Searcharxiv⌕ Search

arXiv subjects

Dan Alistarh

Publications and source records attributed to Dan Alistarh.

At least 19 recordsLinked to original sources
arXiv2026

The Sparsity Whisperer

Pruning reduces the inference cost of large language models, but existing criteria primarily preserve large activations or reconstruct layer outputs. We argue that this overlooks a key computation performed by particularly sparsity-sensitive neurons in the MLP up and gate projections: separating similar inputs into dissimilar outputs. This suggests that effective pruning should preserve not only activations, but also the differences between outputs more broadly. We introduce a family of difference-informed pruning methods built upon this principle. Wisp is a first-order, update-free method that scores weights using input-difference norms, and Wisp+ refines this score neuronwise using the input pairs each neuron separates most strongly. Finally, Whisper is a second-order method that uses a lightly regularized difference Hessian as its reconstruction objective. Across Llama 2 and 3.1 models from 7B to 405B parameters, our second-order variant consistently improves over strong reconstruction-based baselines, while our update-free variants improve over activation-aware baselines, especially in constrained settings. The improvements over Wanda and SparseGPT extend to structured sparsity, downstream evaluations, and other model families. Augmenting stronger techniques such as RIA and ALPS with our difference-informed criteria yields further improvements, shifting the overall accuracy-runtime frontier outward at negligible additional cost. These results suggest that preserving output differences is a broadly useful and composable signal for post-training LLM sparsification.

cs.LG↗
arXiv2026

GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding

Adaptive rounding methods such as GPTQ, or equivalently Babai's nearest plane algorithm, round a real matrix to integers under a quadratic metric. They process the entries in a fixed order, one at a time, propagating each rounding error to the entries not yet processed through a triangular feedback matrix. We study the two-sided version of this task, in which fixed nonsingular basis matrices act on both the left and the right of the residual; the familiar one-sided case is the special case of an identity right basis. Vectorizing the matrix turns the two-sided objective into a quadratic metric whose Gram matrix is a Kronecker product, so the one-dimensional algorithm applies verbatim, but takes quartic time in the matrix dimension. We present GPTQ-2D, which produces the identical rounded matrix in cubic time. It rounds the entries anti-diagonal by anti-diagonal; entries on the same anti-diagonal are independent and are rounded in parallel.

cs.DS↗
arXiv2026

Apertus LLM Family Expansion via Distillation and Quantization

The wide adoption of LLMs has led to their use in great variety of applications and scenarios, such as chatbot assistants and data annotation, creating the need for the models to satisfy certain budget and hardware constraints. This has led to the trend of LLMs being released in batches consisting of similar models of various sizes for the family of models to adhere to as wide of a range of constraints as possible. In this paper, we validate distillation and quantization as a cost-effective way to expand model families to new sizes and hardware formats. Based on the open-recipe Apertus 8B LLM, we produce Apertus-v1.1 - a distilled family of models with up to 4B parameters trained on 1.7T permissive license tokens. We demonstrate cost-efficiency and strong accuracy performance of our approach for covering large ranges of hardware and systems requirements.

cs.LG↗
arXiv2026

Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, 3) PO2(Split87), an explicit-zero asymmetric grid and 4) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation. Source code is available at https://github.com/IST-DASLab/GridGames.

cs.LG↗
arXiv2026

MatryoshkaLoRA: Learning Accurate Hierarchical Low-Rank Representations for LLM Fine-Tuning

With the rise in scale for deep learning models to billions of parameters, the computational cost of fine-tuning remains a significant barrier to deployment. While Low-Rank Adaptation (LoRA) has become the standard for parameter-efficient fine-tuning, the need to set a predefined, static rank $r$ requires exhaustive grid searches to balance efficiency and performance. Existing rank-adaptive solutions such as DyLoRA mitigate this by sampling ranks during the training from a predefined distribution. However, they often yield sub-optimal results at higher ranks due to lack of consistent gradient signals across the full hierarchy of ranks, thus making these methods data-inefficient. In this paper, we propose MatryoshkaLoRA, a general, Matryoshka-inspired training framework for LoRA that learns accurate hierarchical low-rank representations by inserting a fixed, carefully crafted diagonal matrix $P$ between the existing LoRA adapters to scale their sub-ranks accordingly. By introducing this simple modification, our general framework recovers LoRA and DyLoRA only by changing $P$ and ensures all sub-ranks embed the available gradient information efficiently. Our MatryoshkaLoRA supports dynamic rank selection with minimal degradation in accuracy. We further propose Area Under the Rank Accuracy Curve (AURAC), a metric that consistently evaluates the performance of hierarchical low-rank adapters. Our results demonstrate that MatryoshkaLoRA learns more accurate hierarchical low-rank representations than prior rank-adaptive approaches and achieves superior accuracy-performance trade-offs across ranks on the evaluated datasets. Our code is available at https://github.com/IST-DASLab/MatryoshkaLoRA.

