization-aware training. Our results on 11 downstream tasks show that this 16-to-1.58-bit training strategy is preferable over full 1.58-bit training and leaves models closer to those which have undergone 16-bit training. We further investigate the effects of retaining the optimizer state at the transition point and gradually phasing in quantization strength -- finding that both techniques alleviate the magnitude of loss spikes, but also that these effects can be compensated through further training.
The burgeoning computational demands for training large language models (LLMs) necessitate efficient methods, including quantized training, which leverages low-bit arithmetic operations to reduce costs. While FP8 precision has shown potential, leveraging FP4 remains challenging due to inherent quantization errors and limited representation capability. Based on the Transformer architecture, we present an FP4 training scheme for LLMs, overcoming these obstacles through mixed-precision quantization strategies tailed for different modules and training stages. This allows us to apply the precision level suitable to distinct components within the model, ensuring that multi-head attention and linear layers are handled appropriately. Our pretraining recipe ensures stability in backpropagation by incorporating fine-grained quantization methods with a target precision training schedule. Experimental results demonstrate that our FP4 training scheme achieves accuracy comparable to BF16 and FP8, with smaller theoretical computational cost. With the advent of next-generation hardware supporting FP4, our method sets the foundation for efficient ultra-low precision training.
Reasoning has long been viewed as an emergent property of large language models (LLMs), appearing at or above a certain scale ($\sim$100B parameters). However, recent studies challenge this assumption, showing that small language models (SLMs) can also achieve competitive reasoning performance. SLMs are increasingly favored for their efficiency and deployability. However, there is a lack of systematic study on the reasoning abilities of diverse SLMs, including those trained from scratch or derived from LLMs through quantization, pruning, and distillation. This raises a critical question: Can SLMs achieve reasoning abilities comparable to LLMs? In this work, we systematically survey, benchmark, and analyze 72 SLMs from six model families across 14 reasoning benchmarks. For reliable evaluation, we examine four evaluation methods and compare four LLM judges against human evaluations on 800 data points. We repeat all experiments three times to ensure a robust performance assessment. Additionally, we analyze the impact of different prompting strategies in small models. Beyond accuracy, we also evaluate model robustness under adversarial conditions and intermediate reasoning steps. Our findings challenge the assumption that scaling is the only way to achieve strong reasoning. Instead, we foresee a future where SLMs with strong reasoning capabilities can be developed through structured training or post-training compression. They can serve as efficient alternatives to LLMs for reasoning-intensive tasks.
This work introduces NeuroQuant, a novel post-training quantization (PTQ) approach tailored to non-generalized Implicit Neural Representations for variable-rate Video Coding (INR-VC). Unlike existing methods that require extensive weight retraining for each target bitrate, we hypothesize that variable-rate coding can be achieved by adjusting quantization parameters (QPs) of pre-trained weights. Our study reveals that traditional quantization methods, which assume inter-layer independence, are ineffective for non-generalized INR-VC models due to significant dependencies across layers. To address this, we redefine variable-rate INR-VC as a mixed-precision quantization problem and establish a theoretical framework for sensitivity criteria aimed at simplified, fine-grained rate control. Additionally, we propose network-wise calibration and channel-wise quantization strategies to minimize quantization-induced errors, arriving at a unified formula for representation-oriented PTQ calibration. Our experimental evaluations demonstrate that NeuroQuant significantly outperforms existing techniques in varying bitwidth quantization and compression efficiency, accelerating encoding by up to eight times and enabling quantization down to INT2 with minimal reconstruction loss. This work introduces variable-rate INR-VC for the first time and lays a theoretical foundation for future research in rate-distortion optimization, advancing the field of video coding technology. The materials will be available at https://github.com/Eric-qi/NeuroQuant.
