OpenRaiser/Intern-Atlas huggingface dataset:
On the Learnability of Out-of-distribution Detection
Venue: Journal JMLR 2024
Year: 2024

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD) detection, where test data may come from classes that are unknown during training (i.e., OOD data). Due to the unavailability and diversity of OOD data, good generalization ability is crucial for effective OOD detection algorithms, and corresponding learning theory is still an open problem. To study the generalization of OOD detection, this paper investigates the probably approximately correct (PAC) learning theory of OOD detection that fits the commonly used evaluation metrics in the literature. First, we find a necessary condition for the learnability of OOD detection. Then, using this condition, we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating, we find that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation, we next give several necessary and sufficient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly, we offer theoretical support for representative OOD detection works based on our OOD theory.
Sharpness-Aware Minimization and the Edge of Stability
Venue: Journal JMLR 2024
Year: 2024

Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $η$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/η$, after which it fluctuates around this value. The quantity $2/η$ has been called the "edge of stability" based on consideration of a local quadratic approximation of the loss. We perform a similar calculation to arrive at an "edge of stability" for Sharpness-Aware Minimization (SAM), a variant of GD which has been shown to improve its generalization. Unlike the case for GD, the resulting SAM-edge depends on the norm of the gradient. Using three deep learning training tasks, we see empirically that SAM operates on the edge of stability identified by this analysis.
Geometric Learning with Positively Decomposable Kernels
Venue: Journal JMLR 2024
Year: 2024

Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite kernels are difficult to come by. In this case, we propose the use of reproducing kernel Krein space (RKKS) based methods, which require only kernels that admit a positive decomposition. We show that one does not need to access this decomposition in order to learn in RKKS. We then investigate the conditions under which a kernel is positively decomposable. We show that invariant kernels admit a positive decomposition on homogeneous spaces under tractable regularity assumptions. This makes them much easier to construct than positive-definite kernels, providing a route for learning with kernels for non-Euclidean data. By the same token, this provides theoretical foundations for RKKS-based methods in general.
Policy Gradient Methods in the Presence of Symmetries and State Abstractions
Venue: Journal JMLR 2024
Year: 2024

Reinforcement learning (RL) on high-dimensional and complex problems relies on abstraction for improved efficiency and generalization. In this paper, we study abstraction in the continuous-control setting, and extend the definition of Markov decision process (MDP) homomorphisms to the setting of continuous state and action spaces. We derive a policy gradient theorem on the abstract MDP for both stochastic and deterministic policies. Our policy gradient results allow for leveraging approximate symmetries of the environment for policy optimization. Based on these theorems, we propose a family of actor-critic algorithms that are able to learn the policy and the MDP homomorphism map simultaneously, using the lax bisimulation metric. Finally, we introduce a series of environments with continuous symmetries to further demonstrate the ability of our algorithm for action abstraction in the presence of such symmetries. We demonstrate the effectiveness of our method on our environments, as well as on challenging visual control tasks from the DeepMind Control Suite. Our method's ability to utilize MDP homomorphisms for representation learning leads to improved performance, and the visualizations of the latent space clearly demonstrate the structure of the learned abstraction.
aeon: a Python Toolkit for Learning from Time Series
Venue: Journal JMLR 2024
Year: 2024

aeon is a unified Python 3 library for all machine learning tasks involving time series. The package contains modules for time series forecasting, classification, extrinsic regression and clustering, as well as a variety of utilities, transformations and distance measures designed for time series data. aeon also has a number of experimental modules for tasks such as anomaly detection, similarity search and segmentation. aeon follows the scikit-learn API as much as possible to help new users and enable easy integration of aeon estimators with useful tools such as model selection and pipelines. It provides a broad library of time series algorithms, including efficient implementations of the very latest advances in research. Using a system of optional dependencies, aeon integrates a wide variety of packages into a single interface while keeping the core framework with minimal dependencies. The package is distributed under the 3-Clause BSD license and is available at https://github.com/ aeon-toolkit/aeon. This version was submitted to the JMLR journal on 02 Nov 2023 for v0.5.0 of aeon. At the time of this preprint aeon has released v0.9.0, and has had substantial changes.
Optimal Decision Tree and Adaptive Submodular Ranking with Noisy Outcomes
Venue: Journal JMLR 2024
Year: 2024

In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.e., decision tree) that identifies the true hypothesis. This optimization problem has been extensively studied under the assumption that each test generates a deterministic outcome. However, in numerous applications, for example, clinical trials, the outcomes may be uncertain, which renders the ideas from the deterministic setting invalid. In this work, we study a fundamental variant of the ODT problem in which some test outcomes are noisy, even in the more general case where the noise is persistent, i.e., repeating a test gives the same noisy output. Our approximation algorithms provide guarantees that are nearly best possible and hold for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades continuously with this number. We numerically evaluated our algorithms for identifying toxic chemicals and learning linear classifiers, and observed that our algorithms have costs very close to the information-theoretic minimum.
White-Box Transformers via Sparse Rate Reduction: Compression Is All There Is?
Venue: Journal JMLR 2024
Year: 2024

