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Probabilistic Methods · Bayesian Models and Methods

Song Bian, Xiating Ouyang, ZHIWEI FAN, Paris Koutris

We study the certifiable robustness of ML classifiers on dirty datasets that could contain missing values. A test point is certifiably robust for an ML classifier if the classifier returns the same prediction for that test point, regardless of which cleaned version (among exponentially many) of the dirty dataset the classifier is trained on. In this paper, we show theoretically that for Naive Bayes Classifiers (NBC) over dirty datasets with missing values: (i) there exists an efficient polynomial time algorithm to decide whether multiple input test points are all certifiably robust over a dirty dataset; and (ii) the data poisoning attack, which aims to make all input test points certifiably non-robust by inserting missing cells to the clean dataset, is in polynomial time for single test points but NP-complete for multiple test points. Extensive experiments demonstrate that our algorithms are efficient and outperform existing baselines.

Applications · Time Series

Yuxuan Bian, Xuan Ju, Jiangtong Li, Zhijian Xu, Dawei Cheng, Qiang Xu

In this study, we present $\text{aL\small{LM}4T\small{S}}$, an innovative framework that adapts Large Language Models (LLMs) for time-series representation learning. Central to our approach is that we reconceive time-series forecasting as a self-supervised, multi-patch prediction task, which, compared to traditional mask-and-reconstruction methods, captures temporal dynamics in patch representations more effectively. Our strategy encompasses two-stage training: (i). a causal continual pre-training phase on various time-series datasets, anchored on next patch prediction, effectively syncing LLM capabilities with the intricacies of time-series data; (ii). fine-tuning for multi-patch prediction in the targeted time-series context. A distinctive element of our framework is the patch-wise decoding layer, which departs from previous methods reliant on sequence-level decoding. Such a design directly transposes individual patches into temporal sequences, thereby significantly bolstering the model's proficiency in mastering temporal patch-based representations. $\text{aL\small{LM}4T\small{S}}$ demonstrates superior performance in several downstream tasks, proving its effectiveness in deriving temporal representations with enhanced transferability and marking a pivotal advancement in the adaptation of LLMs for time-series analysis.

Theory · Online Learning and Bandits

Neelkamal Bhuyan, Debankur Mukherjee, Adam Wierman

We study the smoothed online quadratic optimization (SOQO) problem where, at each round $t$, a player plays an action $x_t$ in response to a quadratic hitting cost and an additional squared $\ell_2$-norm cost for switching actions. This problem class has strong connections to a wide range of application domains including smart grid management, adaptive control, and data center management, where switching-efficient algorithms are highly sought after. We study the SOQO problem in both adversarial and stochastic settings, and in this process, perform the first stochastic analysis of this class of problems. We provide the online optimal algorithm when the minimizers of the hitting cost function evolve as a general stochastic process, which, for the case of martingale process, takes the form of a *distribution-agnostic dynamic interpolation algorithm* that we call Lazy Adaptive Interpolation (LAI). Next, we present the stochastic-adversarial trade-off by proving an $\Omega(T)$ expected regret for the adversarial optimal algorithm in the literature (ROBD) with respect to LAI and, a sub-optimal competitive ratio for LAI in the adversarial setting. Finally, we present a best-of-both-worlds algorithm that obtains a robust adversarial performance while simultaneously achieving a near-optimal stochastic performance.

Deep Learning · Generative Models and Autoencoders

Pratik Bhowal, Achint Soni, Sirisha Rambhatla

Despite not being designed for this purpose, the use of variational autoencoders (VAEs) has proven remarkably effective for disentangled representation learning (DRL). Recent research attributes this success to certain characteristics of the loss function that prevent latent space rotation, or hypothesize about the orthogonality properties of the decoder by drawing parallels with principal component analysis (PCA). This hypothesis, however, has only been tested experimentally for linear VAEs, and the theoretical justification still remains an open problem. Moreover, since real-world VAEs are often inherently non-linear due to the use of neural architectures, understanding DRL capabilities of real-world VAEs remains a critical task. Our work takes a step towards understanding disentanglement in real-world VAEs to theoretically establish how the orthogonality properties of the decoder promotes disentanglement in practical applications. Complementary to our theoretical contributions, our experimental results corroborate our analysis. Code is available at https://github.com/criticalml-uw/Disentanglement-in-VAE.