cs.CL↗
arXiv2026

Statistically-Lossless Quantization of Large Language Models

Model quantization has become essential for efficient large language model deployment, yet existing approaches present clear trade-offs: methods such as GPTQ and AWQ achieve practical compression but are lossy, while lossless techniques preserve fidelity but lack inference acceleration. This paper explores the middle ground of statistically-lossless compression, examining three complementary aspects of what losslessness means for quantized LLMs. First, task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and is achievable at aggressive bitwidths. Second, we formalize the stricter notion of distribution-lossless compression, requiring the quantized model's next-token distribution to be practically indistinguishable from the original, and propose the Expected Acceptance Rate (EAR), the maximum token-agreement probability under optimal coupling, as a directly interpretable fidelity metric. For example, EAR >= 0.99 means 99% agreement. Third, we prove a gamma-squared variance law showing that symmetric quantization inflates noise variance by gamma^2 relative to asymmetric quantization, making asymmetric quantization a prerequisite for distribution-lossless fidelity but not for task-level preservation. Through SLQ, a layer-wise non-uniform method with asymmetric quantization and wide bitwidth search, we obtain task-lossless compression at well below 4 bits per parameter, as low as 3.3 bits depending on the model, distribution-lossless compression at 5-6 bits per parameter on average, and inference speedups of 1.7-3.7x compared to FP16 using optimized kernels. Source code is available at [https://github.com/IST-DASLab/SLQ](https://github.com/IST-DASLab/SLQ).

cs.LG↗
arXiv2026

Model Compression with Exact Budget Constraints via Riemannian Manifolds

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

cs.LG↗
arXiv2026

GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling

Quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier but are notoriously hard to implement and to scale. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized $\textit{scalar}$ quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus remains compatible with existing scalar inference kernels. We further show that the same discrete-assignment optimization can be applied to practical GGUF K-Quant checkpoints: starting from publicly released GGUF models, GSQ improves accuracy while projecting the result back into the same deployment format. Finally, GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply. The source code is publicly available at https://github.com/IST-DASLab/GSQ.

cs.CL↗
arXiv2026

Towards Robust Scaling Laws for Optimizers

The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data grow, however, almost all existing studies fix the optimizer (typically AdamW). At the same time, a new generation of optimizers (e.g., Muon, Shampoo, SOAP) promises faster and more stable convergence, but their relationship with model and data scaling is not yet well understood. In this work, we study scaling laws across different optimizers. Empirically, we show that 1) separate Chinchilla-style scaling laws for each optimizer are ill-conditioned and have highly correlated parameters. Instead, 2) we propose a more robust law with shared power-law exponents and optimizer-specific rescaling factors, which enable direct comparison between optimizers. Finally, 3) we provide a theoretical analysis of gradient-based methods for the proxy task of a convex quadratic objective, demonstrating that Chinchilla-style scaling laws emerge naturally as a result of loss decomposition into irreducible, approximation, and optimization errors.

cs.LG↗
arXiv2026

LoRDO: Distributed Low-Rank Optimization with Infrequent Communication

Distributed training of foundation models via $\texttt{DDP}$ is limited by interconnect bandwidth. While infrequent communication strategies reduce synchronization frequency, they remain bottlenecked by the memory and communication requirements of optimizer states. Low-rank optimizers can alleviate these constraints; however, in the local-update regime, workers lack access to the full-batch gradients required to compute low-rank projections, which degrades performance. We propose $\texttt{LoRDO}$, a principled framework unifying low-rank optimization with infrequent synchronization. We first demonstrate that, while global projections based on pseudo-gradients are theoretically superior, they permanently restrict the optimization trajectory to a low-rank subspace. To restore subspace exploration, we introduce a full-rank quasi-hyperbolic update. $\texttt{LoRDO}$ achieves near-parity with low-rank $\texttt{DDP}$ in language modeling and downstream tasks at model scales of $125$M--$720$M, while reducing communication by $\approx 10 \times$. Finally, we show that $\texttt{LoRDO}$ improves performance even more in very low-memory settings with small rank/batch size.

