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版本更新 · v2arXiv:2601.14175

A model of errors in transformers

Suvrat Raju, Praneeth Netrapalli

原文摘要

We study the error rate of LLMs on tasks like arithmetic that require a deterministic output, and repetitive processing of tokens drawn from a small set of alternatives. We argue that incorrect predictions arise when small errors in the attention mechanism accumulate to cross a threshold, and use this insight to derive a quantitative two-parameter relationship between the accuracy and the complexity of the task. The two parameters vary with the prompt and the model; they can be interpreted in terms of an elementary noise rate, and the number of plausible erroneous tokens that can be predicted. Our analysis is inspired by an ``effective field theory'' perspective: the LLM's many raw parameters can be reorganized into just two parameters that govern the error rate. We perform extensive empirical tests, using Gemini 2.5 Flash, Gemini 2.5 Pro and DeepSeek R1, and find excellent agreement between the predicted and observed accuracy for a variety of tasks, although we also identify deviations in some cases. Our model provides an alternative to suggestions that errors made by LLMs on long repetitive tasks indicate the ``collapse of reasoning'', or an inability to express ``compositional'' functions. Finally, we show how to construct prompts to reduce the error rate.

cs.LG · cs.AI · cs.CL · hep-th

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.16733

TheoPhysEval: Assessing AI agents at autonomous theoretical physics problem solving

A. Ramesh Chandra, Aaghaz Mahajan, Ainesh Sanyal, Mianqi Wang, Shubhadeep Chakraborty, Sudip Chakraborty, Shailesh Chandrasekharan, Rama Govindarajan 等 35 位作者

原文摘要

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

hep-th · cond-mat.stat-mech · cond-mat.str-el · cs.AI · gr-qc

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2011.04672

Principles of Quantum Communication Theory: A Modern Approach

Sumeet Khatri, Ludovico Lami, Mark M. Wilde

原文摘要

This is a preliminary version of a book in progress on the theory of quantum communication. We adopt an information-theoretic perspective throughout and give a comprehensive account of fundamental results in quantum communication theory from the past decade (and earlier), with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field. In Part I, we cover mathematical preliminaries and provide a detailed study of quantum mechanics from an information-theoretic perspective. We also provide an extensive and thorough review of quantum entropies, and we devote an entire chapter to the study of entanglement measures. Equipped with these essential tools, in Part II we study classical communication (with and without entanglement assistance), entanglement distillation, quantum communication, secret key distillation, and private communication. In Part III, we cover the latest developments in feedback-assisted communication tasks, such as quantum and classical feedback-assisted communication, LOCC-assisted quantum communication, and secret key agreement.

quant-ph · cond-mat.stat-mech · cs.IT · hep-th · math-ph

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.09938

Fast holographic inversion of superconducting domes

Sejin Kim

原文摘要

A holographic superconductor whose scalar mass depends on the gauge field strength, $M(\Fsq)$, reproduces a superconducting dome for a suitable $M$, but recovering $M$ from a dome has taken days. We obtain the condition that fixes the critical temperature from two integrations, started at the horizon and at the boundary, and its derivative with respect to $M$ from the same two solutions, so training needs no finite differences and an inversion takes ten minutes to an hour. With this speed we study the interval between the horizon value of $\Fsq$ at the lowest doping and $\Fsq=0$, which no horizon reaches and at whose end the scalar mass $M(0)$ fixes the dimension of the dual operator. Holding $M(0)$ at several values, the pinned masses, and retraining the rest, we find reconstructions that share the minima of $M$ and agree wherever the horizons reach, apart from the deepest end, but differ on that interval. A rule that keeps the reconstruction with the simplest closed form recovers the scalar mass and the mass function of a dome generated from a quadratic $M$. On Gaussian and double-Gaussian domes and the measured phase diagrams of YBa$_{2}$Cu$_{3}$O$_{y}$ and 2M-WS$_{2}$ its choice rests on ties or narrow margins, and it recovers the scalar mass of only two of the four domes generated from the closed forms it keeps for them. The dome thus constrains $M$ where its horizons reach but not the scalar mass, which a second observable would have to fix.

