Dan Alistarh

ICML Conference 2025 Conference Paper

Cache Me If You Must: Adaptive Key-Value Quantization for Large Language Models

• Alina Shutova
• Vladimir Malinovskii
• Vage Egiazarian
• Denis Kuznedelev
• Denis Mazur
• Nikita Surkov
• Ivan Ermakov
• Dan Alistarh

Efficient real-world deployments of large language models (LLMs) rely on Key-Value (KV) caching for processing and generating long outputs, reducing the need for repetitive computation. For large contexts, Key-Value caches can take up tens of gigabytes of device memory, as they store vector representations for each token and layer. Recent work has shown that the cached vectors can be compressed through quantization, pruning or merging, but these techniques often compromise quality towards higher compression rates. In this work, we aim to improve Key & Value compression by exploiting two observations: 1) the inherent dependencies between keys and values across different layers, and 2) the existence of high-compression methods for internal network states (e. g. attention Keys & Values). We propose AQUA-KV, an adaptive quantization for Key-Value caches that relies on compact adapters to exploit existing dependencies between Keys and Values, and aims to "optimally" compress the information that cannot be predicted. AQUA-KV significantly improves compression rates, while maintaining high accuracy on state-of-the-art LLM families. On Llama 3. 2 LLMs, we achieve near-lossless inference at 2-2. 5 bits per value with under $1%$ relative error in perplexity and LongBench scores. AQUA-KV is one-shot, simple, and efficient: it can be calibrated on a single GPU within 1-6 hours, even for 70B models.

NeurIPS Conference 2025 Conference Paper

Efficient Data Selection at Scale via Influence Distillation

• Mahdi Nikdan
• Vincent Cohen-Addad
• Dan Alistarh
• Vahab Mirrokni

Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a $\textit{landmark-based approximation}$: influence is precisely computed for a small subset of "landmark" samples and then efficiently propagated to all other samples to determine their weights. We validate Influence Distillation by applying it to instruction tuning on the Tulu V2 dataset, targeting a range of tasks including GSM8k, SQuAD, and MMLU, across several models from the Llama and Qwen families. Experiments show that Influence Distillation matches or outperforms state-of-the-art performance while achieving up to $3. 5\times$ faster selection.

ICML Conference 2025 Conference Paper

EvoPress: Accurate Dynamic Model Compression via Evolutionary Search

• Oliver Sieberling
• Denis Kuznedelev
• Eldar Kurtic
• Dan Alistarh

The high computational costs of large language models (LLMs) have led to a flurry of research on LLM compression, via methods such as quantization, sparsification, or structured pruning. A new frontier in this area is given by dynamic, non-uniform compression methods, which adjust the compression levels (e. g. , sparsity) per-block or even per-layer in order to minimize accuracy loss, while guaranteeing a global compression threshold. Yet, current methods rely on estimating the "importance" of a given layer, implicitly assuming that layers contribute independently to the overall compression error. We begin from the motivating observation that this independence assumption does not generally hold for LLM compression: pruning a model further may even significantly recover performance. To address this, we propose EvoPress, a novel evolutionary framework for dynamic LLM compression. By formulating dynamic compression as a general optimization problem, EvoPress identifies optimal compression profiles in a highly efficient manner, and generalizes across diverse models and compression techniques. Via EvoPress, we achieve state-of-the-art performance for dynamic compression of Llama, Mistral, and Phi models, setting new benchmarks for structural pruning (block/layer dropping), unstructured sparsity, and quantization with dynamic bitwidths.

NeurIPS Conference 2025 Conference Paper

HALO: Hadamard-Assisted Lower-Precision Optimization for LLMs

• Saleh Ashkboos
• Mahdi Nikdan
• Rush Tabesh
• Roberto Castro
• Torsten Hoefler
• Dan Alistarh

Quantized training of Large Language Models (LLMs) remains an open challenge, as maintaining accuracy while performing all matrix multiplications in low precision has proven difficult. This is particularly the case when fine-tuning pre-trained models, which can have large weight, activation, and error (output gradient) outlier values that make lower-precision optimization difficult. To address this, we present HALO, a new quantization-aware training approach for Transformers that enables accurate and efficient low-precision training by combining 1) strategic placement of Hadamard rotations in both forward and backward passes, which mitigate outliers, 2) high-performance kernel support, and 3) FSDP integration for low-precision communication. Our approach ensures that all large matrix multiplications during the forward and backward passes are executed in lower precision. Applied to LLaMa models, HALO achieves near-full-precision-equivalent results during fine-tuning on various tasks, while delivering up to 1. 41x end-to-end speedup for full fine-tuning on RTX 4090 GPUs. HALO efficiently supports both standard and parameter-efficient fine-tuning (PEFT). Our results demonstrate the first practical approach to fully quantized LLM fine-tuning that maintains accuracy in INT8 and FP6 precision, while delivering performance benefits.

NeurIPS Conference 2025 Conference Paper

Hogwild! Inference: Parallel LLM Generation via Concurrent Attention

• Gleb Rodionov
• Roman Garipov
• Alina Shutova
• George Yakushev
• Erik Schultheis
• Vage Egiazarian
• Anton Sinitsin
• Denis Kuznedelev

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel, allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

AAAI Conference 2025 Conference Paper

Hybrid Decentralized Optimization: Leveraging Both First- and Zeroth-Order Optimizers for Faster Convergence

• Shayan Talaei
• Matin Ansaripour
• Giorgi Nadiradze
• Dan Alistarh

Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some computationally-bounded nodes may not be able to implement first-order, gradient-based optimization, while they could still contribute to joint optimization tasks. In this paper, we initiate the study of hybrid decentralized optimization, studying settings where nodes with zeroth-order and first-order optimization capabilities co-exist in a distributed system, and attempt to jointly solve an optimization task over some data distribution. We essentially show that, under reasonable parameter settings, such a system can not only withstand noisier zeroth-order agents but can even benefit from integrating such agents into the optimization process, rather than ignoring their information. At the core of our approach is a new analysis of distributed optimization with noisy and possibly-biased gradient estimators, which may be of independent interest. Our results hold for both convex and non-convex objectives. Experimental results on standard optimization tasks confirm our analysis, showing that hybrid first-zeroth order optimization can be practical, even when training deep neural networks.

ICML Conference 2025 Conference Paper

Layer-wise Quantization for Quantized Optimistic Dual Averaging

• Anh Duc Nguyen
• Ilia Markov
• Frank Zhengqing Wu
• Ali Ramezani-Kebrya
• Kimon Antonakopoulos
• Dan Alistarh
• Volkan Cevher

Modern deep neural networks exhibit heterogeneity across numerous layers of various types such as residuals, multi-head attention, etc. , due to varying structures (dimensions, activation functions, etc.), distinct representation characteristics, which impact predictions. We develop a general layer-wise quantization framework with tight variance and code-length bounds, adapting to the heterogeneities over the course of training. We then apply a new layer-wise quantization technique within distributed variational inequalities (VIs), proposing a novel Quantized Optimistic Dual Averaging (QODA) algorithm with adaptive learning rates, which achieves competitive convergence rates for monotone VIs. We empirically show that QODA achieves up to a $150$% speedup over the baselines in end-to-end training time for training Wasserstein GAN on $12+$ GPUs.

ICLR Conference 2025 Conference Paper

LDAdam: Adaptive Optimization from Low-Dimensional Gradient Statistics

• Thomas Robert 0007
• Mher Safaryan
• Ionut-Vlad Modoranu
• Dan Alistarh

We introduce LDAdam, a memory-efficient optimizer for training large models, that performs adaptive optimization steps within lower dimensional subspaces, while consistently exploring the full parameter space during training. This strategy keeps the optimizer's memory footprint to a fraction of the model size. LDAdam relies on a new projection-aware update rule for the optimizer states that allows for transitioning between subspaces, i.e., estimation of the statistics of the projected gradients. To mitigate the errors due to low-rank projection, LDAdam integrates a new generalized error feedback mechanism, which explicitly accounts for both gradient and optimizer state compression. We prove the convergence of LDAdam under standard assumptions, and provide empirical evidence that LDAdam allows for efficient fine-tuning and pre-training of language models.