cs.LG↗
arXiv2026

MatGPTQ: Accurate and Efficient Post-Training Matryoshka Quantization

Matryoshka Quantization (MatQuant) is a recent quantization approach showing that a single integer-quantized model can be served across multiple precisions, by slicing the most significant bits (MSB) at inference time. This enables a single checkpoint to cover a wide range of memory and latency budgets, but renders quantization much more challenging. In particular, the initial MatQuant relies on expensive quantization-aware training (QAT) variants, rather than fast one-shot post training quantization (PTQ), and lacks open-source and kernel support. We address all of these limitations by introducing Post-Training Matryoshka Quantization (MatGPTQ), a new PTQ pipeline that produces a single parent model jointly optimized for multiple target precisions in one-shot, based on a small calibration set. MatGPTQ casts Matryoshka quantization as a multi-precision objective with bit-slicing and cross-bit error compensation, resulting in an algorithm that produces a multi-bit-width, "sliceable" model in a single pass. We also incorporate a new budget-aware search for heterogeneous per-layer bit-witdhs and provide efficient kernels that implement slicing and mixed-precision execution. Across standard LLMs and benchmarks, MatGPTQ preserves high-bit accuracy while substantially improving performance at low-bit-witdh settings. Overall, we establish a new state of the art for Matryoshka-style post-training quantization and make single-checkpoint, multi-precision deployment open and practical. Code is available at https://github.com/IST-DASLab/MatGPTQ.

cs.LG↗
arXiv2026

DASH: Faster Shampoo via Batched Block Preconditioning and Efficient Inverse-Root Solvers

Shampoo is one of the leading approximate second-order optimizers: a variant of it has won the MLCommons AlgoPerf competition, and it has been shown to produce models with lower activation outliers that are easier to compress. Yet, applying Shampoo currently comes at the cost of significant computational slowdown, due to its expensive internal operations. In this paper, we take a significant step to address this shortcoming by proposing \method (for \textbf{D}istributed \textbf{A}ccelerated \textbf{SH}ampoo), a faster implementation of Distributed Shampoo based on two main new techniques: First, we show that preconditioner blocks can be stacked into 3D tensors to significantly improve GPU utilization; second, we introduce the Newton-DB iteration and the Chebyshev polynomial approximations as novel and faster approaches for computing the inverse matrix roots required by Shampoo. Along with these algorithmic contributions, we provide a first in-depth analysis of how matrix scaling critically affects Shampoo convergence. On the practical side, our GPU-aware implementation achieves up to $5.6\times$ faster optimizer steps compared to the well-optimized Distributed Shampoo, while Newton-DB attains the lowest validation perplexity per iteration among all tested methods. Our code is available at https://github.com/IST-DASLab/DASH.

cs.LG↗
arXiv2026

Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimation

The NVFP4 lower-precision format, supported in hardware by NVIDIA Blackwell GPUs, promises to allow, for the first time, end-to-end fully-quantized pre-training of massive models such as LLMs. Yet, existing quantized training methods still sacrifice some of the representation capacity of this format in favor of more accurate unbiased quantized gradient estimation by stochastic rounding (SR), losing noticeable accuracy relative to standard FP16 and FP8 training. In this paper, improve the state of the art for quantized training in NVFP4 via a novel unbiased quantization routine for micro-scaled formats, called MS-EDEN, that has more than 2x lower quantization error than SR. We integrate it into a novel fully-NVFP4 quantization scheme for linear layers, called Quartet II. We show analytically that Quartet II achieves consistently better gradient estimation across all major matrix multiplications, both on the forward and on the backward passes. In addition, our proposal synergizes well with recent training improvements aimed specifically at NVFP4. We further validate Quartet II on end-to-end LLM training with up to 1.9B parameters on 38B tokens. We provide kernels for execution on NVIDIA Blackwell GPUs with up to 4.2x speedup over BF16. Our code is available at https://github.com/IST-DASLab/Quartet-II .

cs.LG↗
arXiv2026

Behemoth: Benchmarking Unlearning in LLMs Using Fully Synthetic Data

As artificial neural networks, and specifically large language models, have improved rapidly in capabilities and quality, they have increasingly been deployed in real-world applications, from customer service to Google search, despite the fact that they frequently make factually incorrect or undesirable statements. This trend has inspired practical and academic interest in model editing, that is, in adjusting the weights of the model to modify its likely outputs for queries relating to a specific fact or set of facts. This may be done either to amend a fact or set of facts, for instance, to fix a frequent error in the training data, or to suppress a fact or set of facts entirely, for instance, in case of dangerous knowledge. Multiple methods have been proposed to do such edits. However, at the same time, it has been shown that such model editing can be brittle and incomplete. Moreover the effectiveness of any model editing method necessarily depends on the data on which the model is trained, and, therefore, a good understanding of the interaction of the training data distribution and the way it is stored in the network is necessary and helpful to reliably perform model editing. However, working with large language models trained on real-world data does not allow us to understand this relationship or fully measure the effects of model editing. We therefore propose Behemoth, a fully synthetic data generation framework. To demonstrate the practical insights from the framework, we explore model editing in the context of simple tabular data, demonstrating surprising findings that, in some cases, echo real-world results, for instance, that in some cases restricting the update rank results in a more effective update. The code is available at https://github.com/IST-DASLab/behemoth.git.