hep-th · cs.AI

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.02084

Black Hole Love Numbers with Physics-Informed Neural Networks

Maria J. Rodriguez, Luis Fernando Temoche, Pavlos Protopapas

原文摘要

We develop and validate a physics-informed neural network (PINN) framework for computing the tidal Love numbers of black holes directly from their perturbation equations. We consider static perturbations of the Kerr black hole, whose exact hypergeometric solutions provide a controlled benchmark for both the numerical solver and the extraction of the physical response. The framework combines exact enforcement of the horizon boundary conditions with an $H^2$-Sobolev loss that incorporates derivatives of the differential-equation residual. The Love number is then obtained by extracting the asymptotic coefficients of the learned solution, without using the analytic connection formula. Across the tested scalar, vector, and tensor perturbations, the method recovers the finite dissipative response with relative errors below $10^{-5}$. Controlled comparisons show that the higher-derivative loss terms improve solution accuracy by orders of magnitude, while independent tests of the extraction procedure distinguish solver errors from errors in recovering the response coefficients. The conservative response, which vanishes analytically, is constrained by the numerical error floor. These results demonstrate that PINNs can accurately compute black-hole tidal response and establish a validated framework for future extensions to frequency-dependent and non-separable perturbation problems.

gr-qc · cs.LG · hep-th · math.NA

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2604.15742

Collective Kernel EFT for Pre-activation ResNets

Hidetoshi Kawase, Toshihiro Ota

原文摘要

In finite-width deep neural networks, the empirical kernel $G$ evolves stochastically across layers. We develop a collective kernel effective field theory (EFT) for a simplified pre-activation residual model. Exact conditional Gaussianity of the residual increment gives finite-width discrete identities for $G$ and its sigma-kernel source. A projected $G$-only closure and a continuous-depth approximation define reference equations for the mean kernel $K_0$, the kernel covariance $V_4$, and the next-to-leading mean correction $K_1$. Numerical tests show that this closure captures the leading mean-kernel evolution, whereas its covariance and next-to-leading accuracy depend on sigma-kernel modes omitted from the $G$-only state. For the scalar ($N=1$) model with $\tanh$ activation, a Hermite--Galerkin extension agrees with the extrapolated $K_1$ value and reduces the $V_4$ endpoint error by $85$--$93\%$ relative to the $G$-only reference. These results clarify the range of validity of the equal-time Markov $G$-only description and identify the additional collective information required beyond it.

cs.LG · hep-th · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36673

Atom as an Agent: Emergent Order by Collective Predictive Coding

Koji Hashimoto, Tadahiro Taniguchi

原文摘要

What is the intrinsic reason of emergence of macroscopic order parameter out of microscopic systems? In this article, we apply to physics the collective predictive coding (CPC), the theory of language/symbol emergence. As our language emerges out of our human communications, physical macroscopic order parameter emerges out of communications among atoms --- each atom is regarded as an agent who predicts each other's behavior through inference. We present three examples of classical spin systems: two-dimensional ferromagnetic and antiferromagnetic Ising models, a two-dimensional spin model with competing stripe orders, and the fully connected Sherrington--Kirkpatrick spin-glass model. In all of these examples, proper macroscopic order parameters including the replica overlap emerge automatically through communication informatics of CPC, only from observed spin configurations. We call the learned macroscopic coordinate the collective predictive order. Furthermore, for the ferromagnetic and antiferromagnetic Ising models, the equilibrium distribution of the collective predictive order yields an emergent potential with the symmetry and thermal evolution characteristic of a Landau potential. Notably, the emergence of the collective predictive order does not refer to any structure of microscopic Hamiltonians/Lagrangians. Thus our ``Atom-as-an-Agent" (AaaA) principle offers a completely data-driven method for the emergence of macroscopic order, that is, machine learning physics.

cs.AI · hep-th

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36113

Scaling and Renormalization in Neural Networks: An Effective Renormalization-Group Description of Grokking

Min Chen, Junqi Wang, Zeguan Wu, Wenhao Huang, Junyu Liu

原文摘要

Grokking is a delayed transition from memorization to generalization in deep neural networks (NNs). We examine whether scaling and renormalization group (RG) theories can describe this dynamics, establishing a quantitative physical framework for neural generalization transitions. For modular addition on a two-layer NN, an ensemble of trained models defines an order parameter (the squared weight norm) and fluctuation proxies for the heat capacity and the susceptibility, with training epoch and weight decay serving as thermal and field control coordinates. To bridge neural architectures to real-space RG, we construct an exact coupling matrix via a second-order expansion of the loss with respect to per-neuron norms and use its Fiedler vector to define an effective geometry. This spectral ordering yields a monotonic spatial decay of coupling strength that is absent under random permutations. We then execute real-space RG by block-spin aggregating adjacent neurons and parameterizing the coupling matrix into off-diagonal band strengths. Linearizing this local RG map yields relevant scaling exponents and five derived critical exponents, with direct empirical estimates matching RG predictions within 1-10%. Overall, our framework provides a consistent effective description of grokking, suggesting the scaling and renormalization group formalism as a tool to investigate NN dynamics.

cs.LG · cs.AI · hep-th · quant-ph

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arXiv ↗PDF ↗