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .
Label Noise Robustness of Conformal Prediction
Venue: Journal JMLR 2024
Year: 2024

We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct uncertainty sets that correctly cover the unobserved noiseless ground truth labels. We further extend our theory and formulate the requirements for correctly controlling a general loss function, such as the false negative proportion, with noisy labels. Our theory and experiments suggest that conformal prediction and risk-controlling techniques with noisy labels attain conservative risk over the clean ground truth labels whenever the noise is dispersive and increases variability. In other adversarial cases, we can also correct for noise of bounded size in the conformal prediction algorithm in order to ensure achieving the correct risk of the ground truth labels without score or data regularity.
A Rainbow in Deep Network Black Boxes
Venue: Journal JMLR 2024
Year: 2024

A central question in deep learning is to understand the functions learned by deep networks. What is their approximation class? Do the learned weights and representations depend on initialization? Previous empirical work has evidenced that kernels defined by network activations are similar across initializations. For shallow networks, this has been theoretically studied with random feature models, but an extension to deep networks has remained elusive. Here, we provide a deep extension of such random feature models, which we call the rainbow model. We prove that rainbow networks define deterministic (hierarchical) kernels in the infinite-width limit. The resulting functions thus belong to a data-dependent RKHS which does not depend on the weight randomness. We also verify numerically our modeling assumptions on deep CNNs trained on image classification tasks, and show that the trained networks approximately satisfy the rainbow hypothesis. In particular, rainbow networks sampled from the corresponding random feature model achieve similar performance as the trained networks. Our results highlight the central role played by the covariances of network weights at each layer, which are observed to be low-rank as a result of feature learning.
Line Graph Vietoris-Rips Persistence Diagram for Topological Graph Representation Learning
Venue: Journal JMLR 2024
Year: 2024

While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the topological information of a graph using persistence diagrams. However, these attempts have faced the problem of losing node embedding information, which in turn prevents them from providing a more expressive graph representation. To tackle this issue, we shift our focus to edge filtration and introduce a novel edge filtration-based persistence diagram, named Topological Edge Diagram (TED), which is mathematically proven to preserve node embedding information as well as contain additional topological information. To implement TED, we propose a neural network based algorithm, named Line Graph Vietoris-Rips (LGVR) Persistence Diagram, that extracts edge information by transforming a graph into its line graph. Through LGVR, we propose two model frameworks that can be applied to any message passing GNNs, and prove that they are strictly more powerful than Weisfeiler-Lehman type colorings. Finally we empirically validate superior performance of our models on several graph classification and regression benchmarks.
BenchMARL: Benchmarking Multi-Agent Reinforcement Learning
Venue: Journal JMLR 2024
Year: 2024

The field of Multi-Agent Reinforcement Learning (MARL) is currently facing a reproducibility crisis. While solutions for standardized reporting have been proposed to address the issue, we still lack a benchmarking tool that enables standardization and reproducibility, while leveraging cutting-edge Reinforcement Learning (RL) implementations. In this paper, we introduce BenchMARL, the first MARL training library created to enable standardized benchmarking across different algorithms, models, and environments. BenchMARL uses TorchRL as its backend, granting it high performance and maintained state-of-the-art implementations while addressing the broad community of MARL PyTorch users. Its design enables systematic configuration and reporting, thus allowing users to create and run complex benchmarks from simple one-line inputs. BenchMARL is open-sourced on GitHub: https://github.com/facebookresearch/BenchMARL
Optimizing Noise for f-Differential Privacy via Anti-Concentration and Stochastic Dominance
Venue: Journal JMLR 2024
Year: 2024

In this paper, we establish anti-concentration inequalities for additive noise mechanisms which achieve $f$-differential privacy ($f$-DP), a notion of privacy phrased in terms of a tradeoff function $f$ which limits the ability of an adversary to determine which individuals were in the database. We show that canonical noise distributions (CNDs), proposed by Awan and Vadhan (2023), match the anti-concentration bounds at half-integer values, indicating that their tail behavior is near-optimal. We also show that all CNDs are sub-exponential, regardless of the $f$-DP guarantee. In the case of log-concave CNDs, we show that they are the stochastically smallest noise compared to any other noise distributions with the same privacy guarantee. In terms of integer-valued noise, we propose a new notion of discrete CND and prove that a discrete CND always exists, can be constructed by rounding a continuous CND, and that the discrete CND is unique when designed for a statistic with sensitivity 1. We further show that the discrete CND at sensitivity 1 is stochastically smallest compared to other integer-valued noises. Our theoretical results shed light on the different types of privacy guarantees possible in the $f$-DP framework and can be incorporated in more complex mechanisms to optimize performance.
PromptBench: A Unified Library for Evaluation of Large Language Models
Venue: Journal JMLR 2024
Year: 2024

