ICML 2023 Papers

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the *data separation function*. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes *kinetic optimal* as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by Mannor & Shamir (2011) and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order $\sqrt{\alpha T}$, where $\alpha$ is the independence number of the graph, and $T$ is the time horizon. However, this is proven only when the number of rounds $T$ is larger than $\alpha^3$, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity $R^*$, called the *problem complexity*, and prove that the minimax regret is proportional to $R^*$ for any graph and time horizon $T$. Introducing an intricate exploration strategy, we define the Exp3-EX algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if $T$ is smaller than $\alpha^3$.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

We consider test-time adaptation (TTA), the task of adapting a trained model to an arbitrary test domain using unlabeled input data on-the-fly during testing. A common practice of TTA is to disregard data used in training due to large memory demand and privacy leakage. However, the training data are the only source of supervision. This motivates us to investigate a proper way of using them while minimizing the side effects. To this end, we propose two lightweight yet informative proxies of the training data and a TTA method fully exploiting them. One of the proxies is composed of a small number of images synthesized (hence, less privacy-sensitive) by data condensation which minimizes their domain-specificity to capture a general underlying structure over a wide spectrum of domains. Then, in TTA, they are translated into labeled test data by stylizing them to match styles of unlabeled test samples. This enables virtually supervised test-time training. The other proxy is inter-class relations of training data, which are transferred to target model during TTA. On four public benchmarks, our method outperforms the state-of-the-art ones at remarkably less computation and memory.

Large language models excel at a wide range of complex tasks. However, enabling general inference in the real world, e.g. for robotics problems, raises the challenge of grounding. We propose embodied language models to directly incorporate real-world continuous sensor modalities into language models and thereby establish the link between words and percepts. Input to our embodied language model are multimodal sentences that interleave visual, continuous state estimation, and textual input encodings. We train these encodings end-to-end, in conjunction with a pre-trained large language model, for multiple embodied tasks including sequential robotic manipulation planning, visual question answering, and captioning. Our evaluations show that PaLM-E, a single large embodied multimodal model, can address a variety of embodied reasoning tasks, from a variety of observation modalities, on multiple embodiments, and further, exhibits positive transfer: the model benefits from diverse joint training across internet-scale language, vision, and visual-language domains. Our largest model with 562B parameters, in addition to being trained on robotics tasks, is a visual-language generalist with state-of-the-art performance on OK-VQA, and retains generalist language capabilities with increasing scale.

Noisy-OR Bayesian Networks (BNs) are a family of probabilistic graphical models which express rich statistical dependencies in binary data. Variational inference (VI) has been the main method proposed to learn noisy-OR BNs with complex latent structures (Jaakkola & Jordan, 1999; Ji et al., 2020; Buhai et al., 2020). However, the proposed VI approaches either (a) use a recognition network with standard amortized inference that cannot induce "explaining-away"; or (b) assume a simple mean-field (MF) posterior which is vulnerable to bad local optima. Existing MF VI methods also update the MF parameters sequentially which makes them inherently slow. In this paper, we propose parallel max-product as an alternative algorithm for learning noisy-OR BNs with complex latent structures and we derive a fast stochastic training scheme that scales to large datasets. We evaluate both approaches on several benchmarks where VI is the state-of-the-art and show that our method (a) achieves better test performance than Ji et al. (2020) for learning noisy-OR BNs with hierarchical latent structures on large sparse real datasets; (b) recovers a higher number of ground truth parameters than Buhai et al. (2020) from cluttered synthetic scenes; and (c) solves the 2D blind deconvolution problem from Lazaro-Gredilla et al. (2021) and variants - including binary matrix factorization - while VI catastrophically fails and is up to two orders of magnitude slower.