NeurIPS Conference 2025 Conference Paper

Quartet: Native FP4 Training Can Be Optimal for Large Language Models

• Roberto Castro
• Andrei Panferov
• Rush Tabesh
• Oliver Sieberling
• Jiale Chen
• Mahdi Nikdan
• Saleh Ashkboos
• Dan Alistarh

Training large language models (LLMs) models directly in low-precision offers a way to address computational costs by improving both throughput and energy efficiency. For those purposes, NVIDIA's recent Blackwell architecture facilitates very low-precision operations using FP4 variants. Yet, current algorithms for training LLMs in FP4 precision face significant accuracy degradation and often rely on mixed-precision fallbacks. In this paper, we investigate hardware-supported FP4 training and introduce a new approach for accurate, end-to-end FP4 training with all the major computations (i. e. , linear layers) in low precision. Through extensive evaluations on Llama-type models, we reveal a new low-precision scaling law that quantifies performance trade-offs across bit-widths and training setups. Guided by this investigation, we design an "optimal" technique in terms of accuracy-vs-computation, called Quartet. We implement Quartet using optimized CUDA kernels tailored for Blackwell, demonstrating that fully FP4-based training is a competitive alternative to FP16 half-precision and to FP8 training. Our code is available at https: //github. com/IST-DASLab/Quartet.

ICML Conference 2025 Conference Paper

QuEST: Stable Training of LLMs with 1-Bit Weights and Activations

• Andrei Panferov
• Jiale Chen 0004
• Soroush Tabesh
• Mahdi Nikdan
• Dan Alistarh

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i. e. , Quantization-Aware Training (QAT), is still open: for example, a recent study put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, for which we demonstrate optimality at 4-bits and stable convergence as low as 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https: //github. com/IST-DASLab/QuEST.

ICLR Conference 2025 Conference Paper

Scalable Mechanistic Neural Networks

• Jiale Chen 0004
• Dingling Yao
• Adeel Pervez
• Dan Alistarh
• Francesco Locatello

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

TMLR Journal 2025 Journal Article

TACO Vision Models Can Be Efficiently Specialized via Few-Shot Task-Aware Compression

• Denis Kuznedelev
• Soroush Tabesh
• Kimia Noorbakhsh
• Elias Frantar
• Sara Beery
• Eldar Kurtic
• Dan Alistarh

Recent vision architectures and self-supervised training methods have enabled training computer vision models that are extremely accurate, but come with massive computational costs. In settings such as identifying species in camera traps in the field, users have limited resources, and may fine-tune a pretrained model on (often limited) data from a small set of specific categories of interest. Such users may still wish to make use of highly-accurate large models, but are often constrained by the computational cost. To address this, we ask: can we quickly compress generalist models into accurate and efficient specialists given a small amount of data? Towards this goal, we propose a simple and versatile technique, which we call Few-Shot Task-Aware COmpression (TACO). Given a general-purpose model pretrained on a broad task, such as classification on ImageNet or iNaturalist datasets with thousands of categories, TACO produces a much smaller model that is accurate on specialized tasks, such as classifying across vehicle types or animal species, based only on a few examples from each target class. The method is based on two key insights - 1) a powerful specialization effect for data-aware compression, which we showcase for the first time; 2) a dedicated finetuning procedure with knowledge distillation, which prevents overfitting even in scenarios where data is very scarce. Specifically, TACO is applied in few-shot fashion, i.e. only a few task-specific samples are used for compression, and the procedure has low computational overhead. We validate this approach experimentally using highly-accurate ResNet, ViT/DeiT, and ConvNeXt models, originally trained on ImageNet and iNaturalist datasets, which we specialize and compress to a diverse set of ``downstream'' subtasks, with notable computational speedups on both CPU and GPU.

ICLR Conference 2025 Conference Paper

The Journey Matters: Average Parameter Count over Pre-training Unifies Sparse and Dense Scaling Laws

• Tian Jin
• Ahmed Imtiaz Humayun
• Utku Evci
• Suvinay Subramanian
• Amir Yazdanbakhsh
• Dan Alistarh
• Gintare Karolina Dziugaite

Pruning eliminates unnecessary parameters in neural networks; it offers a promising solution to the growing computational demands of large language models (LLMs). While many focus on post-training pruning, sparse pre-training--which combines pruning and pre-training into a single phase--provides a simpler alternative. In this work, we present the first systematic exploration of optimal sparse pre-training configurations for LLMs through an examination of 80 unique pruning schedules across different sparsity levels and training durations. We find that initiating pruning at 25\% of total training compute and concluding at 75\% achieves near-optimal final evaluation loss. These findings provide valuable insights for efficient and effective sparse pre-training of LLMs. Furthermore, we propose a new scaling law that modifies the Chinchilla scaling law to use the average parameter count over pre-training. Through empirical and theoretical validation, we demonstrate that this modified scaling law accurately models evaluation loss for both sparsely and densely pre-trained LLMs, unifying scaling laws across pre-training paradigms. Our findings indicate that while sparse pre-training achieves the same final model quality as dense pre-training for equivalent compute budgets, it provides substantial benefits through reduced model size, enabling significant potential computational savings during inference.

NeurIPS Conference 2025 Conference Paper

Unified Scaling Laws for Compressed Representations

• Andrei Panferov
• Alexandra Volkova
• Ionut-Vlad Modoranu
• Vage Egiazarian
• Mher Safaryan
• Dan Alistarh

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression strategies, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include proposing and validating a general scaling law formulation applicable both individually but also composably across compression types. We demonstrate both theoretically and empirically that a simple metric based on Gaussian mean squared error fitting can robustly predict parameter efficiency across compressed models. Additionally, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats. Finally, we identify conditions under which these unified scaling laws fail.

ICLR Conference 2025 Conference Paper

Wasserstein Distances, Neuronal Entanglement, and Sparsity

• Shashata Sawmya
• Linghao Kong
• Ilia Markov
• Dan Alistarh
• Nir Shavit

Disentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight sparsity, a leading post-training optimization technique. We suggest a novel measure for estimating neuronal entanglement: the Wasserstein distance of a neuron's output distribution to a Gaussian. Moreover, we show the existence of a small number of highly entangled "Wasserstein Neurons" in each linear layer of an LLM, characterized by their highly non-Gaussian output distributions, their role in mapping similar inputs to dissimilar outputs, and their significant impact on model accuracy. To study these phenomena, we propose a new experimental framework for disentangling polysemantic neurons. Our framework separates each layer's inputs to create a mixture of experts where each neuron's output is computed by a mixture of neurons of lower Wasserstein distance, each better at maintaining accuracy when sparsified without retraining. We provide strong evidence that this is because the mixture of sparse experts is effectively disentangling the input-output relationship of individual neurons, in particular the difficult Wasserstein neurons.

TMLR Journal 2024 Journal Article

Accurate Neural Network Pruning Requires Rethinking Sparse Optimization

• Denis Kuznedelev
• Eldar Kurtic
• Eugenia Iofinova
• Elias Frantar
• Alexandra Peste
• Dan Alistarh

Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse % is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the community. Yet, much less is known about the interaction between sparsity and the standard stochastic optimization techniques used for training sparse networks, and most existing work uses standard dense schedules and hyperparameters for training sparse networks. In this work, we examine the impact of high sparsity on model training using the standard computer vision and natural language processing sparsity benchmarks. We begin by showing that using standard dense training recipes for sparse training is suboptimal, and provide evidence that this results in *under-training*, loosely defined as using a suboptimal number of passes over the training data. We present training recipes for mitigating this issue for both sparse pre-training of vision models (e.g. ResNet50/ImageNet) and sparse fine-tuning of language models (e.g. BERT/GLUE), achieving state-of-the-art results in both settings in the high-sparsity regime, and providing detailed analyses for the difficulty of sparse training in both scenarios. Our work sets a new benchmark in terms of the accuracies that can be achieved under high sparsity, and should inspire further research into improving sparse model training, to reach higher accuracies under high sparsity, but also to do so efficiently.

ICML Conference 2024 Conference Paper

Error Feedback Can Accurately Compress Preconditioners

• Ionut-Vlad Modoranu
• Aleksei Kalinov
• Eldar Kurtic
• Elias Frantar
• Dan Alistarh

Leveraging second-order information about the loss at the scale of deep networks is one of the main lines of approach for improving the performance of current optimizers for deep learning. Yet, existing approaches for accurate full-matrix preconditioning, such as Full-Matrix Adagrad (GGT) or Matrix-Free Approximate Curvature (M-FAC) suffer from massive storage costs when applied even to small-scale models, as they must store a sliding window of gradients, whose memory requirements are multiplicative in the model dimension. In this paper, we address this issue via a novel and efficient error-feedback technique that can be applied to compress preconditioners by up to two orders of magnitude in practice, without loss of convergence. Specifically, our approach compresses the gradient information via sparsification or low-rank compression before it is fed into the preconditioner, feeding the compression error back into future iterations. Extensive experiments on deep neural networks show that this approach can compress full-matrix preconditioners to up to 99% sparsity without accuracy loss, effectively removing the memory overhead of fullmatrix preconditioners such as GGT and M-FAC.