cs.LG↗
arXiv2026

ECO: Quantized Training without Full-Precision Master Weights

Quantization has significantly improved the compute and memory efficiency of Large Language Model (LLM) training. However, existing approaches still rely on accumulating their updates in high-precision: concretely, gradient updates must be applied to a high-precision weight buffer, known as $\textit{master weights}$. This buffer introduces substantial memory overhead, particularly for Sparse Mixture of Experts (SMoE) models, where model parameters and optimizer states dominate memory usage. To address this, we introduce the Error-Compensating Optimizer (ECO), which eliminates master weights by applying updates directly to quantized parameters. ECO quantizes weights after each step and carefully injects the resulting quantization error into the optimizer momentum, forming an error-feedback loop with no additional memory. We prove that, under standard assumptions and a decaying learning rate, ECO converges to a constant-radius neighborhood of the optimum, while naive master-weight removal can incur an error that is inversely proportional to the learning rate. We show empirical results for pretraining small Transformers (30-800M), a Gemma-3 1B model, and a 2.1B parameter Sparse MoE model with FP8 quantization, and fine-tuning DeepSeek-MoE-16B in INT4 precision. Throughout, ECO matches baselines with master weights up to near-lossless accuracy, significantly shifting the static memory vs validation loss Pareto frontier.

cs.CL↗
arXiv2025

LLMQ: Efficient Lower-Precision Pretraining for Consumer GPUs

We present LLMQ, an end-to-end CUDA/C++ implementation for medium-sized language-model training, e.g. 3B to 32B parameters, on affordable, commodity GPUs. These devices are characterized by low memory availability and slow communication compared to datacentre-grade GPUs. Consequently, we showcase a range of optimizations that target these bottlenecks, including activation checkpointing, offloading, and copy-engine based collectives. LLMQ is able to train or fine-tune a 7B model on a single 16GB mid-range gaming card, or a 32B model on a workstation equipped with 4 RTX 4090s. This is achieved while executing a standard 8-bit training pipeline, without additional algorithmic approximations, and maintaining FLOP utilization of around 50%. The efficiency of LLMQ rivals that of production-scale systems on much more expensive cloud-grade GPUs.

cs.DC↗
arXiv2025

Speculative Decoding Speed-of-Light: Optimal Lower Bounds via Branching Random Walks

Speculative generation has emerged as a promising technique to accelerate inference in large language models (LLMs) by leveraging parallelism to verify multiple draft tokens simultaneously. However, the fundamental limits on the achievable speedup remain poorly understood. In this work, we establish the first ``tight'' lower bounds on the runtime of any deterministic speculative generation algorithm. This is achieved by drawing a parallel between the token generation process and branching random walks, which allows us to analyze the optimal draft tree selection problem. We prove, under basic assumptions, that the expected number of tokens successfully predicted per speculative iteration is bounded as $\mathbb{E}[X] \leq (\mu + \mu_{(2)})\log(P )/\mu^2 + O(1)$, where $P$ is the verifier's capacity, $\mu$ is the expected entropy of the verifier's output distribution, and $\mu_{(2)}$ is the expected second log-moment. This result provides new insights into the limits of parallel token generation, and could guide the design of future speculative decoding systems. Empirical evaluations on Llama models validate our theoretical predictions, confirming the tightness of our bounds in practical settings.

cs.CL↗
arXiv2025

WUSH: Near-Optimal Adaptive Transforms for LLM Quantization

Quantizing LLM weights and activations is a standard approach for efficient deployment, but a few extreme outliers can stretch the dynamic range and amplify low-bit quantization errors. Prior transform-based mitigations (e.g., Hadamard rotations) are fixed and data-agnostic, and their optimality for quantization has remained unclear. We derive closed-form optimal linear blockwise transforms for joint weight-activation quantization under standard RTN AbsMax-scaled block quantizers, covering both integer and floating-point formats. The resulting construction, WUSH, combines a Hadamard backbone with a data-dependent second-moment component to form a non-orthogonal transform that is provably near-optimal for FP and INT quantizers under mild assumptions while admitting an efficient fused GPU implementation. Empirically, WUSH improves W4A4 accuracy over the strongest Hadamard-based baselines (e.g., on Llama-3.1-8B-Instruct in MXFP4, it gains +2.8 average points with RTN and +0.7 with GPTQ) while delivering up to 5.8$\times$ per-layer throughput over BF16 via FP4 MatMul. Source code is available at https://github.com/IST-DASLab/WUSH.

cs.LG↗