Michael Mahoney

Xiaoxuan Liu, Lianmin Zheng, Dequan Wang et al. · berkeley, tsinghua

Training large neural network (NN) models requires extensive memory resources, and Activation Compressed Training (ACT) is a promising approach to reduce training memory footprint. This paper presents GACT, an ACT framework to support a broad range of machine learning tasks for generic NN architectures with limited domain knowledge. By analyzing a linearized version of ACT's approximate gradient, we prove the convergence of GACT without prior knowledge on operator type or model architecture. To make training stable, we propose an algorithm that decides the compression ratio for each tensor by estimating its impact on the gradient at run time. We implement GACT as a PyTorch library that readily applies to any NN architecture. GACT reduces the activation memory for convolutional NNs, transformers, and graph NNs by up to 8.1x, enabling training with a 4.2x to 24.7x larger batch size, with negligible accuracy loss. We implement GACT as a PyTorch library at https://github.com/LiuXiaoxuanPKU/GACT-ICML.

Shashank Subramanian, Peter Harrington, Kurt Keutzer et al.

Pre-trained machine learning (ML) models have shown great performance for a wide range of applications, in particular in natural language processing (NLP) and computer vision (CV). Here, we study how pre-training could be used for scientific machine learning (SciML) applications, specifically in the context of transfer learning. We study the transfer behavior of these models as (i) the pre-trained model size is scaled, (ii) the downstream training dataset size is scaled, (iii) the physics parameters are systematically pushed out of distribution, and (iv) how a single model pre-trained on a mixture of different physics problems can be adapted to various downstream applications. We find that-when fine-tuned appropriately-transfer learning can help reach desired accuracy levels with orders of magnitude fewer downstream examples (across different tasks that can even be out-of-distribution) than training from scratch, with consistent behavior across a wide range of downstream examples. We also find that fine-tuning these models yields more performance gains as model size increases, compared to training from scratch on new downstream tasks. These results hold for a broad range of PDE learning tasks. All in all, our results demonstrate the potential of the "pre-train and fine-tune" paradigm for SciML problems, demonstrating a path towards building SciML foundation models. We open-source our code for reproducibility.

Haocheng Xi, Harman Singh, Yuezhou Hu et al. · berkeley

Block-wise diffusion language models (DLMs) generate multiple tokens in any order, offering a promising alternative to the autoregressive decoding pipeline. However, they still remain bottlenecked by memory-bound attention in long-context scenarios. Naive sparse attention fails on DLMs due to a KV Inflation problem, where different queries select different prefix positions, making the union of accessed KV pages large. To address this, we observe that between consecutive denoising steps, only a small fraction of active tokens exhibit significant hidden-state changes, while the majority of stable tokens remain nearly constant. Based on this insight, we propose LOSA (Locality-aware Sparse Attention), which reuses cached prefix-attention results for stable tokens and applies sparse attention only to active tokens. This substantially shrinks the number of KV indices that must be loaded, yielding both higher speedup and higher accuracy. Across multiple block-wise DLMs and benchmarks, LOSA preserves near-dense accuracy while significantly improving efficiency, achieving up to +9 points in average accuracy at aggressive sparsity levels while maintaining 1.54x lower attention density. It also achieves up to 4.14x attention speedup on RTX A6000 GPUs, demonstrating the effectiveness of the proposed method.

Di Wang, Michael Mahoney, Nishanth Mohan et al.

We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $ε$-approximate packing and covering solvers which run in $\tilde{O}(1/ε^2)$ expected time, i.e., in expectation they take $\tilde{O}(1/ε^2)$ iterations and they do $\tilde{O}(N/ε^2)$ total work, where $N$ is the size of the constraint matrix and $ε$ is the error parameter, and where the $\tilde{O}$ hides logarithmic factors. To achieve our improvement, we introduce an algorithmic technique of broader interest: dynamically-bucketed selective coordinate descent (DB-SCD). At each step of the iterative optimization algorithm, the DB-SCD method dynamically buckets the coordinates of the gradient into those of roughly equal magnitude, and it updates all the coordinates in one of the buckets. This dynamically-bucketed updating permits us to take steps along several coordinates with similar-sized gradients, thereby permitting more appropriate step sizes at each step of the algorithm. In particular, this technique allows us to use in a straightforward manner the recent analysis from the breakthrough results of Allen-Zhu and Orecchia [2] to achieve our still-further improved bounds. More generally, this method addresses "interference" among coordinates, by which we mean the impact of the update of one coordinate on the gradients of other coordinates. Such interference is a core issue in parallelizing optimization routines that rely on smoothness properties. Since our DB-SCD method reduces interference via updating a selective subset of variables at each iteration, we expect it may also have more general applicability in optimization.