This paper addresses the challenge of channel estimation in extremely large-scale multiple-input multiple-output (XL-MIMO) systems, pivotal for the advancement of 6G communications. XL-MIMO systems, characterized by their vast antenna arrays, necessitate accurate channel state information (CSI) to leverage high spatial multiplexing and beamforming gains. However, conventional channel estimation methods for near-field XL-MIMO encounter significant computational complexity due to the exceedingly high parameter quantization levels needed for estimating the parametric near-field channel. To address this, we propose a low-complexity two-stage on-grid channel estimation algorithm designed for near-field XL-MIMO systems. The first stage focuses on estimating the LoS channel component while treating the NLoS paths as interference. This estimation is accomplished through an alternating subarray-wise array gain maximization (ASAGM) approach based on the piecewise outer product model (SOPM). In the second stage, we estimate the NLoS channel component by utilizing the sensing matrix refinement-based orthogonal matching pursuit (SMR-OMP) algorithm. This approach helps reduce the high computational complexity associated with large-dimensional joint sensing matrices. Simulation results demonstrate the effectiveness of our proposed low-complexity method, showcasing its significant superiority over existing near-field XL-MIMO channel estimation techniques, particularly in intermediate and high SNR regimes, and in practical scenarios involving arbitrary array placements.
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures that best approximates the target distribution. While much existing work relies on the Wasserstein distance to quantify approximation errors, maximum mean discrepancy (MMD) has received comparatively less attention, especially when allowing for variable particle weights. We argue that a Wasserstein-Fisher-Rao gradient flow is well-suited for designing quantizations optimal under MMD. We show that a system of interacting particles satisfying a set of ODEs discretizes this flow. We further derive a new fixed-point algorithm called mean shift interacting particles (MSIP). We show that MSIP extends the classical mean shift algorithm, widely used for identifying modes in kernel density estimators. Moreover, we show that MSIP can be interpreted as preconditioned gradient descent and that it acts as a relaxation of Lloyd's algorithm for clustering. Our unification of gradient flows, mean shift, and MMD-optimal quantization yields algorithms that are more robust than state-of-the-art methods, as demonstrated via high-dimensional and multi-modal numerical experiments.
While watermarks for closed LLMs have matured and have been included in large-scale deployments, these methods are not applicable to open-source models, which allow users full control over the decoding process. This setting is understudied yet critical, given the rising performance of open-source models. In this work, we lay the foundation for systematic study of open-source LLM watermarking. For the first time, we explicitly formulate key requirements, including durability against common model modifications such as model merging, quantization, or finetuning, and propose a concrete evaluation setup. Given the prevalence of these modifications, durability is crucial for an open-source watermark to be effective. We survey and evaluate existing methods, showing that they are not durable. We also discuss potential ways to improve their durability and highlight remaining challenges. We hope our work enables future progress on this important problem.
Large language models (LLMs) offer powerful capabilities but come with significant environmental impact, particularly in carbon emissions. Existing studies benchmark carbon emissions but lack a standardized basis for comparison across different model configurations. To address this, we introduce the concept of functional unit (FU) as a standardized basis and develop FUEL, the first FU-based framework for evaluating LLM serving's environmental impact. Through three case studies, we uncover key insights and trade-offs in reducing carbon emissions by optimizing model size, quantization strategy, and hardware choice, paving the way for more sustainable LLM serving. The code is available at https://github.com/jojacola/FUEL.
We propose a beam codebook design to reduce self-interference (SI) in integrated sensing and communication (ISAC) systems. Our optimization methods, which can be applied to both tapered beamforming and phased arrays, adapt the codebooks to the SI channel such that a certain SI level is achieved. Furthermore, we derive an upper bound on the quantization noise in terms of the achieved SI level, which provides guidelines to pose the optimization problem in order to obtain performance guarantees for sensing. By selecting standard reference codebooks in our simulations, we show substantially improved sensing quality with little impact on 5G-NR communication. Our proposed method is not only less dependent on hyperparameters than other approaches in the literature, but it can also reduce SI further, and thus deliver better sensing and communication performance.
Large Language Models (LLMs) have revolutionized natural language processing, setting new standards across a wide range of applications. However, their relevant memory and computational demands make them impractical for deployment on technologically-constrained tiny devices such as wearable devices and Internet-of-Things units. To address this limitation, we introduce EmbBERT-Q, a novel tiny language model specifically designed for tiny devices with stringent memory constraints. EmbBERT-Q achieves state-of-the-art (SotA) accuracy in Natural Language Processing tasks in this scenario, with a total memory footprint (weights and activations) of just 781 kB, representing a 25x reduction in size with respect to SotA models. By combining architectural innovations with hardware-compatible 8-bit quantization, EmbBERT-Q consistently outperforms several baseline models scaled down to a 2 MB memory budget (i.e., the maximum memory typically available in tiny devices), including heavily compressed versions of BERT and MAMBA. Extensive experimental evaluations on both a selected benchmark dataset, TinyNLP, specifically curated to evaluate Tiny Language Models in NLP tasks and real-world scenarios, and the GLUE benchmark, demonstrate EmbBERT-Q ability to deliver competitive accuracy with respect to existing approaches, achieving an unmatched balance between memory and performance. To ensure the complete and immediate reproducibility of all our results, we release all code, scripts, and model checkpoints at https://github.com/RiccardoBravin/tiny-LLM.
