Mehran Shakerinava

arxiv.org

Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models

Oliver Ethan Richardson

Joseph D Viviano

We present a generic algorithm for learning and approximate inference with an intuitive epistemic interpretation: iteratively focus on a sub… (voir plus)set of the model and resolve inconsistencies using the parameters under control. This framework, which we call Local Inconsistency Resolution (LIR) is built upon Probabilistic Dependency Graphs (PDGs), which provide a flexible representational foundation capable of capturing inconsistent beliefs. We show how LIR unifies and generalizes a wide variety of important algorithms in the literature, including the Expectation-Maximization (EM) algorithm, belief propagation, adversarial training, GANs, and GFlowNets. Each of these methods can be recovered as a specific instance of LIR by choosing a procedure to direct focus (attention and control). We implement this algorithm for discrete PDGs and study its properties on synthetically generated PDGs, comparing its behavior to the global optimization semantics of the full PDG.

2026-02-02

International Conference on Artificial Intelligence and Statistics (spotlight)

The Expressive Limits of Diagonal SSMs for State-Tracking

State-Space Models (SSMs) have recently been shown to achieve strong empirical performance on a variety of long-range sequence modeling task… (voir plus)s while remaining efficient and highly-parallelizable. However, the theoretical understanding of their expressive power remains limited. In this work, we study the expressivity of input-Dependent Complex-valued Diagonal (DCD) State-Space Models (SSMs) on sequential state-tracking tasks for abstract groups. It is easy to show that a single DCD SSM layer with a universal decoder can track any Abelian group at finite precision by decomposing it into a product of cyclic groups. We show that this is tight by proving that such a model cannot track any non-Abelian group at finite precision. We further establish the expressivity of multi-layer DCD SSMs. We show that a

2025-12-31

International Conference on Learning Representations (Accept (Poster))

Beyond Scalar Rewards: An Axiomatic Framework for Lexicographic MDPs

Adam Oberman

Recent work has formalized the reward hypothesis through the lens of expected utility theory, by interpreting reward as utility. Hausner's f… (voir plus)oundational work showed that dropping the continuity axiom leads to a generalization of expected utility theory where utilities are lexicographically ordered vectors of arbitrary dimension. In this paper, we extend this result by identifying a simple and practical condition under which preferences cannot be represented by scalar rewards, necessitating a 2-dimensional reward function. We provide a full characterization of such reward functions, as well as the general d-dimensional case, in Markov Decision Processes (MDPs) under a memorylessness assumption on preferences. Furthermore, we show that optimal policies in this setting retain many desirable properties of their scalar-reward counterparts, while in the Constrained MDP (CMDP) setting -- another common multiobjective setting -- they do not.

2025-09-17

NeurIPS.cc/2025/Conference (spotlight)

Parity Requires Unified Input Dependence and Negative Eigenvalues in SSMs

Jayesh Khullar

Franccois Rivest

A. Chandar

2025-06-09

ICML.cc/2025/Workshop/MOSS (publié)

Weight-Sharing Regularization

Weight-sharing is ubiquitous in deep learning. Motivated by this, we propose a "weight-sharing regularization" penalty on the weights …

2024-04-17

Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (publié)

proceedings.mlr.press

Utility Theory for Sequential Decision Making

The von Neumann-Morgenstern (VNM) utility theorem shows that under certain axioms of rationality, decision-making is reduced to maximizing t… (voir plus)he expectation of some utility function. We extend these axioms to increasingly structured sequential decision making settings and identify the structure of the corresponding utility functions. In particular, we show that memoryless preferences lead to a utility in the form of a per transition reward and multiplicative factor on the future return. This result motivates a generalization of Markov Decision Processes (MDPs) with this structure on the agent's returns, which we call Affine-Reward MDPs. A stronger constraint on preferences is needed to recover the commonly used cumulative sum of scalar rewards in MDPs. A yet stronger constraint simplifies the utility function for goal-seeking agents in the form of a difference in some function of states that we call potential functions. Our necessary and sufficient conditions demystify the reward hypothesis that underlies the design of rational agents in reinforcement learning by adding an axiom to the VNM rationality axioms and motivates new directions for AI research involving sequential decision making.

2022-06-27

Proceedings of the 39th International Conference on Machine Learning (publié)

proceedings.mlr.press

Transformation Coding: Simple Objectives for Equivariant Representations

Arnab Kumar Mondal

2022-02-18

ArXiv (prépublication)

arxiv.org

Structuring Representations Using Group Invariants

Arnab Kumar Mondal

2021-12-31

Advances in Neural Information Processing Systems 35 (NeurIPS 2022) (publié)

Equivariant Networks for Pixelized Spheres

Pixelizations of Platonic solids such as the cube and icosahedron have been widely used to represent spherical data, from climate records to… (voir plus) Cosmic Microwave Background maps. Platonic solids have well-known global symmetries. Once we pixelize each face of the solid, each face also possesses its own local symmetries in the form of Euclidean isometries. One way to combine these symmetries is through a hierarchy. However, this approach does not adequately model the interplay between the two levels of symmetry transformations. We show how to model this interplay using ideas from group theory, identify the equivariant linear maps, and introduce equivariant padding that respects these symmetries. Deep networks that use these maps as their building blocks generalize gauge equivariant CNNs on pixelized spheres. These deep networks achieve state-of-the-art results on semantic segmentation for climate data and omnidirectional image processing. Code is available at https://git.io/JGiZA.

2021-06-30

Proceedings of the 38th International Conference on Machine Learning (publié)