In order to build artificial intelligence systems that can perceive and reason with human behavior in the real world, we must first design models that conduct complex spatio-temporal reasoning over motion sequences. Moving towards this goal, we propose the HumanMotionQA task to evaluate complex, multi-step reasoning abilities of models on long-form human motion sequences. We generate a dataset of question-answer pairs that require detecting motor cues in small portions of motion sequences, reasoning temporally about when events occur, and querying specific motion attributes. In addition, we propose NSPose, a neuro-symbolic method for this task that uses symbolic reasoning and a modular design to ground motion through learning motion concepts, attribute neural operators, and temporal relations. We demonstrate the suitability of NSPose for the HumanMotionQA task, outperforming all baseline methods.

The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident predictions, which leads to poor calibration. Recent efforts have sought to address this issue by focal loss to reduce over-confidence, but this approach can also lead to under-confident predictions. While different variants of focal loss have been explored, it is difficult to find a balance between over-confidence and under-confidence. In our work, we propose a new loss function by focusing on dual logits. Our method not only considers the ground truth logit, but also take into account the highest logit ranked after the ground truth logit. By maximizing the gap between these two logits, our proposed dual focal loss can achieve a better balance between over-confidence and under-confidence. We provide theoretical evidence to support our approach and demonstrate its effectiveness through evaluations on multiple models and datasets, where it achieves state-of-the-art performance. Code is available at https://github.com/Linwei94/DualFocalLoss

The success of deep learning is greatly attributed to stochastic gradient descent (SGD), yet it remains unclear how SGD finds well-generalized models. We demonstrate that SGD has an implicit regularization effect on the logit-weight Jacobian norm of neural networks. This regularization effect is weighted with the *impurity* of the probability output, and thus it is active in a certain phase of training. Moreover, based on these findings, we propose a novel optimization method that explicitly regularizes the Jacobian norm, which leads to similar performance as other state-of-the-art sharpness-aware optimization methods.

The learnware paradigm aims to build a learnware market containing numerous learnwares, each of which is a well-performing machine learning model with a corresponding specification to describe its functionality so that future users can identify useful models for reuse according to their own requirements. With the learnware paradigm, model developers can spontaneously submit models to the market without leaking data privacy, and users can leverage models in the market to accomplish different machine learning tasks without having to build models from scratch. Recent studies have attempted to realize the model specification through Reduced Kernel Mean Embedding (RKME). In this paper, we make an attempt to improve the effectiveness of RKME specification for heterogeneous label spaces, where the learnware market does not contain a model that has the same label space as the user's task, by considering a class-specific model specification explicitly, along with a class-wise learnware identification method. Both theoretical and empirical analyses show that our proposal can quickly and accurately find useful learnwares that satisfy users' requirements. Moreover, we find that for a specific task, reusing a small model identified via the specification performs better than directly reusing a pre-trained generic big model.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by ``projecting'' the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

In multi-agent reinforcement learning (MARL), independent learning (IL) often shows remarkable performance and easily scales with the number of agents. Yet, using IL can be inefficient and runs the risk of failing to successfully train, particularly in scenarios that require agents to coordinate their actions. Using centralised learning (CL) enables MARL agents to quickly learn how to coordinate their behaviour but employing CL everywhere is often prohibitively expensive in real-world applications. Besides, using CL in value-based methods often needs strong representational constraints (e.g. individual-global-max condition) that can lead to poor performance if violated. In this paper, we introduce a novel plug & play IL framework named Multi-Agent Network Selection Algorithm (MANSA) which selectively employs CL only at states that require coordination. At its core, MANSA has an additional agent that uses switching controls to quickly learn the best states to activate CL during training, using CL only where necessary and vastly reducing the computational burden of CL. Our theory proves MANSA preserves cooperative MARL convergence properties, boosts IL performance and can optimally make use of a fixed budget on the number CL calls. We show empirically in Level-based Foraging (LBF) and StarCraft Multi-agent Challenge (SMAC) that MANSA achieves fast, superior and more reliable performance while making 40% fewer CL calls in SMAC and using CL at only 1% CL calls in LBF.

