Gintare Karolina Dziugaite

Joo Hyung Lee, Wonpyo Park, Nicole Mitchell et al. · mila

This paper introduces JaxPruner, an open-source JAX-based pruning and sparse training library for machine learning research. JaxPruner aims to accelerate research on sparse neural networks by providing concise implementations of popular pruning and sparse training algorithms with minimal memory and latency overhead. Algorithms implemented in JaxPruner use a common API and work seamlessly with the popular optimization library Optax, which, in turn, enables easy integration with existing JAX based libraries. We demonstrate this ease of integration by providing examples in four different codebases: Scenic, t5x, Dopamine and FedJAX and provide baseline experiments on popular benchmarks.

Mansheej Paul, Feng Chen, Brett W. Larsen et al. · stanford

Modern deep learning involves training costly, highly overparameterized networks, thus motivating the search for sparser networks that can still be trained to the same accuracy as the full network (i.e. matching). Iterative magnitude pruning (IMP) is a state of the art algorithm that can find such highly sparse matching subnetworks, known as winning tickets. IMP operates by iterative cycles of training, masking smallest magnitude weights, rewinding back to an early training point, and repeating. Despite its simplicity, the underlying principles for when and how IMP finds winning tickets remain elusive. In particular, what useful information does an IMP mask found at the end of training convey to a rewound network near the beginning of training? How does SGD allow the network to extract this information? And why is iterative pruning needed? We develop answers in terms of the geometry of the error landscape. First, we find that$\unicode{x2014}$at higher sparsities$\unicode{x2014}$pairs of pruned networks at successive pruning iterations are connected by a linear path with zero error barrier if and only if they are matching. This indicates that masks found at the end of training convey the identity of an axial subspace that intersects a desired linearly connected mode of a matching sublevel set. Second, we show SGD can exploit this information due to a strong form of robustness: it can return to this mode despite strong perturbations early in training. Third, we show how the flatness of the error landscape at the end of training determines a limit on the fraction of weights that can be pruned at each iteration of IMP. Finally, we show that the role of retraining in IMP is to find a network with new small weights to prune. Overall, these results make progress toward demystifying the existence of winning tickets by revealing the fundamental role of error landscape geometry.

Tian Jin, Michael Carbin, Daniel M. Roy et al. · utoronto

Practitioners frequently observe that pruning improves model generalization. A long-standing hypothesis based on bias-variance trade-off attributes this generalization improvement to model size reduction. However, recent studies on over-parameterization characterize a new model size regime, in which larger models achieve better generalization. Pruning models in this over-parameterized regime leads to a contradiction -- while theory predicts that reducing model size harms generalization, pruning to a range of sparsities nonetheless improves it. Motivated by this contradiction, we re-examine pruning's effect on generalization empirically. We show that size reduction cannot fully account for the generalization-improving effect of standard pruning algorithms. Instead, we find that pruning leads to better training at specific sparsities, improving the training loss over the dense model. We find that pruning also leads to additional regularization at other sparsities, reducing the accuracy degradation due to noisy examples over the dense model. Pruning extends model training time and reduces model size. These two factors improve training and add regularization respectively. We empirically demonstrate that both factors are essential to fully explaining pruning's impact on generalization.

Mahdi Haghifam, Borja Rodríguez-Gálvez, Ragnar Thobaben et al. · utoronto

To date, no "information-theoretic" frameworks for reasoning about generalization error have been shown to establish minimax rates for gradient descent in the setting of stochastic convex optimization. In this work, we consider the prospect of establishing such rates via several existing information-theoretic frameworks: input-output mutual information bounds, conditional mutual information bounds and variants, PAC-Bayes bounds, and recent conditional variants thereof. We prove that none of these bounds are able to establish minimax rates. We then consider a common tactic employed in studying gradient methods, whereby the final iterate is corrupted by Gaussian noise, producing a noisy "surrogate" algorithm. We prove that minimax rates cannot be established via the analysis of such surrogates. Our results suggest that new ideas are required to analyze gradient descent using information-theoretic techniques.

Mahdi Haghifam, Shay Moran, Daniel M. Roy et al. · utoronto

We study the mutual information between (certain summaries of) the output of a learning algorithm and its $n$ training data, conditional on a supersample of $n+1$ i.i.d. data from which the training data is chosen at random without replacement. These leave-one-out variants of the conditional mutual information (CMI) of an algorithm (Steinke and Zakynthinou, 2020) are also seen to control the mean generalization error of learning algorithms with bounded loss functions. For learning algorithms achieving zero empirical risk under 0-1 loss (i.e., interpolating algorithms), we provide an explicit connection between leave-one-out CMI and the classical leave-one-out error estimate of the risk. Using this connection, we obtain upper and lower bounds on risk in terms of the (evaluated) leave-one-out CMI. When the limiting risk is constant or decays polynomially, the bounds converge to within a constant factor of two. As an application, we analyze the population risk of the one-inclusion graph algorithm, a general-purpose transductive learning algorithm for VC classes in the realizable setting. Using leave-one-out CMI, we match the optimal bound for learning VC classes in the realizable setting, answering an open challenge raised by Steinke and Zakynthinou (2020). Finally, in order to understand the role of leave-one-out CMI in studying generalization, we place leave-one-out CMI in a hierarchy of measures, with a novel unconditional mutual information at the root. For 0-1 loss and interpolating learning algorithms, this mutual information is observed to be precisely the risk.

