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At least 1,027 records · Page 57Linked to original sources
arXiv2026

OpenCollab: A Multi-Agent Coding Framework with Programmable Collaboration and Controllable Runtime

Multi-agent coding systems are designed to tackle complex software engineering tasks through collaboration. However, existing evaluations typically assume configured organizations are followed faithfully, whereas reality differs. This behavioral gap, combined with differences in underlying system components, prevents clear attribution of observed gains. To this end, we introduce OpenCollab, a multi-agent coding framework that provides a unified infrastructure for programmable collaboration and controllable runtime. Specifically, OpenCollab unifies organization design, enforces experimental control on a shared runtime, and tracks execution through fine-grained event streams. On this basis, we define Adherence to quantify whether the declared organization is actually realized. Our experiments reveal that agents collaborate very differently across configurations: changing any single dimension shifts Adherence, from 47.2% to as high as 97.2%. Furthermore, extensive agentic coding benchmarks show that OpenCollab (Duo) establishes new SOTA performance compared to the mainstream harnesses such as Mini-SWE-agent, OpenHands, Codex CLI, and Claude Code, showing that a well-designed organization can outperform strong existing harnesses, while OpenCollab's single-agent configuration uses the fewest tokens across all evaluated suites. OpenCollab establishes a unified multi-agent infrastructure for easy programmable collaboration and controlled causal evaluation.

cs.SE↗
arXiv2026

The List Total Colouring Conjecture is False

We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin--Kostochka--Woodall, Juvan--Mohar--Škrekovski and Hilton--Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.

math.CO↗
arXiv2026

StreamDecisionBench: Evaluating Decisions in Force on Evolving Language Streams

Language models increasingly make real-time decisions in applications that apply the latest answer until a newer one arrives. A late answer can prolong an outdated decision, such as a call recorder still running while a customer reads out card details, an error offline accuracy misses. We make three contributions. First, we release StreamDecisionBench (SDB), a dataset of eight streaming scenarios in four application families, with executable reference decisions derived from public rules. Second, we propose an evaluation protocol and a metric, in-force accuracy: the share of time the applied decision is correct across update intervals of 0.5-8 s. It reflects accuracy and latency jointly, attributing each error to judgment, latency or both. Third, we evaluate fifteen single-model settings, and this attribution separates speed-limited from judgment-limited models: slower, more accurate models lose 42-47% of the time to outdated answers, a fast model 35% to wrong ones. We therefore test hybrids in which a slow model corrects a fast one; with the right pairing and configuration, a hybrid outperforms every single model. However, even the best evaluated system keeps a correct decision in force only about two-thirds of the time, leaving a substantial gap for real-time use.

cs.CL↗
arXiv2026

Model-free Reinforcement Learning for Continuous Time and State: A Stochastic Maximum Principle Approach

This paper develops a model-free reinforcement learning (RL) algorithm based on the stochastic maximum principle for continuous-time stochastic control problems with continuous state and action spaces. For a parameterized Markovian policy, we establish the existence of the decoupling field for the adjoint backward stochastic differential equation, which allows the Hamiltonian gradient to be represented as a deterministic function of time and state. We then learn this Hamiltonian gradient directly from data and incorporate it into a policy gradient scheme with inexact gradients. We establish the convergence of the resulting policy gradient algorithm and establish the corresponding error estimates. Under suitable conditions on learning rates, exploration parameters, and approximation errors, the objective values converge and the $L^2$-norm of the policy gradient vanishes asymptotically. We further show that the proposed SMP-based policy gradient representation is equivalent to the existing continuous-time deterministic policy gradient representation based on the advantage-rate function. The effectiveness and efficiency of the proposed RL algorithm are demonstrated by numerical experiments.

math.OC↗
arXiv2026

Counting hypergraphs without linear cycles of fixed length

Let $C_{k}^{(r)}$ be the $r$-uniform linear cycle on $k$ hyperedges. An $r$-graph is $C_{k}^{(r)}$-free if it contains no copy of $C_{k}^{(r)}$. Let $\operatorname{ex}_{r}(n,C_{k}^{(r)})$ denote the maximum number of hyperedges in an $n$-vertex $C_{k}^{(r)}$-free $r$-graph. Balogh, Narayanan and Skokan asked whether, for every pair of integers $r,k\ge 3$, the number of $C_k^{(r)}$-free $r$-graphs on $n$ labelled vertices is \[ 2^{(1+o(1))\operatorname{ex}_{r}(n,C_{k}^{(r)})}. \] While the analogous statement is known to fail for graphs ($r=2$), by a construction of Morris and Saxton, the general question remained open for hypergraphs. Very recently, Jiang and Longbrake answered the question affirmatively when $r\geq5$. In this paper, we completely resolve the problem by proving that the answer is affirmative for every pair of integers $r,k\geq3$. When $(r,k)\neq(3,3)$, we establish balanced supersaturation results for linear cycles and combine them with the hypergraph container method. For $(r,k)=(3,3)$, we instead decompose $3$-graphs according to their pair-codegrees, encode the subhypergraph formed by the hyperedges that contain a large codegree pair as a directed graph, and apply a multicolour entropy theorem.