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetrics structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric models to learn optimal value functions. Distinct from prior approaches, the QRL objective is specifically designed for quasimetrics, and provides strong theoretical recovery guarantees. Empirically, we conduct thorough analyses on a discretized MountainCar environment, identifying properties of QRL and its advantages over alternatives. On offline and online goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and performance, across both state-based and image-based observations.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by $1$, we show that our algorithm only needs to explore $\tilde O\left( d^2\varepsilon^{-2}\right)$ episodes to find an $\varepsilon$-optimal policy, where $d$ is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is "horizon-free''. In addition, we provide an $\Omega\left(d^2\varepsilon^{-2}\right)$ sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

Evaluating the performance of machine learning models under distribution shifts is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of *disagreement*, the degree to which two models trained with different randomness differ on the same input, is a key to tackling this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the *disagreement-on-the-line* phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.

Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks can achieve low reconstruction error even when the latent representation is distorted. To avoid such misleading visualizations, we propose first a differential geometric perspective on the decoder, leading to insightful diagnostics for an embedding's distortion, and second a new regularizer mitigating such distortion. Our ``Geometric Autoencoder'' avoids stretching the embedding spuriously, so that the visualization captures the data structure more faithfully. It also flags areas where little distortion could not be achieved, thus guarding against misinterpretation.

Recently, Language Models (LMs) instruction-tuned on multiple tasks, also known as multitask-prompted fine-tuning (MT), have shown capabilities to generalize to unseen tasks. Previous work has shown that scaling the number of finetuning datasets and instructions is the key component in making stronger MT LMs. In this work, we report surprising findings that show an expert LM trained on just a single task can outperform an MT LM trained with 300+ different tasks on 11 different unseen datasets and on 13 datasets of the BIG-bench benchmark by an average of 3.20% and 1.29%, respectively. This finding casts doubt on the previously held belief that simply scaling the number of tasks makes stronger MT LMs. Leveraging this finding, we further show that this distributed approach of training multiple expert LMs instead of a single MT LM for zero-shot inference possesses many benefits including (1) avoiding negative task transfer that often occurs during instruction tuning, (2) being able to continually learn new tasks without having to re-train on previous tasks to avoid catastrophic forgetting, and (3) showing compositional capabilities when merging individual experts together.

Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel data-driven supervision for tabular data by introducing a characteristic -- scale -- as data labels. By representing varied sub-vectors of data instances, we define scale as the relationship between the dimensionality of original sub-vectors and that of representations. Scales serve as labels attached to transformed representations, thus offering ample labeled data for neural network training. This paper further proposes a scale learning-based anomaly detection method. Supervised by the learning objective of scale distribution alignment, our approach learns the ranking of representations converted from varied subspaces of each data instance. Through this proxy task, our approach models inherent regularities and patterns within data, which well describes data "normality". Abnormal degrees of testing instances are obtained by measuring whether they fit these learned patterns. Extensive experiments show that our approach leads to significant improvement over state-of-the-art generative/contrastive anomaly detection methods.

Existing theoretical studies on offline reinforcement learning (RL) mostly consider a dataset sampled directly from the target task. In practice, however, data often come from several heterogeneous but related sources. Motivated by this gap, this work aims at rigorously understanding offline RL with multiple datasets that are collected from randomly perturbed versions of the target task instead of from itself. An information-theoretic lower bound is derived, which reveals a necessary requirement on the number of involved sources in addition to that on the number of data samples. Then, a novel HetPEVI algorithm is proposed, which simultaneously considers the sample uncertainties from a finite number of data samples per data source and the source uncertainties due to a finite number of available data sources. Theoretical analyses demonstrate that HetPEVI can solve the target task as long as the data sources collectively provide a good data coverage. Moreover, HetPEVI is demonstrated to be optimal up to a polynomial factor of the horizon length. Finally, the study is extended to offline Markov games and offline robust RL, which demonstrates the generality of the proposed designs and theoretical analyses.