Mansheej Paul, Brett W. Larsen, Surya Ganguli et al.

A striking observation about iterative magnitude pruning (IMP; Frankle et al. 2020) is that $\unicode{x2014}$ after just a few hundred steps of dense training $\unicode{x2014}$ the method can find a sparse sub-network that can be trained to the same accuracy as the dense network. However, the same does not hold at step 0, i.e. random initialization. In this work, we seek to understand how this early phase of pre-training leads to a good initialization for IMP both through the lens of the data distribution and the loss landscape geometry. Empirically we observe that, holding the number of pre-training iterations constant, training on a small fraction of (randomly chosen) data suffices to obtain an equally good initialization for IMP. We additionally observe that by pre-training only on "easy" training data, we can decrease the number of steps necessary to find a good initialization for IMP compared to training on the full dataset or a randomly chosen subset. Finally, we identify novel properties of the loss landscape of dense networks that are predictive of IMP performance, showing in particular that more examples being linearly mode connected in the dense network correlates well with good initializations for IMP. Combined, these results provide new insight into the role played by the early phase training in IMP.

Tian Jin, Nolan Clement, Xin Dong et al.

How does scaling the number of parameters in large language models (LLMs) affect their core capabilities? We study two natural scaling techniques -- weight pruning and simply training a smaller or larger model, which we refer to as dense scaling -- and their effects on two core capabilities of LLMs: (a) recalling facts presented during pre-training and (b) processing information presented in-context during inference. By curating a suite of tasks that help disentangle these two capabilities, we find a striking difference in how these two abilities evolve due to scaling. Reducing the model size by more than 30\% (via either scaling approach) significantly decreases the ability to recall facts seen in pre-training. Yet, a 60--70\% reduction largely preserves the various ways the model can process in-context information, ranging from retrieving answers from a long context to learning parameterized functions from in-context exemplars. The fact that both dense scaling and weight pruning exhibit this behavior suggests that scaling model size has an inherently disparate effect on fact recall and in-context learning.

Nikita Dhawan, Nicole Mitchell, Zachary Charles et al.

The federated learning paradigm has motivated the development of methods for aggregating multiple client updates into a global server model, without sharing client data. Many federated learning algorithms, including the canonical Federated Averaging (FedAvg), take a direct (possibly weighted) average of the client parameter updates, motivated by results in distributed optimization. In this work, we adopt a function space perspective and propose a new algorithm, FedFish, that aggregates local approximations to the functions learned by clients, using an estimate based on their Fisher information. We evaluate FedFish on realistic, large-scale cross-device benchmarks. While the performance of FedAvg can suffer as client models drift further apart, we demonstrate that FedFish is more robust to longer local training. Our evaluation across several settings in image and language benchmarks shows that FedFish outperforms FedAvg as local training epochs increase. Further, FedFish results in global networks that are more amenable to efficient personalization via local fine-tuning on the same or shifted data distributions. For instance, federated pretraining on the C4 dataset, followed by few-shot personalization on Stack Overflow, results in a 7% improvement in next-token prediction by FedFish over FedAvg.

Zachary Ankner, Alex Renda, Gintare Karolina Dziugaite et al.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Johan Obando-Ceron, Ghada Sokar, Timon Willi et al. · mila

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

Theodore Papamarkou, Pierre Alquier, Matthias Bauer et al.

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness and feasibility of Bayesian approaches remain unclear for LLM inference, this position paper argues that the control layer of an agentic AI system (that orchestrates LLMs and tools) is a clear case where Bayesian principles should shine. Bayesian decision theory provides a framework for agentic systems that can help to maintain beliefs over task-relevant latent quantities, to update these beliefs from observed agentic and human-AI interactions, and to choose actions. Making LLMs themselves explicitly Bayesian belief-updating engines remains computationally intensive and conceptually nontrivial as a general modeling target. In contrast, this paper argues that coherent decision-making requires Bayesian principles at the orchestration level of the agentic system, not necessarily the LLM agent parameters. This paper articulates practical properties for Bayesian control that fit modern agentic AI systems and human-AI collaboration, and provides concrete examples and design patterns to illustrate how calibrated beliefs and utility-aware policies can improve agentic AI orchestration.

Phillip Guo, Aaquib Syed, Abhay Sheshadri et al.

Methods for knowledge editing and unlearning in large language models seek to edit or remove undesirable knowledge or capabilities without compromising general language modeling performance. This work investigates how mechanistic interpretability -- which, in part, aims to identify model components (circuits) associated to specific interpretable mechanisms that make up a model capability -- can improve the precision and effectiveness of editing and unlearning. We find a stark difference in unlearning and edit robustness when training components localized by different methods. We highlight an important distinction between methods that localize components based primarily on preserving outputs, and those finding high level mechanisms with predictable intermediate states. In particular, localizing edits/unlearning to components associated with the lookup-table mechanism for factual recall 1) leads to more robust edits/unlearning across different input/output formats, and 2) resists attempts to relearn the unwanted information, while also reducing unintended side effects compared to baselines, on both a sports facts dataset and the CounterFact dataset across multiple models. We also find that certain localized edits disrupt the latent knowledge in the model more than any other baselines, making unlearning more robust to various attacks.

Idan Attias, Gintare Karolina Dziugaite, Mahdi Haghifam et al.

