arXiv research

The article presents a new entropy model for assessing stock market interest.

The intrinsic entropy model accurately estimates stock market volatility.

The paper introduces a new intrinsic reward method for exploration in reinforcement learning.

The paper corrects biases in estimating intrinsic dimension and differential entropy.

New RL approach uses future state and action visitation measures for better exploration.

Paper introduces CSIE for estimating stock market volatility.

Understanding the inductive bias of neural networks is critical to explaining their ability to generalise. Here, for one of the simplest neural networks -- a single-layer perceptron with n input neurons, one output neuron, and no threshold bias term -- we prove that upon random initialisation of weights, the a priori p…

Study uses CSIE to estimate portfolio volatility relative to market.

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensio…

Nonnegative sectional curvature linked to matrix displacement convexity.

We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various nilpotent quotients. We show that much like the structure of a nilpotent group is dictated to a large degree by its abelianization,…

Maximizes coding rate difference for robust, discriminative features.

Paper proposes a policy-search algorithm to learn entropy-maximizing exploration policies in reward-free environments.

The paper explores convergence and structure of spaces with scalar curvature and entropy bounds, introducing new $d_p$ convergence.

We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the conve…

A new measure of causal influence quantifies intrinsic contributions in DAGs.

The paper proves properties of Renyi entropy power on Riemannian manifolds.

Max entropy exploration guides reinforcement learning agents to pursue achievable goals.

The paper analyzes the intrinsic exploration terms in policy-gradient algorithms.

NES improves robust optimization with noisy inputs.

Inference-Time Scaling can be extended to domains prone to systematic failure using intrinsic statistics.

Machine learning is usually defined in behaviourist terms, where external validation is the primary mechanism of learning. In this paper, I argue for a more holistic interpretation in which finding more probable, efficient and abstract representations is as central to learning as performance. In other words, machine le…

Hyperbolic manifolds are stable under volume-preserving metrics.

Study on entropy stability in product spaces of negatively curved symmetric spaces.

New summary measures reveal geometric structure in weighted measures on manifolds.

This study proposes hidden state curiosity to enhance RL models' resilience against noise.

Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that allows obtaining the true feature ordering of two-dimensional sequential forward feat…

Neural networks' performance scales with data size, explained by data manifold dimensionality.

Entropy-based decoding improves DLM sampling efficiency.

LLMs learn peaked distributions slowly due to power-law losses.

Scaling laws found for reinforcement learning performance with model size and compute.

New method recovers curvature from heat diffusion data.

This paper analyzes several interest rates time series from the United Kingdom during the period 1999 to 2014. The analysis is carried out using a pioneering statistical tool in the financial literature: the complexity-entropy causality plane. This representation is able to classify different stochastic and chaotic reg…

Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors? Better understanding of this question of generalization may improve practical applications of deep networks. In this paper we show that with cross-entropy loss it is surprisingly simple to ind…

New method generates synthetic time series paths with more flexibility.

Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of structured data. This has motivated different research areas such as data poiso…

The fastICA method is a popular dimension reduction technique used to reveal patterns in data. Here we show both theoretically and in practice that the approximations used in fastICA can result in patterns not being successfully recognised. We demonstrate this problem using a two-dimensional example where a clear struc…

Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as functions of the state-visitation frequencies that are induced by how the agent be…

A new AI framework reduces costs and improves performance.

Develops weak PINNs for efficient manifold solutions of hyperbolic equations.

New method uses hindsight to make exploration robust in stochastic environments.

Wavelet analysis reveals financialization effects on oil-food price correlation.

New bounds for agnostic learning with average smoothness.

ML models predict extreme events in the Hénon map with accuracy scaling with system parameters.

New framework detects near vs. far out-of-distribution samples for AI safety.

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …