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Exact computation of various machine learning explanations requires numerous model evaluations and in extreme cases becomes impractical. The computational cost of approximation increases with an ever-increasing size of data and model parameters. Many heuristics have been proposed to approximate post-hoc explanations efficiently. This paper shows that the standard i.i.d. sampling used in a broad spectrum of algorithms for explanation estimation leads to an approximation error worthy of improvement. To this end, we introduce Compress Then Explain (CTE), a new paradigm for more efficient and accurate explanation estimation. CTE uses distribution compression through kernel thinning to obtain a data sample that best approximates the marginal distribution. We show that CTE improves the estimation of removal-based local and global explanations with negligible computational overhead. It often achieves an on-par explanation approximation error using 2-3x less samples, i.e. requiring 2-3x less model evaluations. CTE is a simple, yet powerful, plug-in for any explanation method that now relies on i.i.d. sampling.

Recent work on discrete speech tokenization has paved the way for models that can seamlessly perform multiple tasks across modalities, e.g., speech recognition, text to speech, speech to speech translation. Moreover, large language models (LLMs) pretrained from vast text corpora contain rich linguistic information that can improve accuracy in a variety of tasks. In this paper, we present a decoder-only Discrete Multimodal Language Model (DMLM), which can be flexibly applied to multiple tasks (ASR, T2S, S2TT, etc.) and modalities (text, speech, vision). We explore several critical aspects of discrete multi-modal models, including the loss function, weight initialization, mixed training supervision, and codebook. Our results show that DMLM benefits significantly, across multiple tasks and datasets, from a combination of supervised and unsupervised training. Moreover, for ASR, it benefits from initializing DMLM from a pretrained LLM, and from a codebook derived from Whisper activations.

Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that quantifies how different a model's prediction is from the unknown ground truth value. Essentially, these functions determine the shape and the size of the conformal prediction regions. While prior work has gone into creating score functions that produce multi-model prediction regions, such regions are generally too complex for use in downstream planning and control problems. We propose a method that optimizes parameterized \emph{shape template functions} over calibration data, which results in non-conformity score functions that produce prediction regions with minimum volume. Our approach results in prediction regions that are \emph{multi-modal}, so they can properly capture residuals of distributions that have multiple modes, and \emph{practical}, so each region is convex and can be easily incorporated into downstream tasks, such as a motion planner using conformal prediction regions. Our method applies to general supervised learning tasks, while we illustrate its use in time-series prediction. We provide a toolbox and present illustrative case studies of F16 fighter jets and autonomous vehicles, showing an up to $68\%$ reduction in prediction region area compared to a circular baseline region.

Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian matrices and establish its convergence. The improved version with elimination strategy is proposed to reduce the computational time. Especially, we present a novel three-step Jacobi method to compute such eigenvalues which have identical standard parts but different dual parts. We prove that the proposed three-step Jacobi method terminates after at most finite iterations and can provide $\epsilon$-approximation of eigenvalue. To the best of our knowledge, both the power method and the Rayleigh quotient iteration method can not handle such eigenvalue problem in this scenario. Numerical experiments illustrate the proposed Jacobi-type algorithms are effective and stable, and also outperform the power method and the Rayleigh quotient iteration method.

Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex network architectures that involve graphs, attention layers, and hard pruning steps. Here, we propose a simpler network architecture based on Deep Sets. Given a collection of point matches extracted from two images, our method identifies outlier point matches and models the displacement noise in inlier matches. A weighted DLT module uses these predictions to regress the essential matrix. Our network achieves accurate recovery that is superior to existing networks with significantly more complex architectures.

In the context of machine unlearning, the primary challenge lies in effectively removing traces of private data from trained models while maintaining model performance and security against privacy attacks like membership inference attacks. Traditional gradient-based unlearning methods often rely on extensive historical gradients, which becomes impractical with high unlearning ratios and may reduce the effectiveness of unlearning. Addressing these limitations, we introduce Mini-Unlearning, a novel approach that capitalizes on a critical observation: unlearned parameters correlate with retrained parameters through contraction mapping. Our method, Mini-Unlearning, utilizes a minimal subset of historical gradients and leverages this contraction mapping to facilitate scalable, efficient unlearning. This lightweight, scalable method significantly enhances model accuracy and strengthens resistance to membership inference attacks. Our experiments demonstrate that Mini-Unlearning not only works under higher unlearning ratios but also outperforms existing techniques in both accuracy and security, offering a promising solution for applications requiring robust unlearning capabilities.

Extracting time-varying latent variables from computational cognitive models is a key step in model-based neural analysis, which aims to understand the neural correlates of cognitive processes. However, existing methods only allow researchers to infer latent variables that explain subjects' behavior in a relatively small class of cognitive models. For example, a broad class of relevant cognitive models with analytically intractable likelihood is currently out of reach from standard techniques, based on Maximum a Posteriori parameter estimation. Here, we present an approach that extends neural Bayes estimation to learn a direct mapping between experimental data and the targeted latent variable space using recurrent neural networks and simulated datasets. We show that our approach achieves competitive performance in inferring latent variable sequences in both tractable and intractable models. Furthermore, the approach is generalizable across different computational models and is adaptable for both continuous and discrete latent spaces. We then demonstrate its applicability in real world datasets. Our work underscores that combining recurrent neural networks and simulation-based inference to identify latent variable sequences can enable researchers to access a wider class of cognitive models for model-based neural analyses, and thus test a broader set of theories.

Distributed systems can be subject to various kinds of partial failures, therefore building fault-tolerance or failure mitigation mechanisms for distributed systems remains an important domain of research. In this paper, we present a calculus to formally model distributed systems subject to crash failures with recovery. The recovery model considered in the paper is weak, in the sense that it makes no assumption on the exact state in which a failed node resumes its execution, only its identity has to be distinguishable from past incarnations of itself. Our calculus is inspired in part by the Erlang programming language and in part by the distributed $\pi$-calculus with nodes and link failures (D$\pi$F) introduced by Francalanza and Hennessy. In order to reason about distributed systems with failures and recovery we develop a behavioral theory for our calculus, in the form of a contextual equivalence, and of a fully abstract coinductive characterization of this equivalence by means of a labelled transition system semantics and its associated weak bisimilarity. This result is valuable for it provides a compositional proof technique for proving or disproving contextual equivalence between systems.

One of the most natural approaches to reinforcement learning (RL) with function approximation is value iteration, which inductively generates approximations to the optimal value function by solving a sequence of regression problems. To ensure the success of value iteration, it is typically assumed that Bellman completeness holds, which ensures that these regression problems are well-specified. We study the problem of learning an optimal policy under Bellman completeness in the online model of RL with linear function approximation. In the linear setting, while statistically efficient algorithms are known under Bellman completeness (e.g., Jiang et al. (2017); Zanette et al. (2020)), these algorithms all rely on the principle of global optimism which requires solving a nonconvex optimization problem. In particular, it has remained open as to whether computationally efficient algorithms exist. In this paper we give the first polynomial-time algorithm for RL under linear Bellman completeness when the number of actions is any constant.

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.