In this work, we investigate the interplay between memorization and learning in the context of \emph{stochastic convex optimization} (SCO). We define memorization via the information a learning algorithm reveals about its training data points. We then quantify this information using the framework of conditional mutual information (CMI) proposed by Steinke and Zakynthinou (2020). Our main result is a precise characterization of the tradeoff between the accuracy of a learning algorithm and its CMI, answering an open question posed by Livni (2023). We show that, in the $L^2$ Lipschitz--bounded setting and under strong convexity, every learner with an excess error $\varepsilon$ has CMI bounded below by $Ω(1/\varepsilon^2)$ and $Ω(1/\varepsilon)$, respectively. We further demonstrate the essential role of memorization in learning problems in SCO by designing an adversary capable of accurately identifying a significant fraction of the training samples in specific SCO problems. Finally, we enumerate several implications of our results, such as a limitation of generalization bounds based on CMI and the incompressibility of samples in SCO problems.

Devin Kwok, Nikhil Anand, Jonathan Frankle et al.

Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call "example difficulty scores", are typically used to rank or categorize examples, but the consistency of rankings between different training runs, scoring methods, and model architectures is generally unknown. To determine how example rankings vary due to these random and controlled effects, we systematically compare different formulations of scores over a range of runs and model architectures. We find that scores largely share the following traits: they are noisy over individual runs of a model, strongly correlated with a single notion of difficulty, and reveal examples that range from being highly sensitive to insensitive to the inductive biases of certain model architectures. Drawing from statistical genetics, we develop a simple method for fingerprinting model architectures using a few sensitive examples. These findings guide practitioners in maximizing the consistency of their scores (e.g. by choosing appropriate scoring methods, number of runs, and subsets of examples), and establishes comprehensive baselines for evaluating scores in the future.

Ekansh Sharma, Devin Kwok, Tom Denton et al.

Neural networks typically exhibit permutation symmetries which contribute to the non-convexity of the networks' loss landscapes, since linearly interpolating between two permuted versions of a trained network tends to encounter a high loss barrier. Recent work has argued that permutation symmetries are the only sources of non-convexity, meaning there are essentially no such barriers between trained networks if they are permuted appropriately. In this work, we refine these arguments into three distinct claims of increasing strength. We show that existing evidence only supports "weak linear connectivity"-that for each pair of networks belonging to a set of SGD solutions, there exist (multiple) permutations that linearly connect it with the other networks. In contrast, the claim "strong linear connectivity"-that for each network, there exists one permutation that simultaneously connects it with the other networks-is both intuitively and practically more desirable. This stronger claim would imply that the loss landscape is convex after accounting for permutation, and enable linear interpolation between three or more independently trained models without increased loss. In this work, we introduce an intermediate claim-that for certain sequences of networks, there exists one permutation that simultaneously aligns matching pairs of networks from these sequences. Specifically, we discover that a single permutation aligns sequences of iteratively trained as well as iteratively pruned networks, meaning that two networks exhibit low loss barriers at each step of their optimization and sparsification trajectories respectively. Finally, we provide the first evidence that strong linear connectivity may be possible under certain conditions, by showing that barriers decrease with increasing network width when interpolating among three networks.

Tejas Kasetty, Divyat Mahajan, Gintare Karolina Dziugaite et al.

Numerous decision-making tasks require estimating causal effects under interventions on different parts of a system. As practitioners consider using large language models (LLMs) to automate decisions, studying their causal reasoning capabilities becomes crucial. A recent line of work evaluates LLMs ability to retrieve commonsense causal facts, but these evaluations do not sufficiently assess how LLMs reason about interventions. Motivated by the role that interventions play in causal inference, in this paper, we conduct empirical analyses to evaluate whether LLMs can accurately update their knowledge of a data-generating process in response to an intervention. We create benchmarks that span diverse causal graphs (e.g., confounding, mediation) and variable types, and enable a study of intervention-based reasoning. These benchmarks allow us to isolate the ability of LLMs to accurately predict changes resulting from their ability to memorize facts or find other shortcuts. We evaluate six LLMs on the benchmarks, finding that GPT models show promising accuracy at predicting the intervention effects.

Ekansh Sharma, Daniel M. Roy, Gintare Karolina Dziugaite

Model merging aims to efficiently combine the weights of multiple expert models, each trained on a specific task, into a single multi-task model, with strong performance across all tasks. When applied to all but the last layer of weights, existing methods -- such as Task Arithmetic, TIES-merging, and TALL mask merging -- work well to combine expert models obtained by fine-tuning a common foundation model, operating within a "local" neighborhood of the foundation model. This work explores the more challenging scenario of "non-local" merging, which we find arises when an expert model changes significantly during pretraining or where the expert models do not even share a common foundation model. We observe that standard merging techniques often fail to generalize effectively in this non-local setting, even when accounting for permutation symmetries using standard techniques. We identify that this failure is, in part, due to "variance collapse", a phenomenon identified also in the setting of linear mode connectivity by Jordan et al. (2023). To address this, we propose a multi-task technique to re-scale and shift the output activations of the merged model for each task, aligning its output statistics with those of the corresponding task-specific expert models. Our experiments demonstrate that this correction significantly improves the performance of various model merging approaches in non-local settings, providing a strong baseline for future research on this problem.

Nazanin Mohammadi Sepahvand, Vincent Dumoulin, Eleni Triantafillou et al.