Applications · Robotics

Homanga Bharadhwaj

In this paper, we develop a structured critique of robotic simulations for real-world manipulation, by arguing that scaling simulators is neither necessary nor sufficient for making progress in general-purpose real-world robotic manipulation agents that are compliant with human preferences. With the ubiquity of robotic simulators, and recent efforts to scale them for diverse tasks, and at the same time the interest in generally capable real-world manipulation systems, we believe it is important to address the limitations of using simulation for real-world manipulation, so that as a community, we can focus our collective resources, energy, and time on approaches that have more principled odds of success. We further demonstrate the unique challenges that real-world manipulation presents, and show through examples and arguments why scaling simulation doesn't get us closer to solving these challenges required for diverse real-world deployment.

Optimization · Convex

Aleksandr Beznosikov, David Dobre, Gauthier Gidel

The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient is prohibitively expensive. In this paper, we present two new variants of the FW algorithms for stochastic finite-sum minimization. Our algorithms have the best convergence guarantees of existing stochastic FW approaches for both convex and non-convex objective functions. Our methods do not have the issue of permanently collecting large batches, which is common to many stochastic projection-free approaches. Moreover, our second approach does not require either large batches or full deterministic gradients, which is a typical weakness of many techniques for finite-sum problems. The faster theoretical rates of our approaches are confirmed experimentally.

Deep Learning · Large Language Models

Luca Beurer-Kellner, Marc Fischer, Martin Vechev

To ensure that text generated by large language models (LLMs) is in an expected format, constrained decoding methods propose to enforce strict formal language constraints during generation. However, as we show in this work, not only do such methods often incur performance overhead during generation, but many of them also significantly impair task accuracy, if they do not correctly align the underlying LLM sub-word vocabularies with external constraints. To address this, we present a novel decoding algorithm, DOMINO, that can enforce constraints in a fully subword-aligned fashion, while leveraging pre-computation and speculative decoding to achieve virtually no overhead and in some cases even almost 2$\times$ speedup over unconstrained decoding -- thereby outperforming existing approaches by a wide margin. We release DOMINO as open source at https://github.com/eth-sri/domino.

Theory · Reinforcement Learning and Planning

Michael Beukman, Samuel Coward, Michael Matthews, Mattie Fellows, Minqi Jiang, Michael Dennis, Jakob Foerster

In unsupervised environment design, reinforcement learning agents are trained on environment configurations (levels) generated by an adversary that maximises some objective. Regret is a commonly used objective that theoretically results in a minimax regret (MMR) policy with desirable robustness guarantees; in particular, the agent's maximum regret is bounded. However, once the agent reaches this regret bound on all levels, the adversary will only sample levels where regret cannot be further reduced. Although there may be possible performance improvements to be made outside of these regret-maximising levels, learning stagnates. In this work, we introduce *Bayesian level-perfect MMR* (BLP), a refinement of the minimax regret objective that overcomes this limitation. We formally show that solving for this objective results in a subset of MMR policies, and that BLP policies act consistently with a Perfect Bayesian policy over all levels. We further introduce an algorithm, *ReMiDi*, that results in a BLP policy at convergence. We empirically demonstrate that training on levels from a minimax regret adversary causes learning to prematurely stagnate, but that ReMiDi continues learning.

Reinforcement Learning · Multi-agent

Matteo Bettini, Ryan Kortvelesy, Amanda Prorok

The study of behavioral diversity in Multi-Agent Reinforcement Learning (MARL) is a nascent yet promising field. In this context, the present work deals with the question of how to control the diversity of a multi-agent system. With no existing approaches to control diversity to a set value, current solutions focus on blindly promoting it via intrinsic rewards or additional loss functions, effectively changing the learning objective and lacking a principled measure for it. To address this, we introduce Diversity Control (DiCo), a method able to control diversity to an exact value of a given metric by representing policies as the sum of a parameter-shared component and dynamically scaled per-agent components. By applying constraints directly to the policy architecture, DiCo leaves the learning objective unchanged, enabling its applicability to any actor-critic MARL algorithm. We theoretically prove that DiCo achieves the desired diversity, and we provide several experiments, both in cooperative and competitive tasks, that show how DiCo can be employed as a novel paradigm to increase performance and sample efficiency in MARL. Multimedia results are available on the paper's website: https://sites.google.com/view/dico-marl

Deep Learning · Large Language Models

Bertolotti Francesco, Walter Cazzola

In this work, we analyze both theoretically and empirically the effect of tied input-output embeddings—a popular technique that reduces the model size while often improving training. Interestingly, we found that this technique is connected to Harris (1954)’s distributional hypothesis—often portrayed by the famous Firth (1957)’s quote “a word is characterized by the company it keeps”. Specifically, our findings indicate that words (or, more broadly, symbols) with similar semantics tend to be encoded in similar input embeddings, while words that appear in similar contexts are encoded in similar output embeddings (thus explaining the semantic space arising in input and output embedding of foundational language models). As a consequence of these findings, the tying of the input and output embeddings is encouraged only when the distributional hypothesis holds for the underlying data. These results also provide insight into the embeddings of foundation language models (which are known to be semantically organized). Further, we complement the theoretical findings with several experiments supporting the claims.

