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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

At least 19 recordsLinked to original sources

arXiv2026

The double coset problem for parabolic subgroups of braid groups

We solve the double coset problem for arbitrary parabolic subgroups of the $n$-strand braid group $B_n$, by reducing it to the simultaneous conjugacy problem in the larger group $B_{n+1}$. The resulting decision algorithm is uniform in the braid index and the supplied subgroup generators. We also formulate the reduction for general group embeddings, and apply it to additional commuting constraints, several other spherical Artin types, and finite direct products.

math.GR↗

arXiv2026

Almost-Polynomial Ratio Almost-ETH-Hardness of Approximating Densest $k$-Subgraph

In the Densest $k$-Subgraph problem, given an undirected graph $G$ and an integer $k$, the goal is to find a subgraph of $G$ on $k$ vertices that contains maximum number of edges. Even though the state-of-the-art algorithm for the problem achieves only $O(n^{1/4 + \varepsilon})$ approximation ratio (Bhaskara et al., 2010), previous attempts at proving hardness of approximation, including those under average case assumptions, fail to achieve a polynomial ratio; the best ratios ruled out under any worst case assumption and any average case assumption are only any constant (Raghavendra and Steurer, 2010) and $2^{Ω(\log^{2/3} n)}$ (Alon et al., 2011) respectively. In this work, we propose the Almost-Exponential Time Hypothesis (Almost-ETH), which postulates that no algorithm can solve 3SAT on $n$ variables in $O(2^{n^{1 - γ}})$ time for any constant $γ> 0$. Assuming Almost-ETH, we show that, for any constant $\varepsilon > 0$, there is no polynomial-time algorithm that approximates {\sc D$k$S} to within $2^{(\log n)^{1 - \varepsilon}}$ factor of the optimum. In addition, our result has perfect completeness, meaning that, assuming Almost-ETH, no polynomial-time algorithm can even distinguish between the case in which $G$ contains a $k$-clique and the case in which every induced $k$-subgraph of $G$ has density at most $2^{-(\log n)^{1 - \varepsilon}}$.

cs.CC↗

arXiv2026

Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm

We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.

cs.DS↗

arXiv2026

Aggregative Efficiency of Bayesian Learning in Networks

When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are log-linear functions of observations and admit a signal-counting interpretation of accuracy. Networks where agents observe multiple neighbors but not their common predecessors confound information, and even a small amount of confounding can lead to much lower accuracy. In a class of networks where agents move in generations and observe the previous generations, we quantify the information loss with an aggregative efficiency index. Aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Later generations contribute little additional information, even when generations are arbitrarily large and agents observe arbitrarily far into the past.

econ.TH↗

arXiv2026

The Hardy-Littlewood conjectures on the twin primes and the binary Goldbach problem are true

A celebrated conjecture of Hardy and Littlewood provides with an asymptotic formula for the counting function of the twin primes. We give an unconditional proof of such a formula by means of a finite Ramanujan expansion of the counting function expressed in terms of the von Mangoldt function and its incomplete form. In a completely analogous way, we solve the conjugate conjecture on the representations of any even integer as the sum of two prime numbers.

math.GM↗

arXiv2026

Optimal Inapproximability of Satisfiable $k$-LIN over Non-Abelian Groups

A seminal result of Håstad [J. ACM, 48(4):798--859, 2001] shows that it is NP-hard to find an assignment that satisfies $\frac{1}{|G|}+\varepsilon$ fraction of the constraints of a given $k$-LIN instance over an abelian group, even if there is an assignment that satisfies $(1-\varepsilon)$ fraction of the constraints, for any constant $\varepsilon>0$. Engebretsen et al. [Theoretical Computer Science, 312(1):17--45, 2004] later showed that the same hardness result holds for $k$-LIN instances over any finite non-abelian group. Unlike the abelian case, where we can efficiently find a solution if the instance is satisfiable, in the non-abelian case, it is NP-complete to decide if a given system of linear equations is satisfiable or not, as shown by Goldmann and Russell [Information and Computation, 178(1):253--262. 2002]. Surprisingly, for certain non-abelian groups $G$, given a satisfiable $k$-LIN instance over $G$, one can in fact do better than just outputting a random assignment using a simple but clever algorithm. The approximation factor achieved by this algorithm varies with the underlying group. In this paper, we show that this algorithm is {\em optimal} by proving a tight hardness of approximation of satisfiable $k$-LIN instance over {\em any} non-abelian $G$, assuming $P \neq NP$. As a corollary, we also get $3$-query probabilistically checkable proofs with perfect completeness over large alphabets with improved soundness. Our proof crucially uses structural properties captured by Gowers' notion of {\em quasi-randomness} for non-abelian groups [Combinatorics, Probability and Computing, 17(3):363--387, 2008].