As deep learning models are becoming larger and data-hungrier, there are growing ethical, legal and technical concerns over use of data: in practice, agreements on data use may change over time, rendering previously-used training data impermissible for training purposes. These issues have driven increased attention to machine unlearning: removing "the influence of" a subset of training data from a trained model. In this work, we advocate for a relaxed definition of unlearning that does not address privacy applications but targets a scenario where a data owner withdraws permission of use of their data for training purposes. In this context, we consider the important problem of \emph{transfer unlearning} where a pretrained model is transferred to a target dataset that contains some "non-static" data that may need to be unlearned in the future. We propose a new method that uses a mechanism for selecting relevant examples from an auxiliary "static" dataset, and finetunes on the selected data instead of "non-static" target data; addressing all unlearning requests ahead of time. We also adapt a recent relaxed definition of unlearning to our problem setting and demonstrate that our approach is an exact transfer unlearner according to it, while being highly efficient (amortized). We find that our method outperforms the gold standard "exact unlearning" (finetuning on only the "static" portion of the target dataset) on several datasets, especially for small "static" sets, sometimes approaching an upper bound for test accuracy. We also analyze factors influencing the accuracy boost obtained by data selection.

Anat Kleiman, Gintare Karolina Dziugaite, Jonathan Frankle et al.

In continual learning, where task data arrives in a sequence, fine-tuning on later tasks will often lead to performance degradation on earlier tasks. This is especially pronounced when these tasks come from diverse domains. In this setting, how can we mitigate catastrophic forgetting of earlier tasks and retain what the model has learned with minimal computational expenses? Inspired by other merging methods, and L2-regression, we propose Sequential Fine-tuning with Averaging (SFA), a method that merges currently training models with earlier checkpoints during the course of training. SOTA approaches typically maintain a data buffer of past tasks or impose a penalty at each gradient step. In contrast, our method achieves comparable results without the need to store past data, or multiple copies of parameters for each gradient step. Furthermore, our method outperforms common merging techniques such as Task Arithmetic, TIES Merging, and WiSE-FT, as well as other penalty methods like L2 and Elastic Weight Consolidation. In turn, our method offers insight into the benefits of merging partially-trained models during training across both image and language domains.

Teodora Baluta, Pascal Lamblin, Daniel Tarlow et al.

Machine unlearning aims to solve the problem of removing the influence of selected training examples from a learned model. Despite the increasing attention to this problem, it remains an open research question how to evaluate unlearning in large language models (LLMs), and what are the critical properties of the data to be unlearned that affect the quality and efficiency of unlearning. This work formalizes a metric to evaluate unlearning quality in generative models, and uses it to assess the trade-offs between unlearning quality and performance. We demonstrate that unlearning out-of-distribution examples requires more unlearning steps but overall presents a better trade-off overall. For in-distribution examples, however, we observe a rapid decay in performance as unlearning progresses. We further evaluate how example's memorization and difficulty affect unlearning under a classical gradient ascent-based approach.

Ghada Sokar, Gintare Karolina Dziugaite, Anurag Arnab et al.

Continual learning is conventionally tackled through sequential fine-tuning, a process that, while enabling adaptation, inherently favors plasticity over the stability needed to retain prior knowledge. While existing approaches attempt to mitigate catastrophic forgetting, a bias towards recent tasks persists as they build upon this sequential nature. In this work we present a new perspective based on model merging to maintain stability while still retaining plasticity. Rather than just sequentially updating the model weights, we propose merging newly trained task parameters with previously learned ones, promoting a better balance. To maximize the effectiveness of the merging process, we propose a simple mechanism that promotes learning aligned weights with previous ones, thereby avoiding interference when merging. We evaluate this approach on large Vision-Language Models (VLMs), and demonstrate its effectiveness in reducing forgetting, increasing robustness to various task orders and similarities, and improving generalization.

Reihaneh Torkzadehmahani, Reza Nasirigerdeh, Georgios Kaissis et al.

Machine unlearning refers to removing the influence of a specified subset of training data from a machine learning model, efficiently, after it has already been trained. This is important for key applications, including making the model more accurate by removing outdated, mislabeled, or poisoned data. In this work, we study localized unlearning, where the unlearning algorithm operates on a (small) identified subset of parameters. Drawing inspiration from the memorization literature, we propose an improved localization strategy that yields strong results when paired with existing unlearning algorithms. We also propose a new unlearning algorithm, Deletion by Example Localization (DEL), that resets the parameters deemed-to-be most critical according to our localization strategy, and then finetunes them. Our extensive experiments on different datasets, forget sets and metrics reveal that DEL sets a new state-of-the-art for unlearning metrics, against both localized and full-parameter methods, while modifying a small subset of parameters, and outperforms the state-of-the-art localized unlearning in terms of test accuracy too.

Shoaib Ahmed Siddiqui, Adrian Weller, David Krueger et al.

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50% post-unlearning to nearly 100% with fine-tuning on just the retain set -- i.e., zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, $L_2$-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

Tian Jin, Ahmed Imtiaz Humayun, Utku Evci et al.

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.

Sasha Voitovych, Mahdi Haghifam, Idan Attias et al.