math.CO↗
arXiv2026

Near-Minimax-Optimal Rates for Asynchronous TD Learning with Markovian Data

We study the last iterate of standard importance-weighted temporal-difference (TD) learning from a single trajectory of a finite Markov decision process. The trajectory follows a behavior policy $b$ with an irreducible, possibly periodic state chain; a target policy $π$ covered by $b$ is evaluated with action importance ratios bounded by $\varrho$. Write $H=(1-γ)^{-1}$, with $μ_{\min}$ the minimum stationary probability and $\mathfrak h_\star$ the largest expected hitting time of the reverse behavior state chain. We prove that the last iterate achieves sup-norm error at most $\varepsilon$ with high probability after $\widetilde O(\varrho H^3/(μ_{\min}\varepsilon^2)+\mathfrak h_\star)$ transitions for $0<\varepsilon\le1$. The statistical term retains the cubic effective-horizon dependence of synchronous TD, while the initialization cost is additive in $\mathfrak h_\star$. Setting $b=π$ and $\varrho=1$ recovers the on-policy rate. For aperiodic behavior chains, $\mathfrak h_\star=\widetilde O(t_{\rm mix}/μ_{\min})$ recovers a mixing-time bound. The proof combines an anchored local Poisson equation in reverse time to control fluctuations without a mixing-time factor, a compensation argument for successive hitting costs, and an expected cumulative propagation mass bound for decreasing step sizes. Given the policy ratios and their bound, an empirical state-count rule attains the same rate without prior knowledge of model parameters. The framework covers nonnegative affine importance-weighted prediction updates, including successor features, transition-dependent discounting, and coupled finite-mode predictions. A perturbation estimate yields a time-uniform guarantee for online return-variance estimation. A three-state, two-action construction gives matching minimax lower bounds for both terms up to logarithmic factors on the considered parameter classes.

stat.ML↗
arXiv2026

Stanley-Reisner Theory in Mixed Characteristic

We discuss a class of mixed characteristic rings defined analogously to Stanley-Reisner rings by replacing one variable with a uniformizing parameter for a discrete valuation ring. We adapt Hochster's formula for Tor and Ext modules, Hochster's formula for local cohomology, and Terai's criterion for Serre conditions to this new setting; one of the tools needed is cellular sheaf cohomology, for which we give a brief treatment.

math.AC↗
arXiv2026

Making LLMs Say What They Think: Measuring and Improving CoT-Interpretability Alignment

Chain-of-thought (CoT) traces often serve as a proxy for how Large Language Models (LLMs) arrive at their answers. However, growing evidence shows that models' CoT often fails to reflect their internal computations and can be changed without affecting their final answers. In this work, we measure and improve the alignment between the reasoning described in an LLM's CoT and what it computes internally. We propose CoT-Interpretability Alignment (CIA), a metric that measures the agreement between a model's CoT traces and its internal reasoning strategies as detected by interpretability tools. We evaluate CIA on three tasks (two-hop question answering, hint intervention, and integer multiplication) across three LLMs, finding that LLMs exhibit limited alignment across all tasks (44.8-75.9%). We then experiment with improving CIA via post-training, setting both the task accuracy and parametric faithfulness signals as a reward. Experiments show that we can substantially improve CoT parametric faithfulness while maintaining or improving the task accuracy. We provide rich analysis, such as their generalization patterns. Our work provides both a framework for auditing CoT parametric faithfulness and a pathway toward making models' explicit reasoning more trustworthy. Code and data are available at https://github.com/yihuaihong/CIA-minimal-repro.

cs.CL↗
arXiv2026

Threshold Geometry, Bifurcation, and Data-Driven Analysis of a Vaccination-Treatment Model for Hepatitis B