Applications · Physics

Jules Berman, Benjamin Peherstorfer

This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions. The adaptation can be either purely data-driven or via an equation-driven variational approach that provides Galerkin-optimal approximations. Because CoLoRA approximates solution fields locally in time, the rank of the weights can be kept small, which means that only few training trajectories are required offline so that CoLoRA is well suited for data-scarce regimes. Predictions with CoLoRA are orders of magnitude faster than with classical methods and their accuracy and parameter efficiency is higher compared to other neural network approaches.

Social Aspects

Omri Ben-Dov, Jake Fawkes, Samira Samadi, Amartya Sanyal

Collective action in machine learning is the study of the control that a coordinated group can have over machine learning algorithms. While previous research has concentrated on assessing the impact of collectives against Bayes (sub-)optimal classifiers, this perspective is limited in that it does not account for the choice of learning algorithm. Since classifiers seldom behave like Bayes classifiers and are influenced by the choice of learning algorithms along with their inherent biases, in this work we initiate the study of how the choice of the learning algorithm plays a role in the success of a collective in practical settings. Specifically, we focus on distributionally robust optimization (DRO), popular for improving a worst group error, and on the ubiquitous stochastic gradient descent (SGD), due to its inductive bias for "simpler" functions. Our empirical results, supported by a theoretical foundation, show that the effective size and success of the collective are highly dependent on properties of the learning algorithm. This highlights the necessity of taking the learning algorithm into account when studying the impact of collective action in machine learning.

Nora Belrose, Quintin Pope, Lucia Quirke, Alex Mallen, Xiaoli Fern

The _distributional simplicity bias_ (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token $n$-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.

Social Aspects · Fairness, Equity, Justice and Safety

Ann-Kristin Becker, Oana Dumitrasc, Klaus Broelemann

We propose a standardized version of fairness measures for continuous scores with a reasonable interpretation based on the Wasserstein distance. Our measures are easily computable and well suited for quantifying and interpreting the strength of group disparities as well as for comparing biases across different models, datasets, or time points. We derive a link between the different families of existing fairness measures for scores and show that the proposed standardized fairness measures outperform ROC-based fairness measures because they are more explicit and can quantify significant biases that ROC-based fairness measures miss.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Yongqiang Cai

In recent years, deep learning-based sequence modelings, such as language models, have received much attention and success, which pushes researchers to explore the possibility of transforming non-sequential problems into a sequential form. Following this thought, deep neural networks can be represented as composite functions of a sequence of mappings, linear or nonlinear, where each composition can be viewed as a word. However, the weights of linear mappings are undetermined and hence require an infinite number of words. In this article, we investigate the finite case and constructively prove the existence of a finite vocabulary $V$=$\phi_i: \mathbb{R}^d \to \mathbb{R}^d | i=1,...,n$ with $n=O(d^2)$ for the universal approximation. That is, for any continuous mapping $f: \mathbb{R}^d \to \mathbb{R}^d$, compact domain $\Omega$ and $\varepsilon>0$, there is a sequence of mappings $\phi_{i_1}, ..., \phi_{i_m} \in V, m \in \mathbb{Z}^+$, such that the composition $\phi_{i_m} \circ ... \circ \phi_{i_1} $ approximates $f$ on $\Omega$ with an error less than $\varepsilon$. Our results demonstrate an unusual approximation power of mapping compositions and motivate a novel compositional model for regular languages.

Social Aspects · Fairness, Equity, Justice and Safety

Yahav Bechavod

We revisit the problem of online learning with individual fairness, where an online learner strives to maximize predictive accuracy while ensuring that similar individuals are treated similarly. We first extend the frameworks of Gillen et al. (2018); Bechavod et al. (2020), which rely on feedback from human auditors regarding fairness violations, to allow for auditing schemes that can aggregate feedback from any number of auditors, using a rich class we term monotone aggregation functions, for which we also prove a useful characterization. Using our generalized framework, we present an oracle-efficient algorithm guaranteeing a bound of $\mathcal{O}(T^\frac{3}{4})$ simultaneously for regret and number of fairness violations. We then study an online classification setting where label feedback is available for positively-predicted individuals only, and present an algorithm guaranteeing a bound of $\mathcal{O}(T^\frac{5}{6})$ simultaneously for regret and number of fairness violations. In both settings, our algorithms improve on the best known bounds for oracle-efficient algorithms. Furthermore, our algorithms offer significant improvements in computational efficiency, greatly reducing the number of required calls to an (offline) optimization oracle, as opposed to previous algorithms which required $T$ such calls every round.