In this paper, we investigate the necessity of traceability for accurate learning in stochastic convex optimization (SCO) under $\ell_p$ geometries. Informally, we say a learning algorithm is $m$-traceable if, by analyzing its output, it is possible to identify at least $m$ of its training samples. Our main results uncover a fundamental tradeoff between traceability and excess risk in SCO. For every $p\in [1,\infty)$, we establish the existence of an excess risk threshold below which every sample-efficient learner is traceable with the number of samples which is a constant fraction of its training sample. For $p\in [1,2]$, this threshold coincides with the best excess risk of differentially private (DP) algorithms, i.e., above this threshold, there exist algorithms that are not traceable, which corresponds to a sharp phase transition. For $p \in (2,\infty)$, this threshold instead gives novel lower bounds for DP learning, partially closing an open problem in this setup. En route to establishing these results, we prove a sparse variant of the fingerprinting lemma, which is of independent interest to the community.

Riyasat Ohib, Bishal Thapaliya, Gintare Karolina Dziugaite et al.

In this work, we propose Salient Sparse Federated Learning (SSFL), a streamlined approach for sparse federated learning with efficient communication. SSFL identifies a sparse subnetwork prior to training, leveraging parameter saliency scores computed separately on local client data in non-IID scenarios, and then aggregated, to determine a global mask. Only the sparse model weights are communicated each round between the clients and the server. We validate SSFL's effectiveness using standard non-IID benchmarks, noting marked improvements in the sparsity--accuracy trade-offs. Finally, we deploy our method in a real-world federated learning framework and report improvement in communication time.

Stefan Horoi, Guy Wolf, Eugene Belilovsky et al.

Modern deep learning is increasingly characterized by the use of open-weight foundation models that can be fine-tuned on specialized datasets. This has led to a proliferation of expert models and adapters, often shared via platforms like HuggingFace and AdapterHub. To leverage these resources, numerous model upcycling methods have emerged, enabling the reuse of fine-tuned models in multi-task systems. A natural pipeline has thus formed to harness the benefits of transfer learning and amortize sunk training costs: models are pre-trained on general data, fine-tuned on specific tasks, and then upcycled into more general-purpose systems. A prevailing assumption is that improvements at one stage of this pipeline propagate downstream, leading to gains at subsequent steps. In this work, we challenge that assumption by examining how expert fine-tuning affects model upcycling. We show that long fine-tuning of experts that optimizes for their individual performance leads to degraded merging performance, both for fully fine-tuned and LoRA-adapted models, and to worse downstream results when LoRA adapters are upcycled into MoE layers. We trace this degradation to the memorization of a small set of difficult examples that dominate late fine-tuning steps and are subsequently forgotten during merging. Finally, we demonstrate that a task-dependent aggressive early stopping strategy can significantly improve upcycling performance.

Nazanin Mohammadi Sepahvand, Anvith Thudi, Berivan Isik et al.

We present a principled, per-instance approach to quantifying the difficulty of unlearning via fine-tuning. We begin by sharpening an analysis of noisy gradient descent for unlearning (Chien et al., 2024), obtaining a better utility-unlearning tradeoff by replacing worst-case privacy loss bounds with per-instance privacy losses (Thudi et al., 2024), each of which bounds the (Renyi) divergence to retraining without an individual data point. To demonstrate the practical applicability of our theory, we present empirical results showing that our theoretical predictions are born out both for Stochastic Gradient Langevin Dynamics (SGLD) as well as for standard fine-tuning without explicit noise. We further demonstrate that per-instance privacy losses correlate well with several existing data difficulty metrics, while also identifying harder groups of data points, and introduce novel evaluation methods based on loss barriers. All together, our findings provide a foundation for more efficient and adaptive unlearning strategies tailored to the unique properties of individual data points.

Pranshu Malviya, Goncalo Mordido, Aristide Baratin et al.

Efficiently exploring complex loss landscapes is key to the performance of deep neural networks. While momentum-based optimizers are widely used in state-of-the-art setups, classical momentum can still struggle with large, misaligned gradients, leading to oscillations. To address this, we propose Torque-Aware Momentum (TAM), which introduces a damping factor based on the angle between the new gradients and previous momentum, stabilizing the update direction during training. Empirical results show that TAM, which can be combined with both SGD and Adam, enhances exploration, handles distribution shifts more effectively, and improves generalization performance across various tasks, including image classification and large language model fine-tuning, when compared to classical momentum-based optimizers.

Eleni Triantafillou, Peter Kairouz, Fabian Pedregosa et al.

We present the findings of the first NeurIPS competition on unlearning, which sought to stimulate the development of novel algorithms and initiate discussions on formal and robust evaluation methodologies. The competition was highly successful: nearly 1,200 teams from across the world participated, and a wealth of novel, imaginative solutions with different characteristics were contributed. In this paper, we analyze top solutions and delve into discussions on benchmarking unlearning, which itself is a research problem. The evaluation methodology we developed for the competition measures forgetting quality according to a formal notion of unlearning, while incorporating model utility for a holistic evaluation. We analyze the effectiveness of different instantiations of this evaluation framework vis-a-vis the associated compute cost, and discuss implications for standardizing evaluation. We find that the ranking of leading methods remains stable under several variations of this framework, pointing to avenues for reducing the cost of evaluation. Overall, our findings indicate progress in unlearning, with top-performing competition entries surpassing existing algorithms under our evaluation framework. We analyze trade-offs made by different algorithms and strengths or weaknesses in terms of generalizability to new datasets, paving the way for advancing both benchmarking and algorithm development in this important area.

Yu Yang, Eric Gan, Gintare Karolina Dziugaite et al.