ICML Conference 2024 Conference Paper

Extreme Compression of Large Language Models via Additive Quantization

• Vage Egiazarian
• Andrei Panferov
• Denis Kuznedelev
• Elias Frantar
• Artem Babenko
• Dan Alistarh

The emergence of accurate open large language models (LLMs) has led to a race towards performant quantization techniques which can enable their execution on end-user devices. In this paper, we revisit the problem of “extreme” LLM compression—defined as targeting extremely low bit counts, such as 2 to 3 bits per parameter—from the point of view of classic methods in Multi-Codebook Quantization (MCQ). Our algorithm, called AQLM, generalizes the classic Additive Quantization (AQ) approach for information retrieval to advance the state-of-the-art in LLM compression, via two innovations: 1) learned additive quantization of weight matrices in input-adaptive fashion, and 2) joint optimization of codebook parameters across each transformer blocks. Broadly, AQLM is the first scheme that is Pareto optimal in terms of accuracy-vs-model-size when compressing to less than 3 bits per parameter, and significantly improves upon all known schemes in the extreme compression (2bit) regime. In addition, AQLM is practical: we provide fast GPU and CPU implementations of AQLM for token generation, which enable us to match or outperform optimized FP16 implementations for speed, while executing in a much smaller memory footprint.

NeurIPS Conference 2024 Conference Paper

MicroAdam: Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence

• Ionut-Vlad Modoranu
• Mher Safaryan
• Grigory Malinovsky
• Eldar Kurtic
• Thomas Robert
• Peter Richtárik
• Dan Alistarh

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed into the optimizer state, thereby reducing its memory footprint significantly. We control the resulting compression error via a novel instance of the classical error feedback mechanism from distributed optimization in which the error correction information is itself compressed to allow for practical memory gains. We prove that the resulting approach maintains theoretical convergence guarantees competitive to those of AMSGrad, while providing good practical performance. Specifically, we show that MicroAdam can be implemented efficiently on GPUs: on both million-scale (BERT) and billion-scale (LLaMA) models, MicroAdam provides practical convergence competitive to that of the uncompressed Adam baseline, with lower memory usage and similar running time. Our code is available at https: //github. com/IST-DASLab/MicroAdam.

NeurIPS Conference 2024 Conference Paper

PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression

• Vladimir Malinovskii
• Denis Mazur
• Ivan Ilin
• Denis Kuznedelev
• Konstantin Burlachenko
• Kai Yi
• Dan Alistarh
• Peter Richtarik

There has been significant interest in "extreme" compression of large language models (LLMs), i. e. to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama-2 family models at 2 bits per parameter.

NeurIPS Conference 2024 Conference Paper

QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs

• Saleh Ashkboos
• Amirkeivan Mohtashami
• Maximilian L. Croci
• Bo Li
• Pashmina Cameron
• Martin Jaggi
• Dan Alistarh
• Torsten Hoefler

We introduce QuaRot, a new Quantization scheme based on Rotations, which is able to quantize LLMs end-to-end, including all weights, activations, and KV cache in 4 bits. QuaRot rotates LLMs in a way that removes outliers from the hidden state without changing the output, making quantization easier. This computational invariance is applied to the hidden state (residual) of the LLM, as well as to the activations of the feed-forward components, aspects of the attention mechanism, and to the KV cache. The result is a quantized model where all matrix multiplications are performed in 4 bits, without any channels identified for retention in higher precision. Our 4-bit quantized LLAMA2-70B model has losses of at most 0. 47 WikiText-2 perplexity and retains 99% of the zero-shot performance. We also show that QuaRot can provide lossless 6 and 8 bit LLAMA-2 models without any calibration data using round-to-nearest quantization. Code is available at github. com/spcl/QuaRot.

ICML Conference 2024 Conference Paper

RoSA: Accurate Parameter-Efficient Fine-Tuning via Robust Adaptation

• Mahdi Nikdan
• Soroush Tabesh
• Elvir Crncevic
• Dan Alistarh

We investigate parameter-efficient fine-tuning (PEFT) methods that can provide good accuracy under limited computational and memory budgets in the context of large language models (LLMs). We present a new PEFT method called Robust Adaptation (RoSA) inspired by robust principal component analysis that jointly trains $\textit{low-rank}$ and highly-sparse components on top of a set of fixed pretrained weights to efficiently approximate the performance of a full-fine-tuning (FFT) solution. Across a series of challenging generative tasks such as grade-school math and SQL query generation, which require fine-tuning for good performance, we show that RoSA outperforms LoRA, pure sparse fine-tuning, and alternative hybrid methods at the same parameter budget, and can even recover the performance of FFT on some tasks. We provide system support for RoSA to complement the training algorithm, specifically in the form of sparse GPU kernels which enable memory- and computationally-efficient training, and show that it is also compatible with low-precision base weights, resulting in the first joint representation combining quantization, low-rank and sparse approximations. Our code is available at https: //github. com/IST-DASLab/RoSA.

ICLR Conference 2024 Conference Paper

Scaling Laws for Sparsely-Connected Foundation Models

• Elias Frantar
• Carlos Riquelme
• Neil Houlsby
• Dan Alistarh
• Utku Evci

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements. We provide pruning and scaling law fitting code at: github.com/google-research/jaxpruner/tree/main/jaxpruner/projects/bigsparse.

ICML Conference 2024 Conference Paper

SPADE: Sparsity-Guided Debugging for Deep Neural Networks

• Arshia Soltani Moakhar
• Eugenia Iofinova
• Elias Frantar
• Dan Alistarh

It is known that sparsity can improve interpretability for deep neural networks. However, existing methods in the area either require networks that are pre-trained with sparsity constraints, or impose sparsity after the fact, altering the network’s general behavior. In this paper, we demonstrate, for the first time, that sparsity can instead be incorporated into the interpretation process itself, as a sample-specific preprocessing step. Unlike previous work, this approach, which we call SPADE, does not place constraints on the trained model and does not affect its behavior during inference on the sample. Given a trained model and a target sample, SPADE uses sample-targeted pruning to provide a "trace" of the network’s execution on the sample, reducing the network to the most important connections prior to computing an interpretation. We demonstrate that preprocessing with SPADE significantly increases the accuracy of image saliency maps across several interpretability methods. Additionally, SPADE improves the usefulness of neuron visualizations, aiding humans in reasoning about network behavior. Our code is available at https: //github. com/IST-DASLab/SPADE.

ICLR Conference 2024 Conference Paper

SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression

• Tim Dettmers
• Ruslan Svirschevski
• Vage Egiazarian
• Denis Kuznedelev
• Elias Frantar
• Saleh Ashkboos
• Alexander Borzunov
• Torsten Hoefler

Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. Quantizing models to 3-4 bits per parameter can lead to moderate to high accuracy losses, especially for smaller models (1-10B parameters), which are suitable for edge deployment. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique that enables for the first time \emph{near-lossless} compression of LLMs across model scales while reaching similar compression levels to previous methods. SpQR works by identifying and isolating \emph{outlier weights}, which cause particularly large quantization errors, and storing them in higher precision while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than $1\%$ in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run a 33B parameter LLM on a single 24 GB consumer GPU without performance degradation at 15\% speedup, thus making powerful LLMs available to consumers without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR, which yields faster inference than 16-bit baselines at similar accuracy while enabling memory compression gains of more than 4x.

NeurIPS Conference 2024 Conference Paper

The Iterative Optimal Brain Surgeon: Faster Sparse Recovery by Leveraging Second-Order Information

• Diyuan Wu
• Ionut-Vlad Modoranu
• Mher Safaryan
• Denis Kuznedelev
• Dan Alistarh

The rising footprint of machine learning has led to a focus on imposing model sparsity as a means of reducing computational and memory costs. For deep neural networks (DNNs), the state-of-the-art accuracy-vs-sparsity is achieved by heuristics inspired by the classical Optimal Brain Surgeon (OBS) framework [LeCun et al. , 1989, Hassibi and Stork, 1992, Hassibi et al. , 1993], which leverages loss curvature information to make better pruning decisions. Yet, these results still lack a solid theoretical understanding, and it is unclear whether they can be improved by leveraging connections to the wealth of work on sparse recovery algorithms. In this paper, we draw new connections between these two areas and present new sparse recovery algorithms inspired by the OBS framework that come with theoretical guarantees under reasonable assumptions and have strong practical performance. Specifically, our work starts from the observation that we can leverage curvature information in OBS-like fashion upon the projection step of classic iterative sparse recovery algorithms such as IHT. We show for the first time that this leads both to improved convergence bounds in well-behaved settings and to stronger practical convergence. Furthermore, we present extensions of this approach to training accurate sparse DNNs, and validate it experimentally at scale.

