ICML 2024 Papers

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein barycenter, which is the primal focus of our work. By building upon the dual formulation of Optimal Transport (OT), we propose a new scalable approach for solving the Wasserstein barycenter problem. Our methodology is based on the recent Neural OT solver: it has bi-level adversarial learning objective and works for general cost functions. These are key advantages of our method since the typical adversarial algorithms leveraging barycenter tasks utilize tri-level optimization and focus mostly on quadratic cost. We also establish theoretical error bounds for our proposed approach and showcase its applicability and effectiveness in illustrative scenarios and image data setups. Our source code is available at https://github.com/justkolesov/NOTBarycenters.

We study robust Markov games (RMG) with $s$-rectangular uncertainty. We show a general equivalence between computing a robust Nash equilibrium (RNE) of a $s$-rectangular RMG and computing a Nash equilibrium (NE) of an appropriately constructed regularized MG. The equivalence result yields a planning algorithm for solving $s$-rectangular RMGs, as well as provable robustness guarantees for policies computed using regularized methods. However, we show that even for just reward-uncertain two-player zero-sum matrix games, computing an RNE is PPAD-hard. Consequently, we derive a special uncertainty structure called efficient player-decomposability and show that RNE for two-player zero-sum RMG in this class can be provably solved in polynomial time. This class includes commonly used uncertainty sets such as $L_1$ and $L_\infty$ ball uncertainty sets.

The White House Executive Order on Artificial Intelligence highlights the risks of large language models (LLMs) empowering malicious actors in developing biological, cyber, and chemical weapons. To measure these risks, government institutions and major AI labs are developing evaluations for hazardous capabilities in LLMs. However, current evaluations are private and restricted to a narrow range of malicious use scenarios, which limits further research into reducing malicious use. To fill these gaps, we release the Weapons of Mass Destruction Proxy (WMDP) benchmark, a dataset of 3,668 multiple-choice questions that serve as a proxy measurement of hazardous knowledge in biosecurity, cybersecurity, and chemical security. To guide progress on unlearning, we develop RMU, a state-of-the-art unlearning method based on controlling model representations. RMU reduces model performance on WMDP while maintaining general capabilities in areas such as biology and computer science, suggesting that unlearning may be a concrete path towards reducing malicious use from LLMs. We release our benchmark and code publicly at https://wmdp.ai.

As transformer-based language models are trained on increasingly large datasets and with vast numbers of parameters, finding more efficient alternatives to the standard Transformer has become very valuable. While many efficient Transformers and Transformer alternatives have been proposed, none provide theoretical guarantees that they are a suitable replacement for the standard Transformer. This makes it challenging to identify when to use a specific model and what directions to prioritize for further investigation. In this paper, we aim to understand the capabilities and limitations of efficient Transformers, specifically the Sparse Transformer and the Linear Transformer. We focus on their reasoning capability as exhibited by Chain-of-Thought (CoT) prompts and follow previous works to model them as Dynamic Programming (DP) problems. Our results show that while these models are expressive enough to solve general DP tasks, contrary to expectations, they require a model size that scales with the problem size. Nonetheless, we identify a class of DP problems for which these models can be more efficient than the standard Transformer. We confirm our theoretical results through experiments on representative DP tasks, adding to the understanding of efficient Transformers' practical strengths and weaknesses.

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

Simplicial neural network models are becoming popular for processing and analyzing higher-order graph data, but they suffer from high training complexity and dependence on task-specific labels. To address these challenges, we propose simplicial scattering networks (SSNs), a parameter-free model inspired by scattering transforms designed to extract task-agnostic features from simplicial complex data without labels in a principled manner. Specifically, we propose a simplicial scattering transform based on random walk matrices for various adjacencies underlying a simplicial complex. We then use the simplicial scattering transform to construct a deep filter bank network that captures high-frequency information at multiple scales. The proposed simplicial scattering transform possesses properties such as permutation invariance, robustness to perturbations, and expressivity. We theoretically prove that including higher-order information improves the robustness of SSNs to perturbations. Empirical evaluations demonstrate that SSNs outperform existing simplicial or graph neural models in many tasks like node classification, simplicial closure, graph classification, trajectory prediction, and simplex prediction while being computationally efficient.

