Tootfinder

Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory
Einar Urdshals, Edmund Lau, Jesse Hoogland, Stan van Wingerden, Daniel Murfet
https://arxiv.org/abs/2510.12077

Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory
We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization, factorization, and other compression techniques, we find that complexity estimates based on the local learning coefficient (LLC) are closely, and in some cases, linearly correlated with compressibility. Our results provide a path toward rigorously evaluating…

i stumbled across a fragment of my online dating profile from two decades ago
I'm into Monk, chaos theory, Björk, Vermeer, Frosted Mini-Wheats, Wallace Stevens, Saint-Saëns, Tim O'Brien, Miro, evolutionary biology, Ravel, Gregory Corso, fresh berries, UFOs, Ellington, Bible comics, computational complexity, Nespresso, The Kinks, Diane DiPrima, fresh-squeezed OJ, Köln's Kompakt music label, Giacometti, Mingus, that sort of thing. I'm very curious and never bored.
s…

Nonlocal Games Through Communication Complexity and Quantum Cryptography
Pierre Botteron
https://arxiv.org/abs/2510.09457 https://arxiv.org/pdf/2510.09457

Nonlocal Games Through Communication Complexity and Quantum Cryptography
This thesis explores foundational aspects of quantum information theory and quantum cryptography. First, we investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish quantum correlations from non-signaling correlations by leveraging the principle of communication complexity. To this end, we employ techniques such as distributed computation, majority-function-based distillation protocols, the algebraic and geometric properti…

Exploring Complexity Measures for Analysis of Solar Wind Structures and Streams
Venla Koikkalainen, Emilia Kilpua, Simon Good, Adnane Osmane
https://arxiv.org/abs/2510.05873 htt…

Exploring Complexity Measures for Analysis of Solar Wind Structures and Streams
In this paper we use statistical complexity and information theory metrics to study structure within solar wind time series. We explore this using entropy-complexity and information planes, where the measure for entropy is formed using either permutation entropy or the degree distribution of a horizontal visibility graph (HVG). The entropy is then compared to the Jensen complexity (Jensen-Shannon complexity plane) and Fisher information measure (Fisher-Shannon information plane), formed both fr…

Is #AI really just dumb statistics? "Olympiad-level physics problem-solving presents a significant challenge for both humans and artificial intelligence (AI), as it requires a sophisticated integration of precise calculation, abstract reasoning, and a fundamental grasp of physical principles," says the (abstract of the) paper https://arxiv.org/abs/2511.10515: "The Chinese Physics Olympiad (CPhO), renowned for its complexity and depth, serves as an ideal and rigorous testbed for these advanced capabilities. In this paper, we introduce LOCA-R (LOgical Chain Augmentation for Reasoning), an improved version of the LOCA framework adapted for complex reasoning, and apply it to the CPhO 2025 theory examination. LOCA-R achieves a near-perfect score of 313 out of 320 points, solidly surpassing the highest-scoring human competitor and significantly outperforming all baseline methods." Oops ...?

Polyharmonic Cascade
Yuriy N. Bakhvalov
https://arxiv.org/abs/2512.17671 https://arxiv.org/pdf/2512.17671 https://arxiv.org/html/2512.17671
arXiv:2512.17671v1 Announce Type: new
Abstract: This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of indifference. This makes it possible to approximate nonlinear functions of arbitrary complexity while preserving global smoothness and a probabilistic interpretation. For the polyharmonic cascade, a training method alternative to gradient descent is proposed: instead of directly optimizing the coefficients, one solves a single global linear system on each batch with respect to the function values at fixed "constellations" of nodes. This yields synchronized updates of all layers, preserves the probabilistic interpretation of individual layers and theoretical consistency with the original model, and scales well: all computations reduce to 2D matrix operations efficiently executed on a GPU. Fast learning without overfitting on MNIST is demonstrated.
toXiv_bot_toot