Kristopher W. Reese, Taylor Kulp-McDowall, Michael Majurski et al.

The Intelligence Advanced Research Projects Activity (IARPA) launched the TrojAI program to confront an emerging vulnerability in modern artificial intelligence: the threat of AI Trojans. These AI trojans are malicious, hidden backdoors intentionally embedded within an AI model that can cause a system to fail in unexpected ways, or allow a malicious actor to hijack the AI model at will. This multi-year initiative helped to map out the complex nature of the threat, pioneered foundational detection methods, and identified unsolved challenges that require ongoing attention by the burgeoning AI security field. This report synthesizes the program's key findings, including methodologies for detection through weight analysis and trigger inversion, as well as approaches for mitigating Trojan risks in deployed models. Comprehensive test and evaluation results highlight detector performance, sensitivity, and the prevalence of "natural" Trojans. The report concludes with lessons learned and recommendations for advancing AI security research.

Yuqiu Liu, Jialin Song, Marissa Ramirez de Chanlatte et al.

Real objects that inhabit the physical world follow physical laws and thus behave plausibly during interaction with other physical objects. However, current methods that perform 3D reconstructions of real-world scenes from multi-view 2D images optimize primarily for visual fidelity, i.e., they train with photometric losses and reason about uncertainty in the image or representation space. This appearance-centric view overlooks body contacts and couplings, conflates function-critical regions (e.g., aerodynamic or hydrodynamic surfaces) with ornamentation, and reconstructs structures suboptimally, even when physical regularizers are added. All these can lead to unphysical and implausible interactions. To address this, we consider the question: How can 3D reconstruction become aware of real-world interactions and underlying object functionality, beyond visual cues? To answer this question, we propose FluidGaussian, a plug-and-play method that tightly couples geometry reconstruction with ubiquitous fluid-structure interactions to assess surface quality at high granularity. We define a simulation-based uncertainty metric induced by fluid simulations and integrate it with active learning to prioritize views that improve both visual and physical fidelity. In an empirical evaluation on NeRF Synthetic (Blender), Mip-NeRF 360, and DrivAerNet++, our FluidGaussian method yields up to +8.6% visual PSNR (Peak Signal-to-Noise Ratio) and -62.3% velocity divergence during fluid simulations. Our code is available at https://github.com/delta-lab-ai/FluidGaussian.

Mara Daniels, Liam Hodgkinson, Michael Mahoney

Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting machine learning models to physical data. Popular PIML approaches, including neural operators, physics-informed neural networks, neural ordinary differential equations, and neural discrete equilibria, are typically fit to objectives that simultaneously include both data and physical constraints. However, the multi-objective nature of this approach creates ambiguity in the measurement of model quality. This is related to a poor understanding of epistemic uncertainty, and it can lead to surprising failure modes, even when existing statistical metrics suggest strong fits. Working within a Gaussian process regression framework, we introduce the Physics-Informed Log Evidence (PILE) score. Bypassing the ambiguities of test losses, the PILE score is a single, uncertainty-aware metric that provides a selection principle for hyperparameters of a PIML model. We show that PILE minimization yields excellent choices for a wide variety of model parameters, including kernel bandwidth, least squares regularization weights, and even kernel function selection. We also show that, even prior to data acquisition, a special 'data-free' case of the PILE score identifies a priori kernel choices that are 'well-adapted' to a given PDE. Beyond the kernel setting, we anticipate that the PILE score can be extended to PIML at large, and we outline approaches to do so.

Maxime Lacour, Pu Ren, Rie Nakata et al.