Neural networks trained with (stochastic) gradient descent have an inductive bias towards learning simpler solutions. This makes them highly prone to learning spurious correlations in the training data, that may not hold at test time. In this work, we provide the first theoretical analysis of the effect of simplicity bias on learning spurious correlations. Notably, we show that examples with spurious features are provably separable based on the model's output early in training. We further illustrate that if spurious features have a small enough noise-to-signal ratio, the network's output on the majority of examples is almost exclusively determined by the spurious features, leading to poor worst-group test accuracy. Finally, we propose SPARE, which identifies spurious correlations early in training and utilizes importance sampling to alleviate their effect. Empirically, we demonstrate that SPARE outperforms state-of-the-art methods by up to 21.1% in worst-group accuracy, while being up to 12x faster. We also show that SPARE is a highly effective but lightweight method to discover spurious correlations.

Mahdi Haghifam, Gintare Karolina Dziugaite, Shay Moran et al.

In this work, we investigate the expressiveness of the "conditional mutual information" (CMI) framework of Steinke and Zakynthinou (2020) and the prospect of using it to provide a unified framework for proving generalization bounds in the realizable setting. We first demonstrate that one can use this framework to express non-trivial (but sub-optimal) bounds for any learning algorithm that outputs hypotheses from a class of bounded VC dimension. We prove that the CMI framework yields the optimal bound on the expected risk of Support Vector Machines (SVMs) for learning halfspaces. This result is an application of our general result showing that stable compression schemes Bousquet al. (2020) of size $k$ have uniformly bounded CMI of order $O(k)$. We further show that an inherent limitation of proper learning of VC classes contradicts the existence of a proper learner with constant CMI, and it implies a negative resolution to an open problem of Steinke and Zakynthinou (2020). We further study the CMI of empirical risk minimizers (ERMs) of class $H$ and show that it is possible to output all consistent classifiers (version space) with bounded CMI if and only if $H$ has a bounded star number (Hanneke and Yang (2015)). Moreover, we prove a general reduction showing that "leave-one-out" analysis is expressible via the CMI framework. As a corollary we investigate the CMI of the one-inclusion-graph algorithm proposed by Haussler et al. (1994). More generally, we show that the CMI framework is universal in the sense that for every consistent algorithm and data distribution, the expected risk vanishes as the number of samples diverges if and only if its evaluated CMI has sublinear growth with the number of samples.

Soufiane Hayou, Bobby He, Gintare Karolina Dziugaite

We study an approach to learning pruning masks by optimizing the expected loss of stochastic pruning masks, i.e., masks which zero out each weight independently with some weight-specific probability. We analyze the training dynamics of the induced stochastic predictor in the setting of linear regression, and observe a data-adaptive L1 regularization term, in contrast to the dataadaptive L2 regularization term known to underlie dropout in linear regression. We also observe a preference to prune weights that are less well-aligned with the data labels. We evaluate probabilistic fine-tuning for optimizing stochastic pruning masks for neural networks, starting from masks produced by several baselines. In each case, we see improvements in test error over baselines, even after we threshold fine-tuned stochastic pruning masks. Finally, since a stochastic pruning mask induces a stochastic neural network, we consider training the weights and/or pruning probabilities simultaneously to minimize a PAC-Bayes bound on generalization error. Using data-dependent priors, we obtain a selfbounded learning algorithm with strong performance and numerically tight bounds. In the linear model, we show that a PAC-Bayes generalization error bound is controlled by the magnitude of the change in feature alignment between the 'prior' and 'posterior' data.

Mansheej Paul, Surya Ganguli, Gintare Karolina Dziugaite

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.

Gergely Neu, Gintare Karolina Dziugaite, Mahdi Haghifam et al.

We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the generalization error that depend on local statistics of the stochastic gradients evaluated along the path of iterates calculated by SGD. The key factors our bounds depend on are the variance of the gradients (with respect to the data distribution) and the local smoothness of the objective function along the SGD path, and the sensitivity of the loss function to perturbations to the final output. Our key technical tool is combining the information-theoretic generalization bounds previously used for analyzing randomized variants of SGD with a perturbation analysis of the iterates.

Yiding Jiang, Pierre Foret, Scott Yak et al.

Understanding generalization in deep learning is arguably one of the most important questions in deep learning. Deep learning has been successfully adopted to a large number of problems ranging from pattern recognition to complex decision making, but many recent researchers have raised many concerns about deep learning, among which the most important is generalization. Despite numerous attempts, conventional statistical learning approaches have yet been able to provide a satisfactory explanation on why deep learning works. A recent line of works aims to address the problem by trying to predict the generalization performance through complexity measures. In this competition, we invite the community to propose complexity measures that can accurately predict generalization of models. A robust and general complexity measure would potentially lead to a better understanding of deep learning's underlying mechanism and behavior of deep models on unseen data, or shed light on better generalization bounds. All these outcomes will be important for making deep learning more robust and reliable.

Mahdi Haghifam, Gintare Karolina Dziugaite, Shay Moran et al.

We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from $d \log n +2$ to $O(d)$, where $n$ is the number of i.i.d. training examples. In fact, we exhibit VC classes for which the CMI of any proper learner cannot be bounded by any real-valued function of the VC dimension only.

Stanislav Fort, Gintare Karolina Dziugaite, Mansheej Paul et al.