Context-aware compression techniques have gained increasing attention as model sizes continue to grow, introducing computational bottlenecks that hinder efficient deployment. A structured encoding approach was proposed to selectively eliminate redundant parameter groups while ensuring that representational fidelity was preserved across multiple layers. Contextual Compression Encoding (CCE) introduced a multi-stage encoding mechanism that dynamically restructured parameter distributions, allowing for significant reductions in memory footprint and computational complexity. Experimental evaluations demonstrated that models compressed through CCE retained linguistic expressivity and coherence, maintaining accuracy across a range of text generation and classification tasks. Layer-wise analysis revealed that middle-network layers exhibited higher compression ratios, aligning with the observation that self-attention and feed-forward transformations contained redundancies that could be reorganized without impairing functional capacity. Comparisons against conventional quantization and pruning methods confirmed that CCE provided a more balanced trade-off between efficiency and model retention, achieving reductions in energy consumption and inference latency without requiring extensive retraining. Computational efficiency improvements were particularly evident in deployment scenarios involving resource-constrained environments, where reductions in memory usage enabled more scalable implementations. Further analyses of internal network behavior showed that compressed models exhibited stable activation distributions and adapted dynamically to input variations, reinforcing the viability of structured compression strategies for optimizing large-scale architectures.
Supervised fine-tuning is a standard method for adapting pre-trained large language models (LLMs) to downstream tasks. Quantization has been recently studied as a post-training technique for efficient LLM deployment. To obtain quantized fine-tuned LLMs, conventional pipelines would first fine-tune the pre-trained models, followed by post-training quantization. This often yields suboptimal performance as it fails to leverage the synergy between fine-tuning and quantization. To effectively realize low-bit quantization of weights, activations, and KV caches in LLMs, we propose an algorithm named Rotated Straight-Through-Estimator (RoSTE), which combines quantization-aware supervised fine-tuning (QA-SFT) with an adaptive rotation strategy that identifies an effective rotation configuration to reduce activation outliers. We provide theoretical insights on RoSTE by analyzing its prediction error when applied to an overparameterized least square quantized training problem. Our findings reveal that the prediction error is directly proportional to the quantization error of the converged weights, which can be effectively managed through an optimized rotation configuration. Experiments on Pythia and Llama models of different sizes demonstrate the effectiveness of RoSTE. Compared to existing post-SFT quantization baselines, our method consistently achieves superior performances across various tasks and different LLM architectures.
The deployment of deep learning (DL) models for precoding in massive multiple-input multiple-output (mMIMO) systems is often constrained by high computational demands and energy consumption. In this paper, we investigate the compute energy efficiency of mMIMO precoders using DL-based approaches, comparing them to conventional methods such as zero forcing and weighted minimum mean square error (WMMSE). Our energy consumption model accounts for both memory access and calculation energy within DL accelerators. We propose a framework that incorporates mixed-precision quantization-aware training and neural architecture search to reduce energy usage without compromising accuracy. Using a ray-tracing dataset covering various base station sites, we analyze how site-specific conditions affect the energy efficiency of compressed models. Our results show that deep neural network compression generates precoders with up to 35 times higher energy efficiency than WMMSE at equal performance, depending on the scenario and the desired rate. These results establish a foundation and a benchmark for the development of energy-efficient DL-based mMIMO precoders.
In this paper, it is identified that lowering the reference level at the vector signal analyzer can significantly improve the performance of iterative learning control (ILC). We present a mathematical explanation for this phenomenon, where the signals experience logarithmic transform prior to analogue-to-digital conversion, resulting in non-uniform quantization. This process reduces the quantization noise of low-amplitude signals that constitute a substantial portion of orthogonal frequency division multiplexing (OFDM) signals, thereby improving ILC performance. Measurement results show that compared to setting the reference level to the peak amplitude, lowering the reference level achieves 3 dB improvement on error vector magnitude (EVM) and 15 dB improvement on normalized mean square error (NMSE) for 320 MHz WiFi OFDM signals.