Deep Learning · Generative Models and Autoencoders

Samyadeep Basu, Keivan Rezaei, Priyatham Kattakinda, Vlad Morariu, Nanxuan Zhao, Ryan A Rossi, Varun Manjunatha, Soheil Feizi

Identifying layers within text-to-image models which control visual attributes can facilitate efficient model editing through closed-form updates. Recent work, leveraging causal tracing show that early Stable-Diffusion variants confine knowledge primarily to the first layer of the CLIP text-encoder, while it diffuses throughout the UNet. Extending this framework, we observe that for recent models (e.g., SD-XL, DeepFloyd), causal tracing fails in pinpointing localized knowledge, highlighting challenges in model editing. To address this issue, we introduce the concept of mechanistic localization in text-to-image models, where knowledge about various visual attributes (e.g., "style", "objects", "facts") can be mechanistically localized to a small fraction of layers in the UNet, thus facilitating efficient model editing. We localize knowledge using our method LocoGen which measures the direct effect of intermediate layers to output generation by performing interventions in the cross-attention layers of the UNet. We then employ LocoEdit, a fast closed-form editing method across popular open-source text-to-image models (including the latest SD-XL) and explore the possibilities of neuron-level model editing. Using mechanistic localization, our work offers a better view of successes and failures in localization-based text-to-image model editing.

Miscellaneous Aspects of Machine Learning · Kernel methods

Daniel Barzilai, Ohad Shamir

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable setting of kernel regression. However, as we argue in detail, most past works on this topic either make unrealistic assumptions, or focus on a narrow problem setup. This work aims to provide a unified theory to upper bound the excess risk of kernel regression for nearly all common and realistic settings. When applied to common kernels, our results imply benign overfitting in high input dimensions, nearly tempered overfitting in fixed dimensions, and explicit convergence rates for regularized regression. As a by-product, we obtain time-dependent bounds for neural networks trained in the kernel regime. Our results rely on new relative perturbation bounds for the eigenvalues of kernel matrices, which may be of independent interest. These reveal a self-regularization phenomenon, whereby a heavy tail in the eigendecomposition of the kernel implicitly leads to good generalization.

Deep Learning · Generative Models and Autoencoders

Grigory Bartosh, Dmitry Vetrov, Christian Andersson Naesseth

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs through experiments on many image generation benchmarks, including MNIST, CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood, achieving state-of-the-art results on ImageNet and CelebA-HQ, and produces high-quality samples.

Social Aspects · Trustworthy Machine Learning

Brian Bartoldson, James Diffenderfer, Konstantinos Parasyris, Bhavya Kailkhura

This paper revisits the simple, long-studied, yet still unsolved problem of making image classifiers robust to imperceptible perturbations. Taking CIFAR10 as an example, SOTA clean accuracy is about $100$%, but SOTA robustness to $\ell_{\infty}$-norm bounded perturbations barely exceeds $70$%. To understand this gap, we analyze how model size, dataset size, and synthetic data quality affect robustness by developing the first scaling laws for adversarial training. Our scaling laws reveal inefficiencies in prior art and provide actionable feedback to advance the field. For instance, we discovered that SOTA methods diverge notably from compute-optimal setups, using excess compute for their level of robustness. Leveraging a compute-efficient setup, we surpass the prior SOTA with $20$% ($70$%) fewer training (inference) FLOPs. We trained various compute-efficient models, with our best achieving $74$% AutoAttack accuracy ($+3$% gain). However, our scaling laws also predict robustness slowly grows then plateaus at $90$%: dwarfing our new SOTA by scaling is impractical, and perfect robustness is impossible. To better understand this predicted limit, we carry out a small-scale human evaluation on the AutoAttack data that fools our top-performing model. Concerningly, we estimate that human performance also plateaus near $90$%, which we show to be attributable to $\ell_{\infty}$-constrained attacks' generation of invalid images not consistent with their original labels. Having characterized limiting roadblocks, we outline promising paths for future research.