In suitably initialized wide networks, small learning rates transform deep neural networks (DNNs) into neural tangent kernel (NTK) machines, whose training dynamics is well-approximated by a linear weight expansion of the network at initialization. Standard training, however, diverges from its linearization in ways that are poorly understood. We study the relationship between the training dynamics of nonlinear deep networks, the geometry of the loss landscape, and the time evolution of a data-dependent NTK. We do so through a large-scale phenomenological analysis of training, synthesizing diverse measures characterizing loss landscape geometry and NTK dynamics. In multiple neural architectures and datasets, we find these diverse measures evolve in a highly correlated manner, revealing a universal picture of the deep learning process. In this picture, deep network training exhibits a highly chaotic rapid initial transient that within 2 to 3 epochs determines the final linearly connected basin of low loss containing the end point of training. During this chaotic transient, the NTK changes rapidly, learning useful features from the training data that enables it to outperform the standard initial NTK by a factor of 3 in less than 3 to 4 epochs. After this rapid chaotic transient, the NTK changes at constant velocity, and its performance matches that of full network training in 15% to 45% of training time. Overall, our analysis reveals a striking correlation between a diverse set of metrics over training time, governed by a rapid chaotic to stable transition in the first few epochs, that together poses challenges and opportunities for the development of more accurate theories of deep learning.

Gintare Karolina Dziugaite, Shai Ben-David, Daniel M. Roy

To date, there has been no formal study of the statistical cost of interpretability in machine learning. As such, the discourse around potential trade-offs is often informal and misconceptions abound. In this work, we aim to initiate a formal study of these trade-offs. A seemingly insurmountable roadblock is the lack of any agreed upon definition of interpretability. Instead, we propose a shift in perspective. Rather than attempt to define interpretability, we propose to model the \emph{act} of \emph{enforcing} interpretability. As a starting point, we focus on the setting of empirical risk minimization for binary classification, and view interpretability as a constraint placed on learning. That is, we assume we are given a subset of hypothesis that are deemed to be interpretable, possibly depending on the data distribution and other aspects of the context. We then model the act of enforcing interpretability as that of performing empirical risk minimization over the set of interpretable hypotheses. This model allows us to reason about the statistical implications of enforcing interpretability, using known results in statistical learning theory. Focusing on accuracy, we perform a case analysis, explaining why one may or may not observe a trade-off between accuracy and interpretability when the restriction to interpretable classifiers does or does not come at the cost of some excess statistical risk. We close with some worked examples and some open problems, which we hope will spur further theoretical development around the tradeoffs involved in interpretability.

Gintare Karolina Dziugaite, Alexandre Drouin, Brady Neal et al.

One of the principal scientific challenges in deep learning is explaining generalization, i.e., why the particular way the community now trains networks to achieve small training error also leads to small error on held-out data from the same population. It is widely appreciated that some worst-case theories -- such as those based on the VC dimension of the class of predictors induced by modern neural network architectures -- are unable to explain empirical performance. A large volume of work aims to close this gap, primarily by developing bounds on generalization error, optimization error, and excess risk. When evaluated empirically, however, most of these bounds are numerically vacuous. Focusing on generalization bounds, this work addresses the question of how to evaluate such bounds empirically. Jiang et al. (2020) recently described a large-scale empirical study aimed at uncovering potential causal relationships between bounds/measures and generalization. Building on their study, we highlight where their proposed methods can obscure failures and successes of generalization measures in explaining generalization. We argue that generalization measures should instead be evaluated within the framework of distributional robustness.

Jonathan Frankle, Gintare Karolina Dziugaite, Daniel M. Roy et al.

Recent work has explored the possibility of pruning neural networks at initialization. We assess proposals for doing so: SNIP (Lee et al., 2019), GraSP (Wang et al., 2020), SynFlow (Tanaka et al., 2020), and magnitude pruning. Although these methods surpass the trivial baseline of random pruning, they remain below the accuracy of magnitude pruning after training, and we endeavor to understand why. We show that, unlike pruning after training, randomly shuffling the weights these methods prune within each layer or sampling new initial values preserves or improves accuracy. As such, the per-weight pruning decisions made by these methods can be replaced by a per-layer choice of the fraction of weights to prune. This property suggests broader challenges with the underlying pruning heuristics, the desire to prune at initialization, or both.

Gintare Karolina Dziugaite, Kyle Hsu, Waseem Gharbieh et al.

The dominant term in PAC-Bayes bounds is often the Kullback--Leibler divergence between the posterior and prior. For so-called linear PAC-Bayes risk bounds based on the empirical risk of a fixed posterior kernel, it is possible to minimize the expected value of the bound by choosing the prior to be the expected posterior, which we call the oracle prior on the account that it is distribution dependent. In this work, we show that the bound based on the oracle prior can be suboptimal: In some cases, a stronger bound is obtained by using a data-dependent oracle prior, i.e., a conditional expectation of the posterior, given a subset of the training data that is then excluded from the empirical risk term. While using data to learn a prior is a known heuristic, its essential role in optimal bounds is new. In fact, we show that using data can mean the difference between vacuous and nonvacuous bounds. We apply this new principle in the setting of nonconvex learning, simulating data-dependent oracle priors on MNIST and Fashion MNIST with and without held-out data, and demonstrating new nonvacuous bounds in both cases.

Mahdi Haghifam, Jeffrey Negrea, Ashish Khisti et al.