In this paper, we examine the long-run distribution of stochastic gradient descent (SGD) in general, non-convex problems. Specifically, we seek to understand which regions of the problem's state space are more likely to be visited by SGD, and by how much. Using an approach based on the theory of large deviations and randomly perturbed dynamical systems, we show that the long-run distribution of SGD resembles the Boltzmann-Gibbs distribution of equilibrium thermodynamics with temperature equal to the method's step-size and energy levels determined by the problem's objective and the statistics of the noise. In particular, we show that, in the long run, (*a*) the problem's critical region is visited exponentially more often than any non-critical region; (*b*) the iterates of SGD are exponentially concentrated around the problem's minimum energy state (which does not always coincide with the global minimum of the objective); (*c*) all other connected components of critical points are visited with frequency that is exponentially proportional to their energy level; and, finally, (*d*) any component of local maximizers or saddle points is "dominated" by a component of local minimizers which is visited exponentially more often.

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.

Humans are able to segment images effortlessly without supervision using perceptual grouping. Here, we propose a counter-intuitive computational approach to solving unsupervised perceptual grouping and segmentation: that they arise *because* of neural noise, rather than in spite of it. We (1) mathematically demonstrate that under realistic assumptions, neural noise can be used to separate objects from each other; (2) that adding noise in a DNN enables the network to segment images even though it was never trained on any segmentation labels; and (3) that segmenting objects using noise results in segmentation performance that aligns with the perceptual grouping phenomena observed in humans, and is sample-efficient. We introduce the Good Gestalt (GG) datasets --- six datasets designed to specifically test perceptual grouping, and show that our DNN models reproduce many important phenomena in human perception, such as illusory contours, closure, continuity, proximity, and occlusion. Finally, we (4) show that our model improves performance on our GG datasets compared to other tested unsupervised models by $24.9$%. Together, our results suggest a novel unsupervised segmentation method requiring few assumptions, a new explanation for the formation of perceptual grouping, and a novel potential benefit of neural noise.

Non-convex minimization problems are universally considered hard, and even guaranteeing that a computed solution is locally minimizing is known to be NP-hard. In this general context, our paper focuses on the problem of finding stationary points that satisfy an approximate second-order optimality condition, which serves to exclude strict saddles and other non-minimizing stationary points. Our main result is that the problem of finding approximate second-order stationary points (SOSPs) is PLS-complete, i.e., of the same complexity as the problem of finding first-order stationary points (FOSPs), thus resolving an open question in the field. In particular, our results imply that, under the widely believed complexity conjecture that PLS $\neq$ FNP, finding approximate SOSPs in unconstrained domains is *easier* than in constrained domains, which is known to be NP-hard. This comes in stark contrast with earlier results which implied that, unless PLS = CLS, finding approximate FOSPs in unconstrained domains is *harder* than in constrained domains.

We present quantum algorithms for sampling from possibly non-logconcave probability distributions expressed as $\pi(x) \propto \exp(-\beta f(x))$ as well as quantum algorithms for estimating the partition function for such distributions. We also incorporate a stochastic gradient oracle that implements the quantum walk operators inexactly by only using mini-batch gradients when $f$ can be written as a finite sum. One challenge of quantizing the resulting Markov chains is that they do not satisfy the detailed balance condition in general. Consequently, the mixing time of the algorithm cannot be expressed in terms of the spectral gap of the transition density matrix, making the quantum algorithms nontrivial to analyze. We overcame these challenges by first building a reference reversible Markov chain that converges to the target distribution, then controlling the discrepancy between our algorithm's output and the target distribution by using the reference Markov chain as a bridge to establish the total complexity. Our quantum algorithms exhibit polynomial speedups in terms of dimension or precision dependencies when compared to best-known classical algorithms under similar assumptions.