Despite the availability of excellent vaccines and antiviral medicines, hepatitis B virus (HBV) remains a major public health problem. In this work, we develop a mathematical vaccination-treatment model for HBV transmission to investigate threshold conditions for illness persistence as well as the level of intervention. The analysis gives the characterisation of both disease-free and endemic equilibria and determines the basic reproduction number, $\mathcal{R}_0$, by the next-generation matrix approach. The model indicates that $\mathcal{R}_0=1$ is a critical threshold dividing disease-free from endemic states and characterises a forward transcritical bifurcation regarding the transmission parameter. Numerical equilibrium continuation and stability assessments confirm the analytical results. A two-parameter study of transmission and vaccination rates identifies threshold geometries and assesses impacts of important parameters using sensitivity analysis. The model is calibrated with India-specific data, such as HBsAg prevalence, HBV incidence and mortality rates and fits epidemiological targets closely through limited nonlinear calibration. Additionally, multi-start optimisation and practical identifiability profiling are used to investigate parameter uncertainty. Robustness analyses reveal that the calibrated $\mathcal{R}_0^*=1.1744$ is associated with a super-threshold regime; however, parameter flexibility permits both sub-threshold and super-threshold regimes. This combined analytical and data-driven framework connects epidemic thresholds, bifurcation structures, intervention efficacy, and parameter uncertainty. It provides a quantitative framework for analysing HBV persistence and evaluating control options, especially in the absence of epidemiological evidence.

math.DS↗
arXiv2026

Ekedahl's Equivalence Explained

Ekedahl's theory relates diagonal complexes to \(F\)-gauges, but turning this equivalence into explicit calculations requires careful control of its constructions. These notes explain the equivalence and clarify the generators-and-relations definition of \(\rmt\). At each finite level, we construct bounded projective resolutions of bounded coherent gauge complexes by finite sums of the standard generators. Morita equivalence expresses \(\rmt\) as a tensor product functor. Comparing the constructions across levels yields an exact fully faithful embedding of the diagonal heart into \(\Ch(R)\). Finally, we compute three distinct domino types arising from abelian threefolds that are all supergeneral.

math.AG↗
arXiv2026

Scale and Selection: What Makes Automatic Harness Evolution Work for Visual-Interface Robot Agents

When an off-the-shelf coding agent is used directly as a robot policy, observing a browser-based 3D interface through screenshots and acting by posing a virtual target gripper through a few tools, the agent's harness, its prompts, tools, and control rules, largely determines success, and until now it has been written by hand. We show that this harness can be improved automatically by another coding agent, the optimizer agent, and report two findings about what makes it work. First, the number of rollouts the optimizer agent sees per round governs whether the evolved harness generalizes: with rounds fixed, held-out success rises as the training batch grows from 5 to 100 rollouts, while small batches overfit the training tasks. Second, the optimizer agent must not be given free rein. Accepting every revision it proposes degrades the harness within a few rounds; a simple Champion-Challenger rule that promotes a revision only if it beats the incumbent on the same fixed cases turns the same loop into one that raises held-out success on LIBERO tasks from 51% to 67% over 30 rounds. Combining the evolved harness with a pretrained policy, through one tool that hands it control, reaches 71.2% on the RoboCasa365 leaderboard benchmark, 13.1 points above the best published entry. Automatic harness evolution for visual-interface robot agents is thus feasible, but its gains hinge on the rollout scale behind each decision and on how the optimizer agent's revisions are selected.

cs.RO↗
arXiv2026

An LSST-DESC Precursor Project: Hyper Suprime-Cam Year 1 $3\times2$pt in Harmonic Space

We present the first fully photometric joint analysis of weak gravitational lensing and galaxy clustering (3$\times$2pt) in harmonic space with LSST-DESC analysis pipelines applied to Hyper Suprime-Cam Year 1 (HSC Y1) data. The HSC Y1 dataset, with imaging depth and galaxy number density similar to those expected for the first year of LSST observations, is an ideal testbed for validating DESC measurement and inference tools. We measure the full set of angular power spectra - cosmic shear, galaxy clustering, and galaxy-galaxy lensing - perform null tests, and correct for the impact of observing conditions on both the galaxy density and shear fields via mode deprojection. We validate our likelihood pipeline by reproducing the official HSC Y1 cosmic shear cosmological constraints with the DESC inference code. Jointly analysing all three two-point functions, we constrain $Λ$CDM and $w$CDM cosmologies, reporting results for cosmic shear, the combination of galaxy clustering and galaxy-galaxy lensing (2$\times$2pt), and the full 3$\times$2pt. From the joint 3$\times$2pt $Λ$CDM analysis we find $Ω_m = 0.249^{+0.061}_{-0.051}$, $σ_8 = 0.904^{+0.098}_{-0.091}$, and $S_8 \equiv σ_8\sqrt{Ω_m/0.3} = 0.821^{+0.018}_{-0.021}$. This analysis validates the complete DESC 3x2pt infrastructure on survey data, providing the foundation for the forthcoming LSST Year 1 cosmological analysis.