NeurIPS Conference 2023 Conference Paper

CAP: Correlation-Aware Pruning for Highly-Accurate Sparse Vision Models

• Denis Kuznedelev
• Eldar Kurtić
• Elias Frantar
• Dan Alistarh

Driven by significant improvements in architectural design and training pipelines, computer visionhas recently experienced dramatic progress in terms of accuracy on classic benchmarks such as ImageNet. These highly-accurate models are challenging to deploy, as they appear harder to compress using standard techniques such as pruning. We address this issue by introducing the Correlation Aware Pruner (CAP), a new unstructured pruning framework which significantly pushes the compressibility limits for state-of-the-art architectures. Our method is based on two technical advancements: a new theoretically-justified pruner, which can handle complex weight correlations accurately and efficiently during the pruning process itself, and an efficient finetuning procedure for post-compression recovery. We validate our approach via extensive experiments on several modern vision models such as Vision Transformers (ViT), modern CNNs, and ViT-CNN hybrids, showing for the first time that these can be pruned to high sparsity levels (e. g. $\geq 75$%) with low impact on accuracy ($\leq 1$% relative drop). Our approach is also compatible with structured pruning and quantization, and can lead to practical speedups of 1. 5 to 2. 4x without accuracy loss. To further showcase CAP's accuracy and scalability, we use it to show for the first time that extremely-accurate large vision models, trained via self-supervised techniques, can also be pruned to moderate sparsities, with negligible accuracy loss.

ICLR Conference 2023 Conference Paper

CrAM: A Compression-Aware Minimizer

• Alexandra Peste
• Adrian Vladu
• Eldar Kurtic
• Christoph H. Lampert
• Dan Alistarh

Deep neural networks (DNNs) often have to be compressed, via pruning and/or quantization, before they can be deployed in practical settings. In this work we propose a new compression-aware minimizer dubbed CrAM that modifies the optimization step in a principled way, in order to produce models whose local loss behavior is stable under compression operations such as pruning. Thus, dense models trained via CrAM should be compressible post-training, in a single step, without significant accuracy loss. Experimental results on standard benchmarks, such as residual networks for ImageNet classification and BERT models for language modelling, show that CrAM produces dense models that can be more accurate than the standard SGD/Adam-based baselines, but which are stable under weight pruning: specifically, we can prune models in one-shot to 70-80% sparsity with almost no accuracy loss, and to 90% with reasonable (∼ 1%) accuracy loss, which is competitive with gradual compression methods. Additionally, CrAM can produce sparse models which perform well for transfer learning, and it also works for semi-structured 2:4 pruning patterns supported by GPU hardware. The code for reproducing the results is available at: https://github.com/IST-DASLab/CrAM .

NeurIPS Conference 2023 Conference Paper

Knowledge Distillation Performs Partial Variance Reduction

• Mher Safaryan
• Alexandra Peste
• Dan Alistarh

Knowledge distillation is a popular approach for enhancing the performance of "student" models, with lower representational capacity, by taking advantage of more powerful "teacher" models. Despite its apparent simplicity, the underlying mechanics behind knowledge distillation (KD) are not yet fully understood. In this work, we shed new light on the inner workings of this method, by examining it from an optimization perspective. Specifically, we show that, in the context of linear and deep linear models, KD can be interpreted as a novel type of stochastic variance reduction mechanism. We provide a detailed convergence analysis of the resulting dynamics, which hold under standard assumptions for both strongly-convex and non-convex losses, showing that KD acts as a form of \emph{partial variance reduction}, which can reduce the stochastic gradient noise, but may not eliminate it completely, depending on the properties of the ``teacher'' model. Our analysis puts further emphasis on the need for careful parametrization of KD, in particular w. r. t. the weighting of the distillation loss, and is validated empirically on both linear models and deep neural networks.

ICLR Conference 2023 Conference Paper

OPTQ: Accurate Quantization for Generative Pre-trained Transformers

• Elias Frantar
• Saleh Ashkboos
• Torsten Hoefler
• Dan Alistarh

Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose OPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, OPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.

ICML Conference 2023 Conference Paper

Quantized Distributed Training of Large Models with Convergence Guarantees

• Ilia Markov
• Adrian Vladu
• Qi Guo
• Dan Alistarh

Communication-reduction techniques are a popular way to improve scalability in data-parallel training of deep neural networks (DNNs). The recent emergence of large language models such as GPT has created the need for new approaches to exploit data-parallelism. Among these, fully-sharded data parallel (FSDP) training is highly popular, yet it still encounters scalability bottlenecks. One reason is that applying compression techniques to FSDP is challenging: as the vast majority of the communication involves the model’s weights, direct compression alters convergence and leads to accuracy loss. We present QSDP, a variant of FSDP which supports both gradient and weight quantization with theoretical guarantees, is simple to implement and has essentially no overheads. To derive QSDP we prove that a natural modification of SGD achieves convergence even when we only maintain quantized weights, and thus the domain over which we train consists of quantized points and is, therefore, highly non-convex. We validate this approach by training GPT-family models with up to 1. 3 billion parameters on a multi-node cluster. Experiments show that QSDP preserves model accuracy, while completely removing the communication bottlenecks of FSDP, providing end-to-end speedups of up to 2. 2x.

ICML Conference 2023 Conference Paper

SparseGPT: Massive Language Models Can be Accurately Pruned in One-Shot

• Elias Frantar
• Dan Alistarh

We show for the first time that large-scale generative pretrained transformer (GPT) family models can be pruned to at least 50% sparsity in one-shot, without any retraining, at minimal loss of accuracy. This is achieved via a new pruning method called SparseGPT, specifically designed to work efficiently and accurately on massive GPT-family models. We can execute SparseGPT on the largest available open-source models, OPT-175B and BLOOM-176B, in under 4. 5 hours, and can reach 60% unstructured sparsity with negligible increase in perplexity: remarkably, more than 100 billion weights from these models can be ignored at inference time. SparseGPT generalizes to semi-structured (2: 4 and 4: 8) patterns, and is compatible with weight quantization approaches. The code is available at: https: //github. com/IST-DASLab/sparsegpt.

ICML Conference 2023 Conference Paper

SparseProp: Efficient Sparse Backpropagation for Faster Training of Neural Networks at the Edge

• Mahdi Nikdan
• Tommaso Pegolotti
• Eugenia Iofinova
• Eldar Kurtic
• Dan Alistarh

We provide an efficient implementation of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e. g. , convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

TCS Journal 2023 Journal Article

Wait-free approximate agreement on graphs

• Dan Alistarh
• Faith Ellen
• Joel Rybicki

NeurIPS Conference 2023 Conference Paper

ZipLM: Inference-Aware Structured Pruning of Language Models

• Eldar Kurtić
• Elias Frantar
• Dan Alistarh

The breakthrough performance of large language models (LLMs) comes with major computational footprints and high deployment costs. In this paper, we progress towards resolving this problem by proposing a novel structured compression approach for LLMs, called ZipLM. ZipLM achieves state-of-the-art accuracy-vs-speedup, while matching a set of desired target runtime speedups in any given inference environment. Specifically, given a model, a dataset, an inference environment, as well as a set of speedup targets, ZipLM iteratively identifies and removes components with the worst loss-runtime trade-off. Unlike prior methods that specialize in either the post-training/one-shot or the gradual compression setting, and only for specific families of models such as BERT ( encoder ) or GPT ( decoder ), ZipLM produces state-of-the-art compressed models across all these settings. Furthermore, ZipLM achieves superior results for a fraction of the computational cost relative to prior distillation and pruning techniques, making it a cost-effective approach for generating an entire family of smaller, faster, and highly accurate models, guaranteed to meet the desired inference specifications. In particular, ZipLM outperforms all prior BERT-base distillation and pruning techniques, such as CoFi, MiniLM, and TinyBERT. Moreover, it matches the performance of the heavily optimized MobileBERT model, obtained via extensive architecture search, by simply pruning the baseline BERT-large model. When compressing GPT2, ZipLM outperforms DistilGPT2 while being 60\% smaller and 30\% faster. Our code is available at: https: //github. com/IST-DASLab/ZipLM.