We introduce LaGTran, a novel framework that utilizes text supervision to guide robust transfer of discriminative knowledge from labeled source to unlabeled target data with domain gaps. While unsupervised adaptation methods have been established to address this problem, they show limitations in handling challenging domain shifts due to their exclusive operation within the pixel-space. Motivated by our observation that semantically richer text modality has more favorable transfer properties, we devise a transfer mechanism to use a source-trained text-classifier to generate predictions on the target text descriptions, and utilize these predictions as supervision for the corresponding images. Our approach driven by language guidance is surprisingly easy and simple, yet significantly outperforms all prior approaches on challenging datasets like GeoNet and DomainNet, validating its extreme effectiveness. To further extend the scope of our study beyond images, we introduce a new benchmark called Ego2Exo to study ego-exo transfer in videos and find that our language-aided approach LaGTran yields significant gains in this highly challenging and non-trivial transfer setting. Code, models, and proposed datasets are publicly available at https://tarun005.github.io/lagtran/.

Unsupervised Contrastive learning has gained prominence in fields such as vision, and biology, leveraging predefined positive/negative samples for representation learning. Data augmentation, categorized into hand-designed and model-based methods, has been identified as a crucial component for enhancing contrastive learning. However, hand-designed methods require human expertise in domain-specific data while sometimes distorting the meaning of the data. In contrast, generative model-based approaches usually require supervised or large-scale external data, which has become a bottleneck constraining model training in many domains. To address the problems presented above, this paper proposes DiffAug, a novel unsupervised contrastive learning technique with diffusion mode-based positive data generation. DiffAug consists of a semantic encoder and a conditional diffusion model; the conditional diffusion model generates new positive samples conditioned on the semantic encoding to serve the training of unsupervised contrast learning. With the help of iterative training of the semantic encoder and diffusion model, DiffAug improves the representation ability in an uninterrupted and unsupervised manner. Experimental evaluations show that DiffAug outperforms hand-designed and SOTA model-based augmentation methods on DNA sequence, visual, and bio-feature datasets. The code for review is released at [DiffAug CODE](https://github.com/zangzelin/code_diffaug).

We study the facility location problem in the dynamic setting, where the goal is to efficiently process an intermixed sequence of point insertions and deletions while maintaining a high quality and stable solution. Although the problem has been studied in the context of general metrics and low-dimensional spaces, much remains unknown concerning dynamic facility location in high dimensional spaces. In this work, we present the first fully dynamic algorithm for facility location in high-dimensional spaces $\mathbb{R}^{d}$. For any $c \geq 1$, our algorithm achieves $O(c)$-approximation, supports point updates in $\tilde{O}(\mathrm{poly}(d)n^{1/c + o(1)})$ amortized time and incurs $O(1)$ amortized recourse. More generally, our result shows that despite the linear-time lower bound on the update time for general metrics, it is possible to achieve sub-linear update times for metric spaces that admit dynamic nearest neighbour oracles. Experiments on real datasets confirm that our algorithm achieves high-quality solutions with low running time, and incurs minimal recourse.

Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural representations. Such subsets also have a natural algebraic structure including operations (e.g., union) and corresponding laws (e.g., associativity). How can we learn to "union" two sets using only their latent embeddings while respecting associativity? We propose a general procedure for parameterizing latent space operations that are provably consistent with the laws on the input space. This is achieved by learning a bijection from the latent space to a carefully designed *mirrored algebra* which is constructed on Euclidean space in accordance with desired laws. We evaluate these *structural transport nets* for a range of mirrored algebras against baselines that operate directly on the latent space. Our experiments provide strong evidence that respecting the underlying algebraic structure of the input space is key for learning accurate and self-consistent operations.

Suppose a self-driving car is crashing into pedestrians, or a chatbot is instructing its users to conduct criminal wrongdoing; the stakeholders of such products will undoubtedly want to patch these catastrophic errors as soon as possible. To address such concerns, *Model Editing:* the study of efficiently patching model behaviors without significantly altering their general performance, has seen considerable activity, with hundreds of editing techniques developed in various domains such as CV and NLP. However, **the graph learning community has objectively fallen behind with only a few Graph Neural Network-compatible — and just one GNN-specific — model editing methods available**, where all of which are limited in their practical scope. We argue that the impracticality of these methods lies in their lack of *Sequential Editing Robustness:* the ability to edit multiple errors sequentially, and therefore fall short in effectiveness, as this approach mirrors how errors are discovered and addressed in the real world. In this paper, we delve into the specific reasons behind the difficulty of editing GNNs in succession and observe the root cause to be model overfitting. We subsequently propose a simple yet effective solution — SEED-GNN — by leveraging overfit-prevention techniques in a GNN-specific context to derive the first and only GNN model editing method that scales practically. Additionally, we formally frame the task paradigm of GNN editing and hope to inspire future research in this crucial but currently overlooked field. Please refer to our [GitHub repository](https://github.com/henryzhongsc/gnn_editing) for code and checkpoints.