Recent developments in non-ergodic ground-motion models (GMMs) explicitly model systematic spatial variations in source, site, and path effects, reducing standard deviation to 30-40% of ergodic models and enabling more accurate site-specific seismic hazard analysis. Current non-ergodic GMMs rely on Gaussian Process (GP) methods with prescribed correlation functions and thus have computational limitations for large-scale predictions. This study proposes a deep-learning approach called Conditional Generative Modeling for Fourier Amplitude Spectra (CGM-FAS) as an alternative to GP-based methods for modeling non-ergodic path effects in Fourier Amplitude Spectra (FAS). CGM-FAS uses a Conditional Variational Autoencoder architecture to learn spatial patterns and interfrequency correlation directly from data by using geographical coordinates of earthquakes and stations as conditional variables. Using San Francisco Bay Area earthquake data, we compare CGM-FAS against a recent GP-based GMM for the region and demonstrate consistent predictions of non-ergodic path effects. Additionally, CGM-FAS offers advantages compared to GP-based approaches in learning spatial patterns without prescribed correlation functions, capturing interfrequency correlations, and enabling rapid predictions, generating maps for 10,000 sites across 1,000 frequencies within 10 seconds using a few GB of memory. CGM-FAS hyperparameters can be tuned to ensure generated path effects exhibit variability consistent with the GP-based empirical GMM. This work demonstrates a promising direction for efficient non-ergodic ground-motion prediction across multiple frequencies and large spatial domains.

Zhewei Yao, Amir Gholami, Kurt Keutzer et al.

We present PYHESSIAN, a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks. PYHESSIAN enables fast computations of the top Hessian eigenvalues, the Hessian trace, and the full Hessian eigenvalue/spectral density, and it supports distributed-memory execution on cloud/supercomputer systems and is available as open source. This general framework can be used to analyze neural network models, including the topology of the loss landscape (i.e., curvature information) to gain insight into the behavior of different models/optimizers. To illustrate this, we analyze the effect of residual connections and Batch Normalization layers on the trainability of neural networks. One recent claim, based on simpler first-order analysis, is that residual connections and Batch Normalization make the loss landscape smoother, thus making it easier for Stochastic Gradient Descent to converge to a good solution. Our extensive analysis shows new finer-scale insights, demonstrating that, while conventional wisdom is sometimes validated, in other cases it is simply incorrect. In particular, we find that Batch Normalization does not necessarily make the loss landscape smoother, especially for shallower networks.

Zhewei Yao, Amir Gholami, Peng Xu et al.

Deep Neural Networks are quite vulnerable to adversarial perturbations. Current state-of-the-art adversarial attack methods typically require very time consuming hyper-parameter tuning, or require many iterations to solve an optimization based adversarial attack. To address this problem, we present a new family of trust region based adversarial attacks, with the goal of computing adversarial perturbations efficiently. We propose several attacks based on variants of the trust region optimization method. We test the proposed methods on Cifar-10 and ImageNet datasets using several different models including AlexNet, ResNet-50, VGG-16, and DenseNet-121 models. Our methods achieve comparable results with the Carlini-Wagner (CW) attack, but with significant speed up of up to $37\times$, for the VGG-16 model on a Titan Xp GPU. For the case of ResNet-50 on ImageNet, we can bring down its classification accuracy to less than 0.1\% with at most $1.5\%$ relative $L_\infty$ (or $L_2$) perturbation requiring only $1.02$ seconds as compared to $27.04$ seconds for the CW attack. We have open sourced our method which can be accessed at [1].

Da Long, Zheng Wang, Aditi Krishnapriyan et al.

Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge -- often expressed as differential equations -- is valuable in that it is complementary to data, and it can potentially help overcome issues such as data sparsity, noise, and inaccuracy. In this work, we propose a simple, yet powerful and general framework -- AutoIP, for Automatically Incorporating Physics -- that can integrate all kinds of differential equations into Gaussian Processes (GPs) to enhance prediction accuracy and uncertainty quantification. These equations can be linear or nonlinear, spatial, temporal, or spatio-temporal, complete or incomplete with unknown source terms, and so on. Based on kernel differentiation, we construct a GP prior to sample the values of the target function, equation-related derivatives, and latent source functions, which are all jointly from a multivariate Gaussian distribution. The sampled values are fed to two likelihoods: one to fit the observations, and the other to conform to the equation. We use the whitening method to evade the strong dependency between the sampled function values and kernel parameters, and we develop a stochastic variational learning algorithm. AutoIP shows improvement upon vanilla GPs in both simulation and several real-world applications, even using rough, incomplete equations.