cs.CC↗

arXiv2026

Equating the Area Sums of Alternate Sectors of a Disc Cut by Concurrent Chords

A disc is cut by $n$ chords through a common interior point $O$, which produces $2n$ curvilinear sectors. We determine when the two sums of alternate sectors have equal area for arbitrary chord directions, which need not be equally spaced. We first derive a closed form for the area of a single sector. We then show that the answer depends on the parity of $n$. For even $n$, at fixed orientation the condition is affine in $r_0^2$, where $r_0$ is the distance from $O$ to the centre; it involves only the total angle of the odd sectors and one trigonometric moment of the directions. For odd $n$, the condition is a nonlinear alternating sum of circular-segment functions of the distances of the chords from the centre. We treat four, six and eight pieces in detail. We also hold the chord directions fixed and translate the whole pencil to an arbitrary interior point, and we characterise the direction sets that give equal sums at every such point. For four chords only equally spaced directions have this property, which gives a converse of the pizza theorem; for an odd number of chords no direction set has it. A fair two-chord cut requires the acute angle between the chords to lie within $(r_0/a)^2$ radians of a right angle, where $a$ is the radius. For equally spaced chords the results reduce to the known theorems of Goldberg and of Mabry and Deiermann.

math.GM↗

arXiv2026

Decay of correlations and thermodynamic limit for the circular Riesz gas

We study the circular Riesz gas, a one-dimensional system of particles with power-law repulsion. For the long-range gas, we prove that the correlation between two gaps at distance $d$ decays like $d^{s-2}$, up to an arbitrarily small loss in the exponent, and that this exponent is sharp. As a consequence, the microscopic point process converges as the number of particles tends to infinity, and its limit is hyperuniform. We also prove the decay of correlations and the convergence of the microscopic point process for the hypersingular gas. The proof analyzes the Helffer-Sjöstrand equation, an elliptic system in high dimension that encodes covariances. It combines the deformation of Combes and Thomas with discrete elliptic regularity estimates and a factorization around the equally spaced configuration.

math.PR↗

arXiv2026

NAG-GS: A Semi-Implicit Stochastic Optimizer with Large-Step Stability

Stochastic first-order methods are widely used for large-scale optimization and machine learning, where their performance often depends on the learning rate. We study NAG-GS, a stochastic momentum method based on a semi-implicit Gauss--Seidel discretization of a Nesterov-type flow. For strongly convex quadratics, we determine the exact range of stable step sizes for fixed damping and the step size that minimizes the worst-case spectral radius. When the damping equals the strong-convexity parameter, the method recovers the accelerated asymptotic factor $(\sqrtκ-1)/(\sqrtκ+1)$, where $κ$ is the condition number. We also prove that the quadratic iteration converges linearly with dynamic damping when its limiting fixed-damping iteration is stable. For general strongly convex, possibly nonsmooth objectives, we establish an $O(1/k)$ bound on the expected objective gap of the last iterate, using a conditionally unbiased stochastic first-order oracle with bounded second moment. The result holds with dynamic damping from any $γ_0>0$. We show that NAG-GS can also be written as a Heavy-Ball iteration with explicitly determined step sizes and momentum coefficients. We test the stochastic result on nonsmooth hinge-loss classification problems, and further evaluate NAG-GS on quadratic problems, logistic regression, convolutional neural networks, RoBERTa, and Vision Transformers. The experiments show that NAG-GS can remain effective at learning rates where standard optimizers become unstable or lose accuracy.

math.OC↗

arXiv2026

A Search-Based Algorithm for Multistage Robust Discrete Linear Optimization and its Implementation

Robust optimization models that allow decisions to adapt to newly revealed information remain computationally challenging and are often limited to two decision stages or are addressed heuristically or via approximation schemes. This challenge is further amplified when uncertainty sets depend on earlier decisions. Conventional approaches to such problems often require problem-specific reformulations and tailored algorithms, highlighting the need for an exact model-and-run approach. We address this gap by presenting an algorithmic framework for solving multistage robust discrete linear optimization problems. This exact approach adapts and integrates ideas from game-tree search, quantified conflict-driven clause learning, and integer linear programming to explore the minimax tree and is implemented in the open-source solver Yasol. The solver supports discrete decision variables across multiple stages, discrete uncertainty sets with polyhedral or decision-dependent structure, and mixed-integer recourse in the final stage. It can be used as a standalone executable or through a C++ library interface, allowing it to serve as a reference solver for exact methods in multistage robust discrete linear optimization. In an extensive computational study, we demonstrate the capabilities of our solver. The results show competitive performance against a reference approach from the literature for a protection-interdiction problem, as well as strong performance on bilevel benchmark instances. For a multistage cutting-stock problem, we demonstrate the substantial loss in solution quality that can arise from neglecting the multistage structure and show that our solver significantly outperforms decision-rule approximations in terms of computational efficiency while certifying the true multistage optimum.