Complexity of Einstein-Maxwell-non-minimal coupling $R^2F^2$: the role of the penalty factor
Mojtaba Shahbazi, Mehdi Sadeghi
https://arxiv.org/abs/2509.25165 https://

Complexity of Einstein-Maxwell-non-minimal coupling $R^2F^2$: the role of the penalty factor
In this paper, we examine the holographic complexity of a theory of Einstein-Maxwell with a non-minimal coupling $R^2 F_{μν}F^{μν} $ term via complexity=anything. We introduce a perturbative black brane solution in AdS spacetime up to the first order of the non-minimal coupling. Because the model exhibits the resistivity proportional to the temperature, it could describe strange metals. The complexity of the solution could be characterized by three quantities: the conserved charge, the non-…

Structural Separation and Semantic Incompatibility in the P vs. NP Problem: Computational Complexity Analysis with Construction Defining Functionality
Yumiko Nishiyama
https://arxiv.org/abs/2509.22995 …

Structural Separation and Semantic Incompatibility in the P vs. NP Problem: Computational Complexity Analysis with Construction Defining Functionality
The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can be reduced to SAT, it is at least as hard as SAT, and hence considered NP-complete. However, the CDF framework offers a structural inversion of this traditional view. Rather than treating SAT as merely a representative of NP-completeness, we investigate wheth…

Crosslisted article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- Psi-Turing Machines: Bounded Introspection for Complexity Barriers and Oracle Separations
Rafig Huseynzade

List Decoding Reed--Solomon Codes in the Lee, Euclidean, and Other Metrics
Chris Peikert, Alexandra Veliche Hostetler
https://arxiv.org/abs/2510.11453 https://

List Decoding Reed--Solomon Codes in the Lee, Euclidean, and Other Metrics
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error correction for these codes, like the celebrated Berlekamp--Welch unique decoder and the (Guruswami--)Sudan list decoders, are focused on measuring error in the Hamming metric, which simply counts the number of corrupted codeword symbols. However, for some applica…

Machine learning approach to QCD kinetic theory
Sergio Barrera Cabodevila, Aleksi Kurkela, Florian Lindenbauer
https://arxiv.org/abs/2509.26374 https://arx…

Machine learning approach to QCD kinetic theory
The effective kinetic theory (EKT) of QCD provides a possible picture of various non-equilibrium processes in heavy- and light-ion collisions. While there have been substantial advances in simulating the EKT in simple systems with enhanced symmetry, eventually, event-by-event simulations will be required for a comprehensive phenomenological modeling. As of now, these simulations are prohibitively expensive due to the numerical complexity of the Monte Carlo evaluation of the collision kernels. I…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
toXiv_bot_toot

On The Roots of Independence Polynomial: Quantifying The Gap
Om Prakash, Vikram Sharma
https://arxiv.org/abs/2510.09197 https://arxiv.org/pdf/2510.09197

On The Roots of Independence Polynomial: Quantifying The Gap
The independence polynomial of a graph $G$ is the generating polynomial corresponding to its independent sets of different sizes. More formally, if $a_k(G)$ denotes the number of independent sets of $G$ of size $k$ then \[I(G,z) \as \sum_{k}^{} (-1)^k a_k(G) z^k.\] The study of evaluating $I(G,z)$ has several deep connections to problems in combinatorics, complexity theory and statistical physics. Consequently, the roots of the independence polynomial have been studied in detail. In particula…

Computing moment polytopes - with a focus on tensors, entanglement and matrix multiplication
Maxim van den Berg, Matthias Christandl, Vladimir Lysikov, Harold Nieuwboer, Michael Walter, Jeroen Zuiddam
https://arxiv.org/abs/2510.08336