Vipul Gupta, Avishek Ghosh, Michal Derezinski et al.

To address the communication bottleneck problem in distributed optimization within a master-worker framework, we propose LocalNewton, a distributed second-order algorithm with local averaging. In LocalNewton, the worker machines update their model in every iteration by finding a suitable second-order descent direction using only the data and model stored in their own local memory. We let the workers run multiple such iterations locally and communicate the models to the master node only once every few (say L) iterations. LocalNewton is highly practical since it requires only one hyperparameter, the number L of local iterations. We use novel matrix concentration-based techniques to obtain theoretical guarantees for LocalNewton, and we validate them with detailed empirical evaluation. To enhance practicability, we devise an adaptive scheme to choose L, and we show that this reduces the number of local iterations in worker machines between two model synchronizations as the training proceeds, successively refining the model quality at the master. Via extensive experiments using several real-world datasets with AWS Lambda workers and an AWS EC2 master, we show that LocalNewton requires fewer than 60% of the communication rounds (between master and workers) and less than 40% of the end-to-end running time, compared to state-of-the-art algorithms, to reach the same training~loss.

Tianjun Zhang, Zhewei Yao, Amir Gholami et al.

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is an extension of this approach that also allows evolution of the neural network parameters, in a coupled ODE-based formulation. The Neural ODE method introduced earlier is in fact a special case of this new more general framework. We present the formulation of ANODEV2, derive optimality conditions, and implement a coupled reaction-diffusion-advection version of this framework in PyTorch. We present empirical results using several different configurations of ANODEV2, testing them on multiple models on CIFAR-10. We report results showing that this coupled ODE-based framework is indeed trainable, and that it achieves higher accuracy, as compared to the baseline models as well as the recently-proposed Neural ODE approach.

Zhen Dong, Zhewei Yao, Amir Gholami et al.

Model size and inference speed/power have become a major challenge in the deployment of Neural Networks for many applications. A promising approach to address these problems is quantization. However, uniformly quantizing a model to ultra low precision leads to significant accuracy degradation. A novel solution for this is to use mixed-precision quantization, as some parts of the network may allow lower precision as compared to other layers. However, there is no systematic way to determine the precision of different layers. A brute force approach is not feasible for deep networks, as the search space for mixed-precision is exponential in the number of layers. Another challenge is a similar factorial complexity for determining block-wise fine-tuning order when quantizing the model to a target precision. Here, we introduce Hessian AWare Quantization (HAWQ), a novel second-order quantization method to address these problems. HAWQ allows for the automatic selection of the relative quantization precision of each layer, based on the layer's Hessian spectrum. Moreover, HAWQ provides a deterministic fine-tuning order for quantizing layers, based on second-order information. We show the results of our method on Cifar-10 using ResNet20, and on ImageNet using Inception-V3, ResNet50 and SqueezeNext models. Comparing HAWQ with state-of-the-art shows that we can achieve similar/better accuracy with $8\times$ activation compression ratio on ResNet20, as compared to DNAS~\cite{wu2018mixed}, and up to $1\%$ higher accuracy with up to $14\%$ smaller models on ResNet50 and Inception-V3, compared to recently proposed methods of RVQuant~\cite{park2018value} and HAQ~\cite{wang2018haq}. Furthermore, we show that we can quantize SqueezeNext to just 1MB model size while achieving above $68\%$ top1 accuracy on ImageNet.

Norman Mu, Zhewei Yao, Amir Gholami et al.

Optimal parameter initialization remains a crucial problem for neural network training. A poor weight initialization may take longer to train and/or converge to sub-optimal solutions. Here, we propose a method of weight re-initialization by repeated annealing and injection of noise in the training process. We implement this through a cyclical batch size schedule motivated by a Bayesian perspective of neural network training. We evaluate our methods through extensive experiments on tasks in language modeling, natural language inference, and image classification. We demonstrate the ability of our method to improve language modeling performance by up to 7.91 perplexity and reduce training iterations by up to $61\%$, in addition to its flexibility in enabling snapshot ensembling and use with adversarial training.

Zhewei Yao, Amir Gholami, Daiyaan Arfeen et al.