NeurIPS Conference 2022 Conference Paper

Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning

• Elias Frantar
• Dan Alistarh

We consider the problem of model compression for deep neural networks (DNNs) in the challenging one-shot/post-training setting, in which we are given an accurate trained model, and must compress it without any retraining, based only on a small amount of calibration input data. This problem has become popular in view of the emerging software and hardware support for executing models compressed via pruning and/or quantization with speedup, and well-performing solutions have been proposed independently for both compression approaches. In this paper, we introduce a new compression framework which covers both weight pruning and quantization in a unified setting, is time- and space-efficient, and considerably improves upon the practical performance of existing post-training methods. At the technical level, our approach is based on an exact and efficient realization of the classical Optimal Brain Surgeon (OBS) framework of [LeCun, Denker, and Solla, 1990] extended to also cover weight quantization at the scale of modern DNNs. From the practical perspective, our experimental results show that it can improve significantly upon the compression-accuracy trade-offs of existing post-training methods, and that it can enable the accurate compound application of both pruning and quantization in a post-training setting.

ICML Conference 2022 Conference Paper

SPDY: Accurate Pruning with Speedup Guarantees

• Elias Frantar
• Dan Alistarh

The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular. At the same time, there is rapidly-growing computational support for efficiently executing the unstructured-sparse models obtained via pruning. Yet, most existing pruning methods minimize just the number of remaining weights, i. e. the size of the model, rather than optimizing for inference time. We address this gap by introducing SPDY, a new compression method which automatically determines layer-wise sparsity targets achieving a desired inference speedup on a given system, while minimizing accuracy loss. SPDY is the composition of two new techniques. The first is an efficient and general dynamic programming algorithm for solving constrained layer-wise compression problems, given a set of layer-wise error scores. The second technique is a local search procedure for automatically determining such scores in an accurate and robust manner. Experiments across popular vision and language models show that SPDY guarantees speedups while recovering higher accuracy relative to existing strategies, both for one-shot and gradual pruning scenarios, and is compatible with most existing pruning approaches. We also extend our approach to the recently-proposed task of pruning with very little data, where we achieve the best known accuracy recovery when pruning to the GPU-supported 2: 4 sparsity pattern.

NeurIPS Conference 2021 Conference Paper

AC/DC: Alternating Compressed/DeCompressed Training of Deep Neural Networks

• Alexandra Peste
• Eugenia Iofinova
• Adrian Vladu
• Dan Alistarh

The increasing computational requirements of deep neural networks (DNNs) have led to significant interest in obtaining DNN models that are sparse, yet accurate. Recent work has investigated the even harder case of sparse training, where the DNN weights are, for as much as possible, already sparse to reduce computational costs during training. Existing sparse training methods are often empirical and can have lower accuracy relative to the dense baseline. In this paper, we present a general approach called Alternating Compressed/DeCompressed (AC/DC) training of DNNs, demonstrate convergence for a variant of the algorithm, and show that AC/DC outperforms existing sparse training methods in accuracy at similar computational budgets; at high sparsity levels, AC/DC even outperforms existing methods that rely on accurate pre-trained dense models. An important property of AC/DC is that it allows co-training of dense and sparse models, yielding accurate sparse-dense model pairs at the end of the training process. This is useful in practice, where compressed variants may be desirable for deployment in resource-constrained settings without re-doing the entire training flow, and also provides us with insights into the accuracy gap between dense and compressed models.

NeurIPS Conference 2021 Conference Paper

Asynchronous Decentralized SGD with Quantized and Local Updates

• Giorgi Nadiradze
• Amirmojtaba Sabour
• Peter Davies
• Shigang Li
• Dan Alistarh

Decentralized optimization is emerging as a viable alternative for scalable distributed machine learning, but also introduces new challenges in terms of synchronization costs. To this end, several communication-reduction techniques, such as non-blocking communication, quantization, and local steps, have been explored in the decentralized setting. Due to the complexity of analyzing optimization in such a relaxed setting, this line of work often assumes \emph{global} communication rounds, which require additional synchronization. In this paper, we consider decentralized optimization in the simpler, but harder to analyze, \emph{asynchronous gossip} model, in which communication occurs in discrete, randomly chosen pairings among nodes. Perhaps surprisingly, we show that a variant of SGD called \emph{SwarmSGD} still converges in this setting, even if \emph{non-blocking communication}, \emph{quantization}, and \emph{local steps} are all applied \emph{in conjunction}, and even if the node data distributions and underlying graph topology are both \emph{heterogenous}. Our analysis is based on a new connection with multi-dimensional load-balancing processes. We implement this algorithm and deploy it in a super-computing environment, showing that it can outperform previous decentralized methods in terms of end-to-end training time, and that it can even rival carefully-tuned large-batch SGD for certain tasks.

AAAI Conference 2021 Conference Paper

Asynchronous Optimization Methods for Efficient Training of Deep Neural Networks with Guarantees

• Vyacheslav Kungurtsev
• Malcolm Egan
• Bapi Chatterjee
• Dan Alistarh

Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees exist beyond cases where closed-form proximal operator solutions are available. As training most popular deep neural networks corresponds to optimizing nonsmooth and nonconvex objectives, there is a pressing need for such convergence guarantees. In this paper, we analyze for the first time the convergence of stochastic asynchronous optimization for this general class of objectives. In particular, we focus on stochastic subgradient methods allowing for block variable partitioning, where the shared model is asynchronously updated by concurrent processes. To this end, we use a probabilistic model which captures key features of real asynchronous scheduling between concurrent processes. Under this model, we establish convergence with probability one to an invariant set for stochastic subgradient methods with momentum. From a practical perspective, one issue with the family of algorithms that we consider is that they are not efficiently supported by machine learning frameworks, which mostly focus on distributed data-parallel strategies. To address this, we propose a new implementation strategy for shared-memory based training of deep neural networks for a partitioned but shared model in single- and multi-GPU settings. Based on this implementation, we achieve on average about 1. 2x speedup in comparison to state-of-the-art training methods for popular image classification tasks, without compromising accuracy.

ICLR Conference 2021 Conference Paper

Byzantine-Resilient Non-Convex Stochastic Gradient Descent

• Zeyuan Allen-Zhu
• Faeze Ebrahimianghazani
• Jerry Li 0001
• Dan Alistarh

We study adversary-resilient stochastic distributed optimization, in which $m$ machines can independently compute stochastic gradients, and cooperate to jointly optimize over their local objective functions. However, an $\alpha$-fraction of the machines are Byzantine, in that they may behave in arbitrary, adversarial ways. We consider a variant of this procedure in the challenging non-convex case. Our main result is a new algorithm SafeguardSGD, which can provably escape saddle points and find approximate local minima of the non-convex objective. The algorithm is based on a new concentration filtering technique, and its sample and time complexity bounds match the best known theoretical bounds in the stochastic, distributed setting when no Byzantine machines are present. Our algorithm is very practical: it improves upon the performance of all prior methods when training deep neural networks, it is relatively lightweight, and it is the first method to withstand two recently-proposed Byzantine attacks.

ICML Conference 2021 Conference Paper

Communication-Efficient Distributed Optimization with Quantized Preconditioners

• Foivos Alimisis
• Peter Davies-Peck
• Dan Alistarh

We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of bits. Most previous communication-efficient approaches for this problem are limited to first-order optimization, and therefore have \emph{linear} dependence on the condition number in their communication complexity. We show that this dependence is not inherent: communication-efficient methods can in fact have sublinear dependence on the condition number. For this, we design and analyze the first communication-efficient distributed variants of preconditioned gradient descent for Generalized Linear Models, and for Newton’s method. Our results rely on a new technique for quantizing both the preconditioner and the descent direction at each step of the algorithms, while controlling their convergence rate. We also validate our findings experimentally, showing faster convergence and reduced communication relative to previous methods.

NeurIPS Conference 2021 Conference Paper

Distributed Principal Component Analysis with Limited Communication

• Foivos Alimisis
• Peter Davies
• Bart Vandereycken
• Dan Alistarh

We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a new quantized variant of Riemannian gradient descent to solve this problem, and prove that the algorithm converges with high probability under a set of necessary spherical-convexity properties. We give bounds on the number of bits transmitted by the algorithm under common initialization schemes, and investigate the dependency on the problem dimension in each case.