astro-ph.CO↗
arXiv2026

A Math Circle in Third Grade

Problems developed for a mathematics circle conducted throughout the school year in a primary school class, involving all pupils without any selection, thus working with a heterogeneous group of children.

math.HO↗
arXiv2026

Learning Where to Look: Anatomical Grounding and Guided Attention for Cardiac MRI Vision-Language Models

Cardiac magnetic resonance imaging (CMR) enables assessment of cardiac anatomy, ventricular function, and myocardial tissue characteristics. Clinicians interpret these images by identifying cardiac structures and focusing on the regions relevant to each clinical question, motivating anatomically guided vision-language models (VLMs). Yet CMR-specific supervision for anatomical localisation and clinical question answering remains limited. To address this gap, we investigate fine-grained CMR visual question answering through anatomical grounding and guided attention. We construct 128,915 anatomical-grounding and 42,799 clinical QA pairs across short-axis cine, late gadolinium enhancement, and long-axis cine. These datasets support anatomical recognition, localisation, and clinical assessment without requiring paired reports for individual training images. To help the model learn where to look, we introduce Cardiac Anatomy-Routed Attention (CARA), which selects predicted anatomical priors according to the question and guides decoder attention with learned task-specific strengths. Combining anatomical grounding pretraining with CARA yields our model, CARA-VL. Experiments demonstrate CARA-VL's strengths in clinical assessment and regional localisation across CMR imaging settings, with promising generalization to an external clinical cohort. Together, our data and method provide a practical framework for studying and advancing cardiac visual understanding in VLMs. We will release the QA data derived from public datasets upon publication.

cs.CV↗
arXiv2026

Useful to Whom? The Easy-versus-Coverage Boundary Moves with the Learner

Is the same data equally useful to every learner? The question is whether the value of a training sample belongs to the sample or arises in its interaction with the learner. We test it with a selection experiment. Under a per-class budget, two kinds of samples compete for the slots: easy samples, which a short training run learns first, and coverage samples, which spread over the class in feature space. Easy samples win at small budgets and coverage samples at large ones, and the budget at which the winner flips, the crossover m0, can be measured. We ask whether m0 is set by the data or by the learner. To separate the two, we freeze the selected subsets and change only the learner that trains on them. On low-resolution ImageNet-100, doubling the width of a ResNet-18 moves the crossover from 57 to 85 samples per class on the same subsets. Enlarging the input grid from 32 to 64 pixels at fixed image information moves it from 85 to 57, and a single stride change reproduces or removes this shift. The grid shift shrinks as width grows. Under the native ImageNet-1k protocol, a 4x range of width moves the boundary by at most a few samples per class. On a Vision Transformer, coverage wins at every measured budget, even with easy subsets that work on the convolutional learner. The budget at which one kind of sample stops being the more useful kind therefore belongs to the learner, and the preferred regime of a selection strategy has to be read against the learner that will use the data.

cs.LG↗
arXiv2026

A massive right-handed sterile neutrino in three-body ${\bar B}\to D^*\ell^-{\bar N}_R$ decays - a Monte Carlo simulation study

We investigate the differential decay distributions of $\bar{B}\to D^*\ell^-{\bar N}_R $, where $N_R$ is a heavy right-handed neutrino (RHN) and $\ell = e, μ$. We employ a newly developed Monte Carlo event generator based on the EvtGen framework that can simulate beyond-the-Standard-Model processes. We validate the implementation of the model by comparing the Monte-Carlo results with analytical results for several kinematic variables such as $q^2$ and missing mass, as well as signatures in the angular distributions such as $A_{FB}$, $S_{3}$, $S_{5}$, etc. This MC Generator will enable new experimental searches for RHNs. We discuss the sensitivity of various observables to the presence of an RHN and the feasibility of an experimental analysis at Belle II.

hep-ph↗
arXiv2026

Heteroskedastic Canonical Polyadic Tensor Decomposition

When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

stat.ME↗
arXiv2026

Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon Lyapunov Functions

We study fixed-time input-to-state stability (FxT-ISS) for discrete-time systems subject to exogenous inputs using finite-horizon Lyapunov functions. In the proposed Lyapunov- based characterization, the effect of the initial condition is eliminated after a uniformly bounded number of iterations. This characterization encompasses existing extinction-based Lyapunov conditions while allowing more general finite-memory mechanisms. Building on this framework, we establish a finite-horizon small-gain theorem for interconnected discrete-time systems, providing conditions under which FxT-ISS is preserved under feedback interconnections. The proposed framework is illustrated through examples arising in distributed algorithms, optimization, and feedback optimization.

math.OC↗