The most straightforward method to accelerate Stochastic Gradient Descent (SGD) computation is to distribute the randomly selected batch of inputs over multiple processors. To keep the distributed processors fully utilized requires commensurately growing the batch size. However, large batch training often leads to poorer generalization. A recently proposed solution for this problem is to use adaptive batch sizes in SGD. In this case, one starts with a small number of processes and scales the processes as training progresses. Two major challenges with this approach are (i) that dynamically resizing the cluster can add non-trivial overhead, in part since it is currently not supported, and (ii) that the overall speed up is limited by the initial phase with smaller batches. In this work, we address both challenges by developing a new adaptive batch size framework, with autoscaling based on the Ray framework. This allows very efficient elastic scaling with negligible resizing overhead (0.32\% of time for ResNet18 ImageNet training). Furthermore, we propose a new adaptive batch size training scheme using second order methods and adversarial training. These enable increasing batch sizes earlier during training, which leads to better training time. We extensively evaluate our method on Cifar-10/100, SVHN, TinyImageNet, and ImageNet datasets, using multiple neural networks, including ResNets and smaller networks such as SqueezeNext. Our method exceeds the performance of existing solutions in terms of both accuracy and the number of SGD iterations (up to 1\% and $5\times$, respectively). Importantly, this is achieved without any additional hyper-parameter tuning to tailor our method in any of these experiments.

Garvesh Raskutti, Michael Mahoney

We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices constructed from random projections and leverage-score sampling, if the number of samples $r$ much smaller than the original sample size $n$, then the worst-case (WC) error is the same as solving the original problem, up to a very small relative error. From a \emph{statistical perspective}, one typically considers the mean-squared error performance of randomized sketching algorithms, when data are generated according to a statistical linear model. In this paper, we provide a rigorous comparison of both perspectives leading to insights on how they differ. To do this, we first develop a framework for assessing, in a unified manner, algorithmic and statistical aspects of randomized sketching methods. We then consider the statistical prediction efficiency (PE) and the statistical residual efficiency (RE) of the sketched LS estimator; and we use our framework to provide upper bounds for several types of random projection and random sampling algorithms. Among other results, we show that the RE can be upper bounded when $r$ is much smaller than $n$, while the PE typically requires the number of samples $r$ to be substantially larger. Lower bounds developed in subsequent work show that our upper bounds on PE can not be improved.

Haim Avron, Vikas Sindhwani, Jiyan Yang et al.

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use Quasi-Monte Carlo (QMC) approximations instead, where the relevant integrands are evaluated on a low-discrepancy sequence of points as opposed to random point sets as in the Monte Carlo approach. We derive a new discrepancy measure called box discrepancy based on theoretical characterizations of the integration error with respect to a given sequence. We then propose to learn QMC sequences adapted to our setting based on explicit box discrepancy minimization. Our theoretical analyses are complemented with empirical results that demonstrate the effectiveness of classical and adaptive QMC techniques for this problem.

Garvesh Raskutti, Michael Mahoney

We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data $(X, Y) \in \mathbb{R}^{n \times p} \times \mathbb{R}^n$, sketching algorithms use a sketching matrix, $S\in\mathbb{R}^{r \times n}$ with $r \ll n$. Then, rather than solving the LS problem using the full data $(X,Y)$, sketching algorithms solve the LS problem using only the sketched data $(SX, SY)$. Prior work has typically adopted an algorithmic perspective, in that it has made no statistical assumptions on the input $X$ and $Y$, and instead it has been assumed that the data $(X,Y)$ are fixed and worst-case (WC). Prior results show that, when using sketching matrices such as random projections and leverage-score sampling algorithms, with $p < r \ll n$, the WC error is the same as solving the original problem, up to a small constant. From a statistical perspective, we typically consider the mean-squared error performance of randomized sketching algorithms, when data $(X, Y)$ are generated according to a statistical model $Y = X β+ ε$, where $ε$ is a noise process. We provide a rigorous comparison of both perspectives leading to insights on how they differ. To do this, we first develop a framework for assessing algorithmic and statistical aspects of randomized sketching methods. We then consider the statistical prediction efficiency (PE) and the statistical residual efficiency (RE) of the sketched LS estimator; and we use our framework to provide upper bounds for several types of random projection and random sampling sketching algorithms. Among other results, we show that the RE can be upper bounded when $p < r \ll n$ while the PE typically requires the sample size $r$ to be substantially larger. Lower bounds developed in subsequent results show that our upper bounds on PE can not be improved.