AAAI Conference 2021 Conference Paper

Elastic Consistency: A Practical Consistency Model for Distributed Stochastic Gradient Descent

• Giorgi Nadiradze
• Ilia Markov
• Bapi Chatterjee
• Vyacheslav Kungurtsev
• Dan Alistarh

One key element behind the progress of machine learning in recent years has been the ability to train machine learning models in large-scale distributed shared-memory and messagepassing environments. Most of these models are trained employing variants of stochastic gradient descent (SGD) based optimization. In this paper, we introduce a general consistency condition covering communication-reduced and asynchronous distributed SGD implementations. Our framework, called elastic consistency, decouples the system-specific aspects of the implementation from the SGD convergence requirements, giving a general way to obtain convergence bounds for a wide variety of distributed SGD methods used in practice. Elastic consistency can be used to re-derive or improve several previous convergence bounds in message-passing and sharedmemory settings, but also to analyze new models and distribution schemes. In particular, we propose and analyze a new synchronization-avoiding scheme for distributed SGD, and show that it can be used to efficiently train deep convolutional models for image classification.

NeurIPS Conference 2021 Conference Paper

M-FAC: Efficient Matrix-Free Approximations of Second-Order Information

• Elias Frantar
• Eldar Kurtic
• Dan Alistarh

Efficiently approximating local curvature information of the loss function is a useful tool for the optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or storage costs, limiting their practicality. In this work, we investigate matrix-free approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices, as in the classic approximation of the Hessian by the empirical Fisher matrix. The first algorithm we propose is tailored towards network compression and can compute the IHVP for dimension $d$ given a fixed set of $m$ rank-one matrices using $O(dm^2)$ precomputation, $O(dm)$ cost for computing the IHVP and query cost $O(m)$ for computing any single element of the inverse Hessian approximation. The second algorithm targets an optimization setting, where we wish to compute the product between the inverse Hessian, estimated over a sliding window of optimization steps, and a given gradient direction. We give an algorithm with cost $O(dm + m^2)$ for computing the IHVP and $O(dm + m^3)$ for adding or removing any gradient from the sliding window. We show that both algorithms yield competitive results for network pruning and optimization, respectively, with significantly lower computational overhead relative to existing second-order methods.

ICLR Conference 2021 Conference Paper

New Bounds For Distributed Mean Estimation and Variance Reduction

• Peter Davies-Peck
• Vijaykrishna Gurunanthan
• Niusha Moshrefi
• Saleh Ashkboos
• Dan Alistarh

We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $\mathbf x_v \in \mathbb R^d$, and must cooperate to estimate the mean of their inputs $\mathbf \mu = \frac 1n\sum_{v = 1}^n \mathbf x_v$, while minimizing total communication cost. DME is a fundamental construct in distributed machine learning, and there has been considerable work on variants of this problem, especially in the context of distributed variance reduction for stochastic gradients in parallel SGD. Previous work typically assumes an upper bound on the norm of the input vectors, and achieves an error bound in terms of this norm. However, in many real applications, the input vectors are concentrated around the correct output $\mathbf \mu$, but $\mathbf \mu$ itself has large norm. In such cases, previous output error bounds perform poorly. In this paper, we show that output error bounds need not depend on input norm. We provide a method of quantization which allows distributed mean estimation to be performed with solution quality dependent only on the distance between inputs, not on input norm, and show an analogous result for distributed variance reduction. The technique is based on a new connection with lattice theory. We also provide lower bounds showing that the communication to error trade-off of our algorithms is asymptotically optimal. As the lattices achieving optimal bounds under $\ell_2$-norm can be computationally impractical, we also present an extension which leverages easy-to-use cubic lattices, and is loose only up to a logarithmic factor in $d$. We show experimentally that our method yields practical improvements for common applications, relative to prior approaches.

JMLR Journal 2021 Journal Article

NUQSGD: Provably Communication-efficient Data-parallel SGD via Nonuniform Quantization

• Ali Ramezani-Kebrya
• Fartash Faghri
• Ilya Markov
• Vitalii Aksenov
• Dan Alistarh
• Daniel M. Roy

As the size and complexity of models and datasets grow, so does the need for communication-efficient variants of stochastic gradient descent that can be deployed to perform parallel model training. One popular communication-compression method for data-parallel SGD is QSGD (Alistarh et al., 2017), which quantizes and encodes gradients to reduce communication costs. The baseline variant of QSGD provides strong theoretical guarantees, however, for practical purposes, the authors proposed a heuristic variant which we call QSGDinf, which demonstrated impressive empirical gains for distributed training of large neural networks. In this paper, we build on this work to propose a new gradient quantization scheme, and show that it has both stronger theoretical guarantees than QSGD, and matches and exceeds the empirical performance of the QSGDinf heuristic and of other compression methods. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

JMLR Journal 2021 Journal Article

Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks

• Torsten Hoefler
• Dan Alistarh
• Tal Ben-Nun
• Nikoli Dryden
• Alexandra Peste

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, sometimes even better than, the original dense networks. Sparsity promises to reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

NeurIPS Conference 2021 Conference Paper

Towards Tight Communication Lower Bounds for Distributed Optimisation

• Janne H. Korhonen
• Dan Alistarh

We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in large-scale distributed optimisation, where a standard solution is to apply variants of (stochastic) gradient descent. We focus on the communication complexity of this problem: our main result provides the first fully unconditional bounds on total number of bits which need to be sent and received by the $N$ machines to solve this problem under point-to-point communication, within a given error-tolerance. Specifically, we show that $\Omega( Nd \log d / N\varepsilon)$ total bits need to be communicated between the machines to find an additive $\epsilon$-approximation to the minimum of $\sum_{i = 1}^N f_i (x)$. The result holds for both deterministic and randomised algorithms, and, importantly, requires no assumptions on the algorithm structure. The lower bound is tight under certain restrictions on parameter values, and is matched within constant factors for quadratic objectives by a new variant of quantised gradient descent, which we describe and analyse. Our results bring over tools from communication complexity to distributed optimisation, which has potential for further applications.

NeurIPS Conference 2020 Conference Paper

Adaptive Gradient Quantization for Data-Parallel SGD

• Fartash Faghri
• Iman Tabrizian
• Ilia Markov
• Dan Alistarh
• Daniel M. Roy
• Ali Ramezani-Kebrya

Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training. We empirically observe that the statistics of gradients of deep models change during the training. Motivated by this observation, we introduce two adaptive quantization schemes, ALQ and AMQ. In both schemes, processors update their compression schemes in parallel by efficiently computing sufficient statistics of a parametric distribution. We improve the validation accuracy by almost 2% on CIFAR-10 and 1% on ImageNet in challenging low-cost communication setups. Our adaptive methods are also significantly more robust to the choice of hyperparameters.

ICML Conference 2020 Conference Paper

Inducing and Exploiting Activation Sparsity for Fast Inference on Deep Neural Networks

• Mark Kurtz
• Justin Kopinsky
• Rati Gelashvili
• Alexander Matveev
• John Carr
• Michael Goin
• William M. Leiserson
• Sage Moore

Optimizing convolutional neural networks for fast inference has recently become an extremely active area of research. One of the go-to solutions in this context is weight pruning, which aims to reduce computational and memory footprint by removing large subsets of the connections in a neural network. Surprisingly, much less attention has been given to exploiting sparsity in the activation maps, which tend to be naturally sparse in many settings thanks to the structure of rectified linear (ReLU) activation functions. In this paper, we present an in-depth analysis of methods for maximizing the sparsity of the activations in a trained neural network, and show that, when coupled with an efficient sparse-input convolution algorithm, we can leverage this sparsity for significant performance gains. To induce highly sparse activation maps without accuracy loss, we introduce a new regularization technique, coupled with a new threshold-based sparsification method based on a parameterized activation function called Forced-Activation-Threshold Rectified Linear Unit (FATReLU). We examine the impact of our methods on popular image classification models, showing that most architectures can adapt to significantly sparser activation maps without any accuracy loss. Our second contribution is showing that these these compression gains can be translated into inference speedups: we provide a new algorithm to enable fast convolution operations over networks with sparse activations, and show that it can enable significant speedups for end-to-end inference on a range of popular models on the large-scale ImageNet image classification task on modern Intel CPUs, with little or no retraining cost.