Computing moment polytopes - with a focus on tensors, entanglement and matrix multiplication
Tensors are fundamental in mathematics, computer science, and physics. Their study through algebraic geometry and representation theory has proved very fruitful in the context of algebraic complexity theory and quantum information. In particular, moment polytopes have been understood to play a key role. In quantum information, moment polytopes (also known as entanglement polytopes) provide a framework for the single-particle quantum marginal problem and offer a geometric characterization of ent…

Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers
Peter Shaw, James Cohan, Jacob Eisenstein, Kristina Toutanova
https://arxiv.org/abs/2509.22445

Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers
The Minimum Description Length (MDL) principle offers a formal framework for applying Occam's razor in machine learning. However, its application to neural networks such as Transformers is challenging due to the lack of a principled, universal measure for model complexity. This paper introduces the theoretical notion of asymptotically optimal description length objectives, grounded in the theory of Kolmogorov complexity. We establish that a minimizer of such an objective achieves optimal compre…

Preserving Core Structures of Social Networks via Information Guided Multi-Step Graph Pruning
Yutong Hu, Bingxin Zhou, Jing Wang, Weishu Zhao, Liang Hong
https://arxiv.org/abs/2510.10499

Preserving Core Structures of Social Networks via Information Guided Multi-Step Graph Pruning
Social networks often contain dense and overlapping connections that obscure their essential interaction patterns, making analysis and interpretation challenging. Identifying the structural backbone of such networks is crucial for understanding community organization, information flow, and functional relationships. This study introduces a multi-step network pruning framework that leverages principles from information theory to balance structural complexity and task-relevant information. The fra…

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- The Query Complexity of Uniform Pricing
Houshuang Chen, Yaonan Jin, Pinyan Lu, Chihao Zhang

Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
Paul A. Johnson, Charles-\'Emile Fecteau, Samuel Nadeau, Mauricio Rodr\'iguez-Mayorga, Pierre-Fran\c{c}ois Loos
https://arxiv.org/abs/2510.06144

Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally capture static correlation in bond-breaking and multireference problems, though at the expense of implementation complexity and limited treatment of dynamic effects. In this work, we examine the interplay between orbital and geminal frameworks, focusing on perfect-pairing (PP) wavefunctions and thei…

Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory
Praveen Balaji, Cianan Conefrey-Shinozaki, Patrick Draper, Jason K. Elhaderi, Drishti Gupta, Luis Hidalgo, Andrew Lytle
https://arxiv.org/abs/2509.25865

Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory
We study methods for efficient preparation of approximate ground states of $SU(3)$ lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, …

The Log-Rank Conjecture: New Equivalent Formulations
Lianna Hambardzumyan, Shachar Lovett, Morgan Shirley
https://arxiv.org/abs/2510.02583 https://arxiv.or…

The Log-Rank Conjecture: New Equivalent Formulations
The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the rank and partitioning number of a Boolean matrix are quasi-polynomially related. We propose a relaxed but still equivalent version of the conjecture based on a new matrix parameter, signed rectangle rank: the minimum number of all-1 rectangles needed to express the Boolean matrix as a $\pm 1$-sum. Signed rectangle …

Is it Gaussian? Testing bosonic quantum states
Filippo Girardi, Freek Witteveen, Francesco Anna Mele, Lennart Bittel, Salvatore F. E. Oliviero, David Gross, Michael Walter
https://arxiv.org/abs/2510.07305

Is it Gaussian? Testing bosonic quantum states
Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental question: given copies of an unknown CV state, how can we efficiently test whether it is Gaussian? We address this problem from the perspective of representation theory and quantum learning theory, characterizing the sample complexity of Gaussianity testing as a fu…

Optimized Control of Duplex Networks
Haoyu Zheng, Xizhe Zhang
https://arxiv.org/abs/2509.21767 https://arxiv.org/pdf/2509.21767

Optimized Control of Duplex Networks
Many real-world complex systems can be modeled as multiplex networks, where each layer represents a distinct set of interactions among the same entities. Controlling such systems-steering them toward desired states using external inputs-is crucial across many domains. However, existing network control theory largely focuses on single-layer networks, and applying separate controls to each layer of a multiplex system often leads to redundant sets of driver nodes, increasing cost and complexity. …