The information-theoretic framework of Russo and J. Zou (2016) and Xu and Raginsky (2017) provides bounds on the generalization error of a learning algorithm in terms of the mutual information between the algorithm's output and the training sample. In this work, we study the proposal, by Steinke and Zakynthinou (2020), to reason about the generalization error of a learning algorithm by introducing a super sample that contains the training sample as a random subset and computing mutual information conditional on the super sample. We first show that these new bounds based on the conditional mutual information are tighter than those based on the unconditional mutual information. We then introduce yet tighter bounds, building on the "individual sample" idea of Bu, S. Zou, and Veeravalli (2019) and the "data dependent" ideas of Negrea et al. (2019), using disintegrated mutual information. Finally, we apply these bounds to the study of Langevin dynamics algorithm, showing that conditioning on the super sample allows us to exploit information in the optimization trajectory to obtain tighter bounds based on hypothesis tests.

Elnaz Barshan, Marc-Etienne Brunet, Gintare Karolina Dziugaite

In this work, we focus on the use of influence functions to identify relevant training examples that one might hope "explain" the predictions of a machine learning model. One shortcoming of influence functions is that the training examples deemed most "influential" are often outliers or mislabelled, making them poor choices for explanation. In order to address this shortcoming, we separate the role of global versus local influence. We introduce RelatIF, a new class of criteria for choosing relevant training examples by way of an optimization objective that places a constraint on global influence. RelatIF considers the local influence that an explanatory example has on a prediction relative to its global effects on the model. In empirical evaluations, we find that the examples returned by RelatIF are more intuitive when compared to those found using influence functions.

Jonathan Frankle, Gintare Karolina Dziugaite, Daniel M. Roy et al.

We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a linearly connected region. We use this technique to study iterative magnitude pruning (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained in isolation to full accuracy. We find that these subnetworks only reach full accuracy when they are stable to SGD noise, which either occurs at initialization for small-scale settings (MNIST) or early in training for large-scale settings (ResNet-50 and Inception-v3 on ImageNet).

Jeffrey Negrea, Gintare Karolina Dziugaite, Daniel M. Roy

We propose to study the generalization error of a learned predictor $\hat h$ in terms of that of a surrogate (potentially randomized) predictor that is coupled to $\hat h$ and designed to trade empirical risk for control of generalization error. In the case where $\hat h$ interpolates the data, it is interesting to consider theoretical surrogate classifiers that are partially derandomized or rerandomized, e.g., fit to the training data but with modified label noise. We also show that replacing $\hat h$ by its conditional distribution with respect to an arbitrary $σ$-field is a convenient way to derandomize. We study two examples, inspired by the work of Nagarajan and Kolter (2019) and Bartlett et al. (2019), where the learned classifier $\hat h$ interpolates the training data with high probability, has small risk, and, yet, does not belong to a nonrandom class with a tight uniform bound on two-sided generalization error. At the same time, we bound the risk of $\hat h$ in terms of surrogates constructed by conditioning and denoising, respectively, and shown to belong to nonrandom classes with uniformly small generalization error.

Jeffrey Negrea, Mahdi Haghifam, Gintare Karolina Dziugaite et al.

In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-dependent estimates. Our approach is based on the variational characterization of mutual information and the use of data-dependent priors that forecast the mini-batch gradient based on a subset of the training samples. Our approach is broadly applicable within the information-theoretic framework of Russo and Zou (2015) and Xu and Raginsky (2017). Our bound can be tied to a measure of flatness of the empirical risk surface. As compared with other bounds that depend on the squared norms of gradients, empirical investigations show that the terms in our bounds are orders of magnitude smaller.

Chin-Wei Huang, Ahmed Touati, Pascal Vincent et al.

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner that adequately captures the dependencies among the various parameters. In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks. We apply our method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits. In all setups, our methods prove to be competitive with existing methods and better than the baselines.

Jonathan Frankle, Gintare Karolina Dziugaite, Daniel M. Roy et al.

Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroactively on small vision tasks. However, IMP fails on deeper networks, and proposed methods to prune before training or train pruned networks encounter similar scaling limitations. In this paper, we argue that these efforts have struggled on deeper networks because they have focused on pruning precisely at initialization. We modify IMP to search for subnetworks that could have been obtained by pruning early in training (0.1% to 7% through) rather than at iteration 0. With this change, it finds small subnetworks of deeper networks (e.g., 80% sparsity on Resnet-50) that can complete the training process to match the accuracy of the original network on more challenging tasks (e.g., ImageNet). In situations where IMP fails at iteration 0, the accuracy benefits of delaying pruning accrue rapidly over the earliest iterations of training. To explain these behaviors, we study subnetwork "stability," finding that - as accuracy improves in this fashion - IMP subnetworks train to parameters closer to those of the full network and do so with improved consistency in the face of gradient noise. These results offer new insights into the opportunity to prune large-scale networks early in training and the behaviors underlying the lottery ticket hypothesis

Gintare Karolina Dziugaite, Daniel M. Roy

The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult, especially when the data distribution is presumed to be unknown. We show how an ε-differentially private data-dependent prior yields a valid PAC-Bayes bound, and then show how non-private mechanisms for choosing priors can also yield generalization bounds. As an application of this result, we show that a Gaussian prior mean chosen via stochastic gradient Langevin dynamics (SGLD; Welling and Teh, 2011) leads to a valid PAC-Bayes bound given control of the 2-Wasserstein distance to an ε-differentially private stationary distribution. We study our data-dependent bounds empirically, and show that they can be nonvacuous even when other distribution-dependent bounds are vacuous.