ICML Conference 2020 Conference Paper

On the Sample Complexity of Adversarial Multi-Source PAC Learning

• Nikola Konstantinov
• Elias Frantar
• Dan Alistarh
• Christoph H. Lampert

We study the problem of learning from multiple untrusted data sources, a scenario of increasing practical relevance given the recent emergence of crowdsourcing and collaborative learning paradigms. Specifically, we analyze the situation in which a learning system obtains datasets from multiple sources, some of which might be biased or even adversarially perturbed. It is known that in the single-source case, an adversary with the power to corrupt a fixed fraction of the training data can prevent PAC-learnability, that is, even in the limit of infinitely much training data, no learning system can approach the optimal test error. In this work we show that, surprisingly, the same is not true in the multi-source setting, where the adversary can arbitrarily corrupt a fixed fraction of the data sources. Our main results are a generalization bound that provides finite-sample guarantees for this learning setting, as well as corresponding lower bounds. Besides establishing PAC-learnability our results also show that in a cooperative learning setting sharing data with other parties has provable benefits, even if some participants are malicious.

NeurIPS Conference 2020 Conference Paper

Scalable Belief Propagation via Relaxed Scheduling

• Vitalii Aksenov
• Dan Alistarh
• Janne H. Korhonen

The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of knowledge on parallelization, some classic machine learning algorithms often prove hard to parallelize efficiently while maintaining convergence. In this paper, we focus on efficient parallel algorithms for the key machine learning task of inference on graphical models, in particular on the fundamental belief propagation algorithm. We address the challenge of efficiently parallelizing this classic paradigm by showing how to leverage scalable relaxed schedulers, which reduce parallelization overheads, in this context. We investigate the overheads of relaxation analytically, and present an extensive empirical study, showing that our approach outperforms previous parallel belief propagation implementations both in terms of scalability and in terms of wall-clock convergence time, on a range of practical applications.

NeurIPS Conference 2020 Conference Paper

WoodFisher: Efficient Second-Order Approximation for Neural Network Compression

• Sidak Pal Singh
• Dan Alistarh

Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work considers this question, examines the accuracy of existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for one-shot pruning. Further, even when iterative, gradual pruning is allowed, our method results in a gain in test accuracy over the state-of-the-art approaches for popular image classification datasets such as ImageNet ILSVRC. Further, we show how our method can be extended to take into account first-order information, and illustrate its ability to automatically set layer-wise pruning thresholds, or perform compression in the limited-data regime.

ICML Conference 2019 Conference Paper

Distributed Learning over Unreliable Networks

• Chen Yu 0009
• Hanlin Tang
• Cédric Renggli
• Simon Kassing
• Ankit Singla
• Dan Alistarh
• Ce Zhang 0001
• Ji Liu 0002

Most of today’s distributed machine learning systems assume reliable networks: whenever two machines exchange information (e. g. , gradients or models), the network should guarantee the delivery of the message. At the same time, recent work exhibits the impressive tolerance of machine learning algorithms to errors or noise arising from relaxed communication or synchronization. In this paper, we connect these two trends, and consider the following question: Can we design machine learning systems that are tolerant to network unreliability during training? With this motivation, we focus on a theoretical problem of independent interest—given a standard distributed parameter server architecture, if every communication between the worker and the server has a non-zero probability $p$ of being dropped, does there exist an algorithm that still converges, and at what speed? In the context of prior art, this problem can be phrased as distributed learning over random topologies. The technical contribution of this paper is a novel theoretical analysis proving that distributed learning over random topologies can achieve comparable convergence rate to centralized or distributed learning over reliable networks. Further, we prove that the influence of the packet drop rate diminishes with the growth of the number of parameter servers. We map this theoretical result onto a real-world scenario, training deep neural networks over an unreliable network layer, and conduct network simulation to validate the system improvement by allowing the networks to be unreliable.

NeurIPS Conference 2019 Conference Paper

Powerset Convolutional Neural Networks

• Chris Wendler
• Markus Püschel
• Dan Alistarh

We present a novel class of convolutional neural networks (CNNs) for set functions, i. e. , data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.

STOC Conference 2019 Conference Paper

Why extension-based proofs fail

• Dan Alistarh
• James Aspnes
• Faith Ellen
• Rati Gelashvili
• Leqi Zhu

It is impossible to deterministically solve wait-free consensus in an asynchronous system. The classic proof uses a valency argument, which constructs an infinite execution by repeatedly extending a finite execution. We introduce extension-based proofs , a class of impossibility proofs that are modelled as an interaction between a prover and a protocol and that include valency arguments. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k -set agreement among n > k ≥ 2 processes in a wait-free manner. However, it was unknown whether proofs based on simpler techniques were possible. We show that this impossibility result cannot be obtained by an extension-based proof and, hence, extension-based proofs are limited in power.

NeurIPS Conference 2018 Conference Paper

Byzantine Stochastic Gradient Descent

• Dan Alistarh
• Zeyuan Allen-Zhu
• Jerry Li

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of $m$ machines which allegedly compute stochastic gradients every iteration, an $\alpha$-fraction are Byzantine, and may behave adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\varepsilon$-approximate minimizers of convex functions in $T = \tilde{O}\big( \frac{1}{\varepsilon^2 m} + \frac{\alpha^2}{\varepsilon^2} \big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\big( \frac{1}{\varepsilon^2 m} \big)$ iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sample complexity and time complexity.

SODA Conference 2018 Conference Paper

Space-Optimal Majority in Population Protocols

• Dan Alistarh
• James Aspnes
• Rati Gelashvili

Population protocols are a popular model of distributed computing, in which n agents with limited local state interact randomly, and cooperate to collectively compute global predicates. Inspired by recent developments in DNA programming, an extensive series of papers, across different communities, has examined the computability and complexity characteristics of this model. Majority, or consensus, is a central task in this model, in which agents need to collectively reach a decision as to which one of two states A or B had a higher initial count. Two metrics are important: the time that a protocol requires to stabilize to an output decision, and the state space size that each agent requires to do so. It is known that majority requires Ω(log log n ) states per agent to allow for fast (poly-logarithmic time) stabilization, and that O (log 2 n ) states are sufficient. Thus, there is an exponential gap between the space upper and lower bounds for this problem. This paper addresses this question. On the negative side, we provide a new lower bound of Ω(log n ) states for any protocol which stabilizes in O ( n 1– c ) expected time, for any constant c > 0. This result is conditional on monotonicity and output assumptions, satisfied by all known protocols. Technically, it represents a departure from previous lower bounds, in that it does not rely on the existence of dense configurations. Instead, we introduce a new generalized surgery technique to prove the existence of incorrect executions for any algorithm which would contradict the lower bound. Subsequently, our lower bound also applies to general initial configurations, including ones with a leader. On the positive side, we give a new algorithm for majority which uses O (log n ) states, and stabilizes in O (log 2 n ) expected time. Central to the algorithm is a new leaderless phase clock technique, which allows agents to synchronize in phases of Θ( n log n ) consecutive interactions using O (log n ) states per agent, exploiting a new connection between population protocols and power-of-two-choices load balancing mechanisms. We also employ our phase clock to build a leader election algorithm with a state space of size O (log n ), which stabilizes in O (log 2 n ) expected time.

NeurIPS Conference 2018 Conference Paper

The Convergence of Sparsified Gradient Methods

• Dan Alistarh
• Torsten Hoefler
• Mikael Johansson
• Nikola Konstantinov
• Sarit Khirirat
• Cedric Renggli

Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed. To date, gradient sparsification methods--where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally--are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to \emph{three orders of magnitude}, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.

NeurIPS Conference 2017 Conference Paper

QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding

• Dan Alistarh
• Demjan Grubic
• Jerry Li
• Ryota Tomioka
• Milan Vojnovic

Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to its excellent scalability properties. A fundamental barrier when parallelizing SGD is the high bandwidth cost of communicating gradient updates between nodes; consequently, several lossy compresion heuristics have been proposed, by which nodes only communicate quantized gradients. Although effective in practice, these heuristics do not always guarantee convergence, and it is not clear whether they can be improved. In this paper, we propose Quantized SGD (QSGD), a family of compression schemes for gradient updates which provides convergence guarantees. QSGD allows the user to smoothly trade off \emph{communication bandwidth} and \emph{convergence time}: nodes can adjust the number of bits sent per iteration, at the cost of possibly higher variance. We show that this trade-off is inherent, in the sense that improving it past some threshold would violate information-theoretic lower bounds. QSGD guarantees convergence for convex and non-convex objectives, under asynchrony, and can be extended to stochastic variance-reduced techniques. When applied to training deep neural networks for image classification and automated speech recognition, QSGD leads to significant reductions in end-to-end training time. For example, on 16GPUs, we can train the ResNet152 network to full accuracy on ImageNet 1. 8x faster than the full-precision variant.