Crosslisted article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Optimal control of Volterra integral diffusions and application to contract theory
Dylan Possama\"i, Mehdi Talbi
https://arxiv.org/abs/2511.09701 https://mastoxiv.page/@arXiv_mathPR_bot/115547093766733637
- Generalized infinite dimensional Alpha-Procrustes based geometries
Salvish Goomanee, Andi Han, Pratik Jawanpuria, Bamdev Mishra
https://arxiv.org/abs/2511.09801 https://mastoxiv.page/@arXiv_statML_bot/115547135711272091
- Sample Complexity of Quadratically Regularized Optimal Transport
Alberto Gonz\'alez-Sanz, Eustasio del Barrio, Marcel Nutz
https://arxiv.org/abs/2511.09807 https://mastoxiv.page/@arXiv_mathST_bot/115546975796760368
- On the Convergence of Overparameterized Problems: Inherent Properties of the Compositional Struct...
Arthur Castello Branco de Oliveira, Dhruv Jatkar, Eduardo Sontag
https://arxiv.org/abs/2511.09810 https://mastoxiv.page/@arXiv_csLG_bot/115547543989283588
- Implicit Multiple Tensor Decomposition
Kunjing Yang, Libin Zheng, Minru Bai
https://arxiv.org/abs/2511.09916 https://mastoxiv.page/@arXiv_mathNA_bot/115547169767663335
- Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies
Takehiro Tottori, Tetsuya J. Kobayashi
https://arxiv.org/abs/2511.10184 https://mastoxiv.page/@arXiv_physicsbioph_bot/115546979073652600
- Zeroes and Extrema of Functions via Random Measures
Athanasios Christou Micheas
https://arxiv.org/abs/2511.10293 https://mastoxiv.page/@arXiv_statME_bot/115547493525198835
- Operator Models for Continuous-Time Offline Reinforcement Learning
Nicolas Hoischen, Petar Bevanda, Max Beier, Stefan Sosnowski, Boris Houska, Sandra Hirche
https://arxiv.org/abs/2511.10383 https://mastoxiv.page/@arXiv_statML_bot/115547254989932993
- On topological properties of closed attractors
Wouter Jongeneel
https://arxiv.org/abs/2511.10429 https://mastoxiv.page/@arXiv_mathDS_bot/115547276594491411
- Learning parameter-dependent shear viscosity from data, with application to sea and land ice
Gonzalo G. de Diego, Georg Stadler
https://arxiv.org/abs/2511.10452 https://mastoxiv.page/@arXiv_mathNA_bot/115547323782478749
- Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Con...
Jun Liu
https://arxiv.org/abs/2511.10510 https://mastoxiv.page/@arXiv_eessSY_bot/115547429321496393
- Direction-of-Arrival and Noise Covariance Matrix joint estimation for beamforming
Vitor Gelsleichter Probst Curtarelli
https://arxiv.org/abs/2511.10639 https://mastoxiv.page/@arXiv_eessAS_bot/115547188796143762
toXiv_bot_toot

List coloring ordered graphs with forbidden induced subgraphs
Marta Piecyk, Pawe{\l} Rz\k{a}\.zewski
https://arxiv.org/abs/2509.22160 https://arxiv.org/pdf…

List coloring ordered graphs with forbidden induced subgraphs
In the List $k$-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of $\{1,\ldots,k\}$. We need to decide if $G$ admits a proper coloring, where every vertex receives a color from its list. The complexity of the problem in classes defined by forbidding induced subgraphs is a widely studied topic in algorithmic graph theory. Recently, Hajebi, Li, and Spirkl [SIAM J. Discr. Math. 38 (2024)] initiated the study of List $3$-Coloring in ordered grap…