Finite Groups

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6 papers in the last four weeks, up 50% on the four weeks before. 0.1% of all new papers.

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CAS II: Orbits as Models: Kolmogorov's Structure Function under Symmetry
Sep 30, 2026Romie BanerjeeFinite Groups Symmetry
Tracking States or Tracking Cosets? An Algebraic Account of Learned State Tracking
Sep 24, 2026Zhiyu Zhang, Yupeng LiFinite Groups Recurrent State
Conflux Labs Ltd · Michigan State University
RLVR landscapes for iterated multiplications can be benign: Insights from spin-glass theory
Sep 23, 2026Noa Rubin, Zohar RingelReinforcement Learning With Verifiable Reward Verifiable Rewards
Racah Institute of Physics The Hebrew University of Jerusalem
The Linear Representation Hypothesis Needs a Group Action
Sep 22, 2026Louie Hong Yao, Yuhao Li, Shengchao LiuRepresentation Space Interpretability
The Chinese University of Hong Kong
PermuFormer: Multi-Task Pretraining for Permutation Representation in Algebraic Combinatorics
Sep 21, 2026Henry KvingePretraining Permutation
Pacific Northwest National Laboratory · University of Washington
Groupoid-Based Internal State Representations for Reinforcement Learning with Local Symmetries
Sep 14, 2026Ben Opperman, Eduardo Alonso, Esther MondragónGroup-Based Reinforcement Learning Symmetry
CitAI, AI Research Centre, City St George’s, University of London, London, United Kingdom
Relative Prime Factorization and Finite-State Presentations under Fixed Finite-Monoid Observation
Sep 3, 2026Takayuki KuriyamaAutomata Finite Groups
Independent Researcher, Tokyo, Japan
What is Smoothness?
Sep 3, 2026Zachary P BradshawSmoothness Finite Groups
QodeX Quantum
"More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks
Aug 31, 2026Nima DehghaniNeural Circuits Neurons
McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Cambridge, Massachusetts, USAa)
M-Fibration Theory with Applications to Weighted Graphs
Aug 26, 2026Paolo Boldi, Osvaldo M. Velarde, Hernan A. MakseAlgebraic Structures Finite Groups
Dipartimento di Informatica, Universit`a degli Studi di Milano, Milan, Italy · Levich Institute and Physics Department, City College of New York, New York, NY, USA
A Finite E-Group of Nilpotency Class Three
Aug 7, 2026Xinan Dai, Wenhao Deng, Yidong Shi +2Finite Groups
Xinan Dai is currently a Ph.D. student at Fudan University and a visiting student at the AI for Scientific Simulation and Discovery Lab, Westlake University. · Wenhao Deng is a student at the University of Glasgow and is currently an intern at the AI for Scientific Simulation and Discovery Lab, Westlake University.
Sample Complexity of Multicalibration for Multilevel Properties
Aug 4, 2026Jiuyao Lu, Krishnakumar Balasubramanian, Aleksandr Podkopaev +1Optimal Sample Complexity Sample Complexity
Department of Statistics and Data Science, The Wharton School, University of Pennsylvania · 2Amazon · Department of Statistics, University of California, Davis
Learning the Word Problem: Geodesic Lengths and Cryptographic Applications
Jul 28, 2026Elisabeth FinkDiffie-Hellman Finite Groups
Middlesex University, Department of Computer Science, The Burroughs, Hendon, London NW4 4BT, UK
An Exact Counterexample to Carlson's Associated-Prime Depth Conjecture from a Group of Order 128
Jul 26, 2026Xinan Dai, Wenhao Deng, Yingdong Shi +2Finite Groups Counterexample
Fudan University
Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist
Jul 25, 2026Mohsen Aliabadi, Keith Driscoll, Elliot Krop +3Finite Groups Extremes
Clayton State University · Google Cloud AI Research · Google DeepMind
CAS I: A Geometric Coding Theorem
Jul 15, 2026Romie BanerjeeFinite Groups Symmetry
Learning the Graphical Nature of Symmetries
Jul 13, 2026Rashid Barket, Enrico Grimaldi, Yacoub Hendi +3Acyclic Graphs Finite Groups
Coventry University, Coventry, UK · Department of Computer, Control and Management Engineering, Sapienza University of Rome, Rome, Italy · Uppsala University, Uppsala, Sweden +5
Learning Subgroup Relations Using Siamese Graph Neural Networks
Jul 13, 2026Tal WeissblatFinite Groups Subgroups
A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks
Jun 24, 2026Tal WeissblatFinite Groups Acyclic Graphs
Tal Weissblat
The algebra of Krom logic programs
Jun 14, 2026Christian AntićAlgebraic Structures Finite Groups
Vienna University of Technology Vienna, Austria
A Held-Out Transition-Pair Falsifier for Long-Horizon Non-Abelian State Tracking
Jun 5, 2026Jeonghoon LeeRecurrent State State-Tracking
Attractor Dynamics
GroupToM-Bench: Benchmarking Group Theory of Mind and Nonlinear Social Emergence in MLLMs
Jun 2, 2026Weidong Tang, Jierui Li, Yueling Hou +7Theory-Of-Mind Reasoning Cognitive Science
1Xidian University · 2National University of Singapore · University of Electronic Science and Technology of China +1
Graph Neural Networks for Predicting Solvability of Finite Groups
May 30, 2026Tal WeissblatFinite Groups Graph Neural Networks
Free energy Estimation on Any State Space
May 29, 2026Jiajun He, Zijing Ou, Francisco Vargas +4Free Energy Principle State Space
University of Cambridge · Imperial College London · Xaira Therapeutics +1
Finite Sentence-Interface Control for Learning Bounded-Fan-Out Linear MCFGs under Fixed Monoid Typing
May 12, 2026Takayuki KuriyamaContext-Free Grammars Finite Groups
Every finite group admits a just finite presentation
May 11, 2026Marc LackenbyFinite Groups
On (not) learning the Möbius function
Apr 25, 2026Alexey PozdnyakovFinite Groups Learnability
Reconstructing Rational Functions on Finite Abelian Groups with Higher Autocorrelations
Mar 26, 2025W. Riley Casper, Bobby OrozcoFinite Groups Autocorrelations