math.OC↗

arXiv2026

Epsilon-Identifiability of Causal Quantities

Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the available data sources. This paper shows how approximate identifiability is still possible for several probabilities of causation. We term this epsilon-identifiability and demonstrate its usefulness in cases where the behavior of certain subpopulations can be restricted within sufficiently narrow bounds. In particular, we show how unidentifiable causal effects and counterfactual probabilities can be epsilon-identified when such allowances are made. Often, these allowances are easily measured and reasonably assumed. Finally, epsilon-identifiability is applied to the unit selection problem.

cs.AI↗

arXiv2026

Bend-Twist Coupling and its Design from Geometrical Constraints in Double Stranded DNA

Under the strongly coupled condition in the adiabatic environment, the fast dynamics originated from the boundary of the target system, governed by target and environmental Hamiltonians, is closely related to the energy gain and loss between the two distinct Hamiltonians. Leveraging this restriction, we investigate how the bi-Hamiltonian condition regulates stochastic dynamics to shape the macroscopic behavior of a semiflexible polymer, analyzing the intrinsic drift from the Dzhanibekov effect and a diffusion process derived from the Smoluchowski equation within a coarse-grained system. The Smoluchowski picture, defined within the framework of stochastic thermodynamics, justifies the usage of a diffusion process in the canonical equations of motion replacing the memory effect defined in the non-Markovian regime. The results of the numerical experiments on the collision, including a previous study on free thermal vibration replicated using the same framework, confirm that heat diffusion process compensates the precision in both equilibrium and far-from-equilibrium states.

nlin.AO↗

arXiv2026

SemDiff: Binary Similarity Detection by Diffing Key-Semantics Graphs

Binary similarity detection is a critical technique that has been applied in many real-world scenarios where source code is not available, e.g., bug search, malware analysis, and code plagiarism detection. Existing works are ineffective in detecting similar binaries in cases where different compiling optimizations, compilers, source code versions, or obfuscation are deployed. We observe that all the cases do not change a binary's key code behaviors although they significantly modify its syntax and structure. With this key observation, we extract a set of key instructions from a binary to capture its key code behaviors. By detecting the similarity between two binaries' key instructions, we can address well the ineffectiveness limitation of existing works. Specifically, we translate each extracted key instruction into a self-defined key expression, generating a key-semantics graph based on the binary's control flow. Each node in the key-semantics graph denotes a key instruction, and the node attribute is the key expression. To quantify the similarity between two given key-semantics graphs, we first serialize each graph into a sequence of key expressions by topological sort. Then, we tokenize and concatenate key expressions to generate token lists. We calculate the locality-sensitive hash value for all token lists and quantify their similarity. %We implement a prototype, called SemDiff, consisting of two modules: graph generation and graph diffing. The first module generates a pair of key-semantics graphs and the second module diffs the graphs. Our evaluation results show that overall, SemDiff outperforms state-of-the-art tools when detecting the similarity of binaries generated from different optimization levels, compilers, and obfuscations. SemDiff is also effective for library version search and finding similar vulnerabilities in firmware.

cs.CR↗

arXiv2026

Inferring Inference

Patterns of microcircuitry in the cerebral cortex suggest that the brain has an array of repeated canonical computational units. However, neural representations are distributed, so the relevant computations may only be related indirectly to single-neuron transformations. It thus remains an open challenge how to define canonical distributed computations. Here we integrate normative and algorithmic theories of neural computation to present a mathematical framework for inferring canonical distributed computations from large-scale neural activity patterns. At the normative level, we hypothesize that the brain learns a structured internal model of its environment and its latent causes. At the algorithmic level, we propose that this inference process is a nonlinear message-passing algorithm on a graph-structured model of the world. Given a time series of neural activity during a perceptual inference task, our analysis framework finds (i) the neural representation of the relevant latent variables, (ii) interactions between these latent variables that define the brain's internal model of the world, and (iii) message functions that specify the inference algorithm. With enough data, key computational properties are identifiable due to constraints from the symmetries inherent in any canonical computation, up to a joint global transformation of all interactions and the message-passing functions. As a demonstration of this framework, we analyze artificial neural recordings generated by a simulated brain that implicitly implements an approximate inference algorithm. Given simulated inputs and neural activity we successfully recover the latent variables, their neural representation and dynamics, and canonical message functions that govern the dynamics. Analysis of these models reveals features of experimental design required to extract canonical computations from neural data.