SODA Conference 2017 Conference Paper

Time-Space Trade-offs in Population Protocols

• Dan Alistarh
• James Aspnes
• David Eisenstat
• Rati Gelashvili
• Ronald L. Rivest

Population protocols are a popular model of distributed computing, in which randomly-interacting agents with little computational power cooperate to jointly perform computational tasks. Inspired by developments in molecular computation, and in particular DNA computing, recent algorithmic work has focused on the complexity of solving simple yet fundamental tasks in the population model, such as leader election (which requires convergence to a single agent in a special “leader” state), and majority (in which agents must converge to a decision as to which of two possible initial states had higher initial count). Known results point towards an inherent trade-off between the time complexity of such algorithms, and the space complexity, i. e. size of the memory available to each agent. In this paper, we explore this trade-off and provide new upper and lower bounds for majority and leader election. First, we prove a unified lower bound, which relates the space available per node with the time complexity achievable by a protocol: for instance, our result implies that any protocol solving either of these tasks for n agents using O (log log n ) states must take Ω( n /polylog n ) expected time. This is the first result to characterize time complexity for protocols which employ super-constant number of states per node, and proves that fast, poly-logarithmic running times require protocols to have relatively large space costs. On the positive side, we give algorithms showing that fast, poly-logarithmic convergence time can be achieved using O (log 2 n ) space per node, in the case of both tasks. Overall, our results highlight a time complexity separation between O (log log n ) and Θ(log 2 n ) state space size for both majority and leader election in population protocols, and introduce new techniques, which should be applicable more broadly.

ICML Conference 2017 Conference Paper

ZipML: Training Linear Models with End-to-End Low Precision, and a Little Bit of Deep Learning

• Hantian Zhang
• Jerry Li 0001
• Kaan Kara
• Dan Alistarh
• Ji Liu 0002
• Ce Zhang 0001

Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train models at end-to-end low precision with provable guarantees? Can this lead to consistent order-of-magnitude speedups? We mainly focus on linear models, and the answer is yes for linear models. We develop a simple framework called ZipML based on one simple but novel strategy called double sampling. Our ZipML framework is able to execute training at low precision with no bias, guaranteeing convergence, whereas naive quantization would introduce significant bias. We validate our framework across a range of applications, and show that it enables an FPGA prototype that is up to $6. 5\times$ faster than an implementation using full 32-bit precision. We further develop a variance-optimal stochastic quantization strategy and show that it can make a significant difference in a variety of settings. When applied to linear models together with double sampling, we save up to another $1. 7\times$ in data movement compared with uniform quantization. When training deep networks with quantized models, we achieve higher accuracy than the state-of-the-art XNOR-Net.

NeurIPS Conference 2015 Conference Paper

Streaming Min-max Hypergraph Partitioning

• Dan Alistarh
• Jennifer Iglesias
• Milan Vojnovic

In many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges. Equivalently, we are given an input bipartite graph with two types of vertices: items, and associations (which we refer to as topics). We consider the problem of partitioning the set of items into a given number of parts such that the maximum number of topics covered by a part of the partition is minimized. This is a natural clustering problem, with various applications, e. g. partitioning of a set of information objects such as documents, images, and videos, and load balancing in the context of computation platforms. In this paper, we focus on the streaming computation model for this problem, in which items arrive online one at a time and each item must be assigned irrevocably to a part of the partition at its arrival time. Motivated by scalability requirements, we focus on the class of streaming computation algorithms with memory limited to be at most linear in the number of the parts of the partition. We show that a greedy assignment strategy is able to recover a hidden co-clustering of items under a natural set of recovery conditions. We also report results of an extensive empirical evaluation, which demonstrate that this greedy strategy yields superior performance when compared with alternative approaches.

STOC Conference 2014 Conference Paper

Are lock-free concurrent algorithms practically wait-free?

• Dan Alistarh
• Keren Censor-Hillel
• Nir Shavit

Lock-free concurrent algorithms guarantee that some concurrent operation will always make progress in a finite number of steps. Yet programmers prefer to treat concurrent code as if it were wait-free , guaranteeing that all operations always make progress. Unfortunately, designing wait-free algorithms is generally a very complex task, and the resulting algorithms are not always efficient. While obtaining efficient wait-free algorithms has been a long-time goal for the theory community, most non-blocking commercial code is only lock-free. This paper suggests a simple solution to this problem. We show that, for a large class of lock-free algorithms, under scheduling conditions which approximate those found in commercial hardware architectures, lock-free algorithms behave as if they are wait-free. In other words, programmers can keep on designing simple lock-free algorithms instead of complex wait-free ones, and in practice, they will get wait-free progress. Our main contribution is a new way of analyzing a general class of lock-free algorithms under a stochastic scheduler . Our analysis relates the individual performance of processes with the global performance of the system using Markov chain lifting between a complex per-process chain and a simpler system progress chain. We show that lock-free algorithms are not only wait-free with probability 1, but that in fact a general subset of lock-free algorithms can be closely bounded in terms of the average number of steps required until an operation completes. To the best of our knowledge, this is the first attempt to analyze progress conditions, typically stated in relation to a worst case adversary, in a stochastic model capturing their expected asymptotic behavior.

SODA Conference 2014 Conference Paper

Dynamic Task Allocation in Asynchronous Shared Memory

• Dan Alistarh
• James Aspnes
• Michael A. Bender
• Rati Gelashvili
• Seth Gilbert

Task allocation is a classic distributed problem in which a set of p potentially faulty processes must cooperate to perform a set of tasks. This paper considers a new dynamic version of the problem, in which tasks are injected adversarially during an asynchronous execution. We give the first asynchronous shared-memory algorithm for dynamic task allocation, and we prove that our solution is optimal within logarithmic factors. The main algorithmic idea is a randomized concurrent data structure called a dynamic to-do tree, which allows processes to pick new tasks to perform at random from the set of available tasks, and to insert tasks at random empty locations in the data structure. Our analysis shows that these properties avoid duplicating work unnecessarily. On the other hand, since the adversary controls the input as well the scheduling, it can induce executions where lots of processes contend for a few available tasks, which is inefficient. However, we prove that every algorithm has the same problem: given an arbitrary input, if OPT is the worst-case complexity of the optimal algorithm on that input, then the expected work complexity of our algorithm on the same input is O ( OPT log 3 m ), where m is an upper bound on the number of tasks that are present in the system at any given time.

FOCS Conference 2012 Conference Paper

How to Allocate Tasks Asynchronously

• Dan Alistarh
• Michael A. Bender
• Seth Gilbert
• Rachid Guerraoui

Asynchronous task allocation is a fundamental problem in distributed computing in which p asynchronous processes must execute a set of m tasks. Also known as write-all or do-all, this problem been studied extensively, both independently and as a key building block for various distributed algorithms. In this paper, we break new ground on this classic problem: we introduce the To-Do Tree concurrent data structure, which improves on the best known randomized and deterministic upper bounds. In the presence of an adaptive adversary, the randomized To-Do Tree algorithm has O(m+plogplog2m) work complexity. We then show that there exists a deterministic variant of the To-Do Tree algorithm with work complexity O(m+p log5 m log2 max(m, p)). For all values of m and p, our algorithms are within log factors of the O(m + p log p) lower bound for this problem. The key technical ingredient in our results is a new approach for analyzing concurrent executions against a strong adaptive scheduler. This technique allows us to handle the complex dependencies between the processes' coin flips and their scheduling, and to tightly bound the work needed to perform subsets of the tasks.

FOCS Conference 2011 Conference Paper

The Complexity of Renaming

• Dan Alistarh
• James Aspnes
• Seth Gilbert
• Rachid Guerraoui

We study the complexity of renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct names from a given namespace. We prove an individual lower bound of \Omega( k ) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. This bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic fetch-and-increment registers, queues and stacks. The proof of the bound is interesting in its own right, for it relies on the first reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement our individual bound with a global lower bound of \Omega( k \log ( k / c ) ) on the total step complexity of renaming into a namespace of size ck, for any c \geq 1. This applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter and fetch-and-increment implementations, all tight within logarithmic factors.