Learning with expert advice and multi-armed bandit are two classic online decision problems which differ on how the information is observed in each round of the game. We study a family of problems interpolating the two. For a vector $\mathbf{m}=(m_1,\dots,m_K)\in \mathbb N^K$, an instance of $\mathbf m$-MAB indicates that the arms are partitioned into $K$ groups and the $i$-th group contains $m_i$ arms. Once an arm is pulled, the losses of all arms in the same group are observed. We prove tight minimax regret bounds for $\mathbf m$-MAB and design an optimal PAC algorithm for its pure exploration version, $\mathbf m$-BAI, where the goal is to identify the arm with minimum loss with as few rounds as possible. We show that the minimax regret of $\mathbf m$-MAB is $\Theta\left(\sqrt{T\sum_{k=1}^K\log (m_k+1)}\right)$ and the minimum number of pulls for an $(\varepsilon,0.05)$-PAC algorithm of $\mathbf m$-BAI is $\Theta\left(\frac{1}{\varepsilon^2}\cdot \sum_{k=1}^K\log (m_k+1)\right)$. Both our upper bounds and lower bounds for $\mathbf m$-MAB can be extended to a more general setting, namely the bandit with graph feedback, in terms of the *clique cover* and related graph parameters. As consequences, we obtained tight minimax regret bounds for several families of feedback graphs.

Deep neural networks (DNNs) have become pivotal in machine learning, but the impact of weight precision, such as in networks with rectified linear units (ReLU), remains underexplored. We analytically investigate the interplay of three key factors: the precision of ReLU network weights, the number of neurons, and the time of the preprocessing algorithm that generates the network description. Our study, which, to the best of our knowledge, is the first formal work on weight precision, yields three main results. (1) We present an exponential time preprocessing algorithm that showcases the possibility of trading ReLU nodes for weight precision. Specifically, our method achieves an exponential reduction in neuron count when computing any function of high complexity with boolean input encoding. What is the implication of the above result in theoretical and practical works? (2) In theory of computing, in general, there is no free lunch. In our case, if you significantly reduce the number of neurons then you should pay the cost in weight precision. To address this, we introduce a notion of network size that considers weight precision in addition to the network's number of neurons. We establish that under this redefined notion of network size, it is generally impossible to exchange neurons for weight precision in ReLU networks of the same (redefined) size. (3) In practice, we show that high weight precision alone cannot help in reducing the neuron count. If instead of our exponential time preprocessing algorithm one uses any polynomial time algorithm, then it is impossible to non-trivially reduce the neuron count, regardless of the high weight precision.

We propose TopDis (Topological Disentanglement), a method for learning disentangled representations via adding a multi-scale topological loss term. Disentanglement is a crucial property of data representations substantial for the explainability and robustness of deep learning models and a step towards high-level cognition. The state-of-the-art methods are based on VAE and encourage the joint distribution of latent variables to be factorized. We take a different perspective on disentanglement by analyzing topological properties of data manifolds. In particular, we optimize the topological similarity for data manifolds traversals. To the best of our knowledge, our paper is the first one to propose a differentiable topological loss for disentanglement learning. Our experiments have shown that the proposed TopDis loss improves disentanglement scores such as MIG, FactorVAE score, SAP score, and DCI disentanglement score with respect to state-of-the-art results while preserving the reconstruction quality. Our method works in an unsupervised manner, permitting us to apply it to problems without labeled factors of variation. The TopDis loss works even when factors of variation are correlated. Additionally, we show how to use the proposed topological loss to find disentangled directions in a trained GAN.