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Value function approximation is important in modern reinforcement learning (RL) problems especially when the state space is (infinitely) large. Despite the importance and wide applicability of value function approximation, its theoretical…
A central notion of physics is the rate of change. While mathematically the concept of derivative represents an idealization of the linear growth, power law types of non-linearities even in noiseless physical signals cause derivative…
Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be…
Geometric shape features have been widely used as strong predictors for image classification. Nevertheless, most existing classifiers such as deep neural networks (DNNs) directly leverage the statistical correlations between these shape…
In robot manipulation, Reinforcement Learning (RL) often suffers from low sample efficiency and uncertain convergence, especially in large observation and action spaces. Foundation Models (FMs) offer an alternative, demonstrating promise in…
In Deep Reinforcement Learning (RL), it is a challenge to learn representations that do not exhibit catastrophic forgetting or interference in non-stationary environments. Successor Features (SFs) offer a potential solution to this…
We propose a framework for verifiable and compositional reinforcement learning (RL) in which a collection of RL subsystems, each of which learns to accomplish a separate subtask, are composed to achieve an overall task. The framework…
Conventional state representations in reinforcement learning often omit critical task-related details, presenting a significant challenge for value networks in establishing accurate mappings from states to task rewards. Traditional methods…
Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive…
In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation…
N=2 noncritical strings are closely related to the $\Slr/\Slr$ Wess-Zumino- Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the…
Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into…
Unsupervised visual representation learning offers the opportunity to leverage large corpora of unlabeled trajectories to form useful visual representations, which can benefit the training of reinforcement learning (RL) algorithms. However,…
Robots could learn their own state and world representation from perception and experience without supervision. This desirable goal is the main focus of our field of interest, state representation learning (SRL). Indeed, a compact…
LCRL is a software tool that implements model-free Reinforcement Learning (RL) algorithms over unknown Markov Decision Processes (MDPs), synthesising policies that satisfy a given linear temporal specification with maximal probability. LCRL…
Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In…
Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required…
A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \in \R^d$ is mapped to much higher dimension $m \gg d$ by a random linear transformation, and is then sparsified by…
Effective personalization on large-scale job platforms requires modeling members based on heterogeneous textual sources, including profiles, professional data, and search activity logs. As recommender systems increasingly adopt Large…
We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…