The evaluation of large language models (LLMs) is crucial to assess their performance and mitigate potential security risks. In this paper, we introduce PromptBench, a unified library to evaluate LLMs. It consists of several key components that are easily used and extended by researchers: prompt construction, prompt engineering, dataset and model loading, adversarial prompt attack, dynamic evaluation protocols, and analysis tools. PromptBench is designed to be an open, general, and flexible codebase for research purposes that can facilitate original study in creating new benchmarks, deploying downstream applications, and designing new evaluation protocols. The code is available at: https://github.com/microsoft/promptbench and will be continuously supported.
Goal-Space Planning with Subgoal Models
Venue: Journal JMLR 2024
Year: 2024

This paper investigates a new approach to model-based reinforcement learning using background planning: mixing (approximate) dynamic programming updates and model-free updates, similar to the Dyna architecture. Background planning with learned models is often worse than model-free alternatives, such as Double DQN, even though the former uses significantly more memory and computation. The fundamental problem is that learned models can be inaccurate and often generate invalid states, especially when iterated many steps. In this paper, we avoid this limitation by constraining background planning to a set of (abstract) subgoals and learning only local, subgoal-conditioned models. This goal-space planning (GSP) approach is more computationally efficient, naturally incorporates temporal abstraction for faster long-horizon planning and avoids learning the transition dynamics entirely. We show that our GSP algorithm can propagate value from an abstract space in a manner that helps a variety of base learners learn significantly faster in different domains.
Sample Complexity of Neural Policy Mirror Descent for Policy Optimization on Low-Dimensional Manifolds
Venue: Journal JMLR 2024
Year: 2024

Policy gradient methods equipped with deep neural networks have achieved great success in solving high-dimensional reinforcement learning (RL) problems. However, current analyses cannot explain why they are resistant to the curse of dimensionality. In this work, we study the sample complexity of the neural policy mirror descent (NPMD) algorithm with deep convolutional neural networks (CNN). Motivated by the empirical observation that many high-dimensional environments have state spaces possessing low-dimensional structures, such as those taking images as states, we consider the state space to be a $d$-dimensional manifold embedded in the $D$-dimensional Euclidean space with intrinsic dimension $d\ll D$. We show that in each iteration of NPMD, both the value function and the policy can be well approximated by CNNs. The approximation errors are controlled by the size of the networks, and the smoothness of the previous networks can be inherited. As a result, by properly choosing the network size and hyperparameters, NPMD can find an $ε$-optimal policy with $\widetilde{O}(ε^{-\frac{d}α-2})$ samples in expectation, where $α\in(0,1]$ indicates the smoothness of environment. Compared to previous work, our result exhibits that NPMD can leverage the low-dimensional structure of state space to escape from the curse of dimensionality, explaining the efficacy of deep policy gradient algorithms.
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
Venue: Journal JMLR 2024
Year: 2024

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.
Pearl: A Production-Ready Reinforcement Learning Agent
Venue: Journal JMLR 2024
Year: 2024

Reinforcement learning (RL) is a versatile framework for optimizing long-term goals. Although many real-world problems can be formalized with RL, learning and deploying a performant RL policy requires a system designed to address several important challenges, including the exploration-exploitation dilemma, partial observability, dynamic action spaces, and safety concerns. While the importance of these challenges has been well recognized, existing open-source RL libraries do not explicitly address them. This paper introduces Pearl, a Production-Ready RL software package designed to embrace these challenges in a modular way. In addition to presenting benchmarking results, we also highlight examples of Pearl's ongoing industry adoption to demonstrate its advantages for production use cases. Pearl is open sourced on GitHub at github.com/facebookresearch/pearl and its official website is pearlagent.github.io.
Generalization on the Unseen, Logic Reasoning and Degree Curriculum
Venue: Journal JMLR 2024
Year: 2024

This paper considers the learning of logical (Boolean) functions with a focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for sparse functions and a class of network models including instances of Transformers, random features models, and linear networks, a min-degree-interpolator is learned on the unseen. More specifically, this means an interpolator of the training data that has minimal Fourier mass on the higher degree basis elements. These findings lead to two implications: (1) we provide an explanation to the length generalization problem for Boolean functions (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports. Finally, we discuss extensions to other models or non-sparse regimes where the min-degree bias may still occur or fade, as well as how it can be potentially corrected when undesirable.
Information Capacity Regret Bounds for Bandits with Mediator Feedback
Venue: Journal JMLR 2024
Year: 2024

This work addresses the mediator feedback problem, a bandit game where the decision set consists of a number of policies, each associated with a probability distribution over a common space of outcomes. Upon choosing a policy, the learner observes an outcome sampled from its distribution and incurs the loss assigned to this outcome in the present round. We introduce the policy set capacity as an information-theoretic measure for the complexity of the policy set. Adopting the classical EXP4 algorithm, we provide new regret bounds depending on the policy set capacity in both the adversarial and the stochastic settings. For a selection of policy set families, we prove nearly-matching lower bounds, scaling similarly with the capacity. We also consider the case when the policies' distributions can vary between rounds, thus addressing the related bandits with expert advice problem, which we improve upon its prior results. Additionally, we prove a lower bound showing that exploiting the similarity between the policies is not possible in general under linear bandit feedback. Finally, for a full-information variant, we provide a regret bound scaling with the information radius of the policy set.