Related papers: Entropy Collapse: A Universal Failure Mode of Inte…

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping,…

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed…

A key challenge in systems biology is the elucidation of the underlying principles, or fundamental laws, which determine the cellular phenotype. Understanding how these fundamental principles are altered in diseases like cancer is important…

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second…

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…

Entropy bounds in black hole physics, based on a wide variety of different approaches, have had a long and distinguished history. Recently the current authors have turned attention to uncollapsed systems and obtained a robust entropy bound…

We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when…

Ongoing studies have identified similarities between neural representations in biological networks and in deep artificial neural networks. This has led to renewed interest in developing analogies between the backpropagation learning…

The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In…

This paper introduces a formal framework for modeling observer-dependent collapse dynamics and temporal identity drift within artificial and mathematical systems, grounded entirely in the symbolic foundations of Alpay Algebra. Building upon…

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with $(1,2)$-neighbourhood and threshold $r = 3$. The first order asymptotics for the critical probability…

We study the well-known grokking phenomena in neural networks (NNs) using a 3-layer MLP trained on 1 k-sample subset of MNIST, with and without weight decay, and discover a novel third phase -- \emph{anti-grokking} -- that occurs very late…

How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent…

Biological systems leverage top-down feedback for visual processing, yet most artificial vision models succeed in image classification using purely feedforward or recurrent architectures, calling into question the functional significance of…

This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…

In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the…

Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…

We consider a bilayer quantum spin model with anisotropic intra-layer exchange couplings. By varying the anisotropy, the quantum critical phenomena changes from XY to Heisenberg to Ising universality class, with two, three and one modes…

In this letter we show that the R\'enyi entanglement entropy of a region of large size $\ell$ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field…

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of…