q-bio.NC↗

arXiv2026

DyRA: Portable Dynamic Resolution Adjustment Network for Existing Detectors

Achieving constant accuracy in object detection is challenging due to the inherent variability of object sizes. One effective approach to this problem involves optimizing input resolution, referred to as a multi-resolution strategy. Previous approaches to resolution optimization have often been based on pre-defined resolutions with manual selection. However, there is a lack of study on run-time resolution optimization for existing architectures. This paper introduces DyRA, a dynamic resolution adjustment network providing an image-specific scale factor for existing detectors. This network is co-trained with detectors utilizing specially designed loss functions, namely ParetoScaleLoss and BalanceLoss. ParetoScaleLoss determines an adaptive scale factor for robustness, while BalanceLoss optimizes overall scale factors according to the localization performance of the detector. The loss function is devised to minimize the accuracy drop across contrasting objectives of different-sized objects for scaling. Our proposed network can improve accuracy across various models, including RetinaNet, Faster-RCNN, FCOS, DINO, and H-Deformable-DETR. The code is available at https://github.com/DaEunFullGrace/DyRA.git.

cs.CV↗

arXiv2026

Spectrum in alternative topological algebras and a new look at old theorems

In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. As an example, we demonstrate that a quadratic algebra over a field of characteristic not $2$ is flexible if and only if it is proper--a concept introduced in this paper. In Section 3, we show how to develop the spectral theory in the context of complex (resp. real) one-sided alternative topological algebras. Along the way, spectral theory is used to prove several topological counterparts of the well-known theorems of Frobenius, Hurwitz, Gelfand-Mazur, and Zorn. This is done, for example, in the context of left (resp. right) alternative topological algebras whose duals separate their elements. In Section 4, we consider real and complex algebras in various topological settings and reconsider and prove several results. For instance, it is shown that given a $ 1 < k \in \mathbb{N}$, on any locally complex algebra, there exists a unique nonzero vector space norm, say, $\|.\|$, satisfying the identity $\|a^k\| = \|a\|^k$ on the algebra. In Section 5, among other things, we revisit and slightly strengthen the celebrated theorems of Frobenius, Zorn, Gelfand-Mazur, and Hurwitz, and also give slight extensions of their topological counterparts, e.g., theorems of Albert, Kaplansky, and Urbanik-Wright to name a few, in several

math.RA↗

arXiv2026

Operator quantum singular value transformation: Spectral mapping, design and topological invariants

Quantum singular value transformation (QSVT) provides a unifying framework for quantum algorithms by applying the polynomials of quantum signal processing (QSP) to block-encoded matrices. We connect this framework with spectral analysis, design and topological protection in condensed matter physics. Extending QSVT beyond matrices to possibly infinite-dimensional operators (operator QSVT), we establish the following. First, it transforms every block of the operator by the QSP polynomials; no singular value decomposition is needed. Second, a spectral mapping theorem determines the full spectrum of the QSVT operator, including continuous spectra, from the embedded operator through the QSP polynomial, allowing spectral analysis without translation invariance. Third, the spectral mapping turns QSP into spectral design: the QSP phases can stretch, fold and separate the bands and place the eigenvalues. Finally, the kernel sectors that conventional QSVT usually sets aside carry a topological index, invariant under the choice of QSP phases, local perturbations and gap-preserving deformations, which guarantees topologically protected states. These results unify two quantum walks: Szegedy's walk from quantum algorithms and the split-step walk from condensed matter physics. Their kernel sectors encode the graph's Euler characteristic and the difference of bulk winding numbers, respectively. For the split-step walk, QSP breaks chiral symmetry but not the topological protection, and can move the protected state into a continuous band to form a bound state in the continuum (BIC).

quant-ph↗

arXiv2026

Generative Semi-supervised Graph Anomaly Detection

This work considers a practical semi-supervised graph anomaly detection (GAD) scenario, where part of the nodes in a graph are known to be normal, contrasting to the extensively explored unsupervised setting with a fully unlabeled graph. We reveal that having access to the normal nodes, even just a small percentage of normal nodes, helps enhance the detection performance of existing unsupervised GAD methods when they are adapted to the semi-supervised setting. However, their utilization of these normal nodes is limited. In this paper, we propose a novel Generative GAD approach (namely GGAD) for the semi-supervised scenario to better exploit the normal nodes. The key idea is to generate pseudo anomaly nodes, referred to as 'outlier nodes', for providing effective negative node samples in training a discriminative one-class classifier. The main challenge here lies in the lack of ground truth information about real anomaly nodes. To address this challenge, GGAD is designed to leverage two important priors about the anomaly nodes -- asymmetric local affinity and egocentric closeness -- to generate reliable outlier nodes that assimilate anomaly nodes in both graph structure and feature representations. Comprehensive experiments on six real-world GAD datasets are performed to establish a benchmark for semi-supervised GAD and show that GGAD substantially outperforms state-of-the-art unsupervised and semi-supervised GAD methods with varying numbers of training normal nodes. Code will be made available at https://github.com/mala-lab/GGAD.

cs.LG↗