Sep 30, 2026, cs.ITJ/K move · Enter open · S save

CAS II: Orbits as Models: Kolmogorov's Structure Function under Symmetry

Romie Banerjee

Finite Groups Symmetry Combinations Subgroups Partitioning Lattice+2

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In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model at each level of complexity. Strong models, those computable from the data by a total algorithm, are essentially the cells of simple partitions, so a partition of {0,1}^n can be read as a hypothesis and the cell containing x as the model it assigns. We develop algorithmic statistics over symmetric partitions, the orbit partitions of groups acting on strings. The Galois connection between subgroups and partitions gives each ambient group G a lattice of symmetric partitions with canonical certificates, joins and meets. A set is a cell of a symmetric partition exactly when its setwise stabiliser in G acts transitively on it, so the resulting structure function is Kolmogorov's restricted to these G-homogeneous sets. With a symmetric sophistication, it measures which part of the regularity of x is symmetric. Under the full symmetric group, cells recover all models and cells of cheap partitions recover exactly the strong models, so normal and strange strings are characterised by symmetry. For GL(n,2) the homogeneous sets are the linearly homogeneous ones, whose XOR dependencies look the same from every point. The GL structure function of a nonzero x lies in a band between C(x) - alpha and n - alpha, and both edges are attained: some stochastic normal strings have simple structure invisible to linear symmetry, with sophistication near 0 but GL-sophistication near C(x). We coordinatise permutation groups by a Burnside ring element (type) and a permutation (placement). In these coordinates a linear hypothesis is determined by its type up to n^2 bits, and any space of symmetry hypotheses small enough to search is small enough to miss simple structure. This sets up learned search over orbit models, the subject of later papers in the series.

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