Mathematics

The work presents LiveMathematicianBench, a dynamic multiple-choice benchmark for research-level mathematical reasoning built from recent arXiv papers published after model training cutoffs; it introduces a thirteen-category logical taxonomy of theorem types, a proof-sketch-guided distractor pipeline, and a substitution-resistant mechanism, and evaluation shows the benchmark is far from saturated—the best model, Gemini-3.1-pro-preview, achieves only 43.5%, while under substitution-resistant evaluation GPT-5.4 scores highest at 30.6% and Gemini-3.1-pro-preview falls to 17.6%, below the 20% random baseline; a dual-mode protocol shows proof-sketch access yields consistent accuracy gains.

Lu and Tsai propose a multilevel stochastic-gradient neural solver (MLSG) for second-kind boundary integral equations that represents the unknown boundary density with a neural network optimized by stochastic residual minimization over a hierarchy of successively refined Nyström discretizations, warm-starting each level with the previous level's network parameters; the algorithm avoids grid-transfer operators and hierarchical fast-summation machinery, relying instead on batched kernel evaluations and standard network forward and backward passes, and is demonstrated on Laplace/Poisson and Helmholtz problems in two and three dimensions plus an exterior Robin problem on a hypersurface in R^4, under both parametric and signed-distance surface representations at up to million-scale discretizati

The study builds a reaction-diffusion predator-prey model with additional food and predator intraspecific competition, locates the Hopf bifurcation of the coexistence state exactly in the well-mixed setting and shows the resulting cycle is stable, derives the diffusion-driven Turing threshold in the spatial setting, and finds that with prey mobility and competition strength as control parameters the pattern-forming and oscillatory instabilities meet at a single point, with simulations confirming that weak competition gives a whole-field oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time.

The work introduces fluctuation-supervised pretraining (FSP), labeling each synthetic table by its average treatment effect plus its efficient influence-function fluctuation while deployment remains a frozen forward pass; the author proves an endpoint transition along the path T_{λ,P}=θ(P)+λP_nψ_P, where every fixed λ<1 retains label ambiguity of order (1-λ)^2/n whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order n^{-2}; experiments show that across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells, validation-selected Summary FSP deploys 11.

Working on the 3D Euler equations on the unbounded domain R^3, the authors use a physics-informed neural network (PINN) with a self-similar ansatz to obtain an approximate singular profile at the critical blowup rate 0.5, certify it using a spline representation, observe that the associated transport field has a local outgoing property throughout the domain suggesting linear damping as a key stabilizing mechanism, and set up a framework that reduces a proof of nonlinear stability of the approximate self-similar profile to a large but finite collection of explicit estimates and computable constants.

The work scales Embedded Language Flows (ELF) to mathematical reasoning and code generation and introduces ELF-REG, which uses a frozen autoregressive teacher to supervise intermediate denoiser features and to supply a global representation jointly denoised with the response (REPA+REG); evaluated on GSM8K, MATH-500, HumanEval, and MBPP, ELF-REG-L reaches 55.96% pass@1 on GSM8K at 64 NFE and 13.39% on MATH-500 and 22.56% on HumanEval at 128 NFE, outperforming the evaluated comparable-scale dLMs on GSM8K and code and improving MATH-500 from the ELF-L baseline of 10.55% to 13.39%, while the same task-specific checkpoints support strong low-NFE performance through early-stop without few-step training, reaching 41.21% HumanEval pass@10 at 16 NFE.

Stojnic studies the statistical-computational gap (SCG) of the symmetric binary perceptron (SBP) via a parametric use of fully lifted random duality theory (fl-RDT): at κ=1 the second lifting level gives αc≈1.8159 matching the theoretical satisfiability threshold, the seventh level gives αa≈1.6021 with predicted convergence to about 1.59–1.60, close to the local-entropy replica prediction αLE≈1.58 for clustering defragmentation; in the α→0 regime the third lifting level gives κ≈1.2385√(α/−log α), qualitatively matching OGP predictions and identically matching local-entropy predictions; the author also designs a CLuP-SBP algorithm whose practical performance approaches the theoretical predictions.

The authors conducted a comprehensive neutral simulation comparison based on two reference datasets from randomized controlled trials, evaluating the Cox proportional hazards model and random survival forest for patient-specific survival probability prediction across multiple performance measures following TRIPOD recommendations, and found that conclusions based solely on the C index may not generalize to other aspects of predictive performance, that measures of overall performance may generally give more reasonable results, that the standard log-rank splitting rule for the random survival forest may be outperformed by alternative splitting rules particularly in nonproportional hazards settings, that the random survival forest performance suffered less in data with treatment-covariate inte