Search: “lorentzian-polynomials”

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Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · security·Sep 14, 12:23 UTC · 2d agoAI researchHN 22↑ · 19 comments

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Variational Continuation for Double Pendulum Periodic Orbits

Researchers introduce a Hessian-based, integrator-free method using automatic differentiation to continue periodic orbits in the double pendulum, uncovering previously unreported orbit families.

A new arXiv paper presents a variational, Hessian-based framework for numerically continuing periodic orbits in dynamical systems, parametrizing candidate loops as Fourier series and minimizing deviation from the governing differential equations. Automatic differentiation replaces hand-derived Jacobians, and flat directions of the loss landscape guide the continuation search. The method is demonstrated on the double pendulum, mapping bifurcations along orbit families, including periodic orbits where neither pendulum mass is ever simultaneously at rest.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 16:42 UTC · 12d agoAI research

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On APN Functions with Boomerang Uniformity One over $\mathbb F_{3^n}$: Differential and Boomerang Spectra and CCZ-Inequivalence

Cryptographic construction yields infinite APN function families with boomerang uniformity one over odd-characteristic fields, proving CCZ-inequivalence to power functions.

For q=3^n with odd n>1, every sign-switch of a perfect nonlinear Dembowski-Ostrom polynomial is proven APN with boomerang uniformity one or two, attaining uniformity one for (q-3)/2 parameters. This gives the first general construction of infinite APN families achieving boomerang uniformity one over odd-characteristic finite fields. The authors determine common differential and complete boomerang spectra, ruling out CCZ equivalence with power and Ness-Helleseth binomials, and exhibit three pairwise CCZ-inequivalent PN functions for infinitely many n, with the smallest degree n=45.

arXiv cs.CR·Sep 8, 16:19 UTC · 8d agoResearch

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A Chosen Future Can Still Be Rewritten: Causal Writability in Video Models

Study shows video models often learn correct physics but fail to use it; low-dimensional 'causal writability' edits can restore correct motion.

The paper demonstrates 'causal writability' in video generation models: physically correct motion remains available inside the model even when the model outputs incorrect motion. In a red/blue mass oscillation setup, a low-dimensional edit predicted from simple physical variables restores correct fast motion, with a sharp depth boundary marking commitment. Early causal writability predicts which training errors later get corrected, and both writability and closure reproduce in a pretrained 1.3B video model.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:58 UTC · 2d agoAI research

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Towards a Deterministic Math Solver for Clinical Language Models

Paper shows handing arithmetic to a deterministic Python solver beats direct model calculation at 32B but not reliably at 7B on MedCalc-Bench.

Researchers test a Program-Solve interface where clinical LLMs write case-specific Python executed by a restricted local solver instead of doing arithmetic directly. On MedCalc-Bench Verified (1,100 cases, 55 calculators), Qwen2.5-32B-AWQ scored 90.53% with solver handoff versus 83.47% with direct arithmetic (+7.05 points), while Qwen2.5-7B gained an unreliable +3.29 points with a confidence interval spanning zero. The authors audited the benchmark against clinical guidelines and flagged 16 of 55 calculators for version, use, or coefficient concerns.

Hugging Face daily papers·Sep 8, 20:00 UTC · 8d agoAI research

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Silver Rate Is (Almost) Optimal for Gradient Descent Acceleration

New optimization theory paper proves near-optimal lower bounds for gradient descent with predetermined stepsizes, confirming silver-schedule optimality.

The paper studies the limits of accelerating gradient descent using predetermined nonnegative stepsizes in smooth convex optimization, with the key constant p_sil = log2(1 + sqrt(2)). It proves a non-anytime lower bound of Omega(n^(-p_sil - O(sqrt(log log n / log n)))) on the error achievable by any such stepsize schedule. In the anytime setting, it shows every infinite nonnegative schedule must incur error Omega(n^(-2*p_sil/(1+p_sil) - O(sqrt(log log n / log n)))) at infinitely many horizons. Combined with the silver-schedule upper bound of Altschuler and Parrilo (2025) and the anytime upper bound of Zhang et al. (2025), these results determine the optimal polynomial convergence exponents in both settings.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:59 UTC · 8d agoAI research

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ZGCM-1: A Fully Open and Extremely Efficient Foundation Model for Math and Agentic Search

ZGCM-1 is a fully open 7B foundation model with 256K context that stays competitive with frontier models on math reasoning and agentic search.

ZGCM-1 is a fully open 7B dense foundation model trained from scratch using an efficiency-focused recipe: interleaved gated sliding-window and full attention, a stable FP8 Muon optimizer, and MDP-based mid-training with context scaling across 16K, 64K, and 256K. On mathematical reasoning and agentic search suites it remains competitive with much larger frontier models such as Qwen3-235B-A22B and GLM-5.1. The recipe yields a ~4.2x improvement in 16K pre-training time-to-loss, and all weights, checkpoints, training code, data recipes, and W&B logs are open-sourced.

Hugging Face daily papers·Sep 10, 20:00 UTC · 6d agoModel release

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Beyond the Turing threshold: Productive grammars generate essentially undecidable languages

A theoretical paper designs formal grammars that emulate Post's productive sets, generating languages that are provably beyond Turing decidability.

The paper elaborates on Emil Post's productive sets, which are not even semi-computable, and builds formal grammars that emulate their construction over natural numbers. The resulting languages are shown to be essentially undecidable, placing them beyond Turing decidability. This is pure computability and formal language theory with limited direct security relevance.

arXiv cs.CR·Sep 10, 11:20 UTC · 6d agoResearch1

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Semigroup-JEPA: Latent Dynamics Consistency for Zero-Shot Physics Generalization

SG-JEPA world model conditions latent prediction on physical parameters, halving open-loop prediction error versus DINO-WM and boosting robotic control success.

SG-JEPA extends the LeWorldModel JEPA framework by supplying the governing physics parameter to the temporal model via action-conditioning and jointly training an encoder and predictor through autoregressive latent rollout. On out-of-distribution gravitational-field tasks it reduces open-loop prediction error by up to 2x versus DINO-WM on 2D datasets and increases 3D robotic control success rate up to 2.5x using independently trained diffusion policies. A linear feature analysis attributes most of the gain to the encoder learning features that the predictor can carry forward through rollout.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:08 UTC · 7d agoAI research

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AI Doesn't Mean the End of Mathematics—at Least Not Yet

Schneier and Rafi argue frontier AI models produce notable mathematical results but cannot yet build genuinely new conceptual frameworks.

Bruce Schneier and Kasra Rafi, writing in The Guardian, argue current AI models are not yet as capable as experienced academic mathematicians despite striking results. They cite OpenAI's disproof of the unit distance conjecture, Anthropic's published cryptanalysis results, and Claude's attempt at the Riemann hypothesis as achievements in counterexample search and recombining known techniques. They contend AI has not yet developed substantial new conceptual frameworks, though they expect that capability sooner rather than later.

Schneier on Security·Aug 28, 11:03 UTC · 19d agoAI research1

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Proximity Gaps for Gabidulin Codes and Applications

Researchers prove proximity-gap bounds for rank-metric and Gabidulin codes, enabling the first polynomial commitment scheme framework based on rank-metric error-correcting codes.

The paper proves every linear rank-metric code admits a proximity gap for deltas up to (d-1)/(3n) with error at most q^(e+1)/q^m, and improves the gap to (d-1)/(2n) for Gabidulin codes with error at most 10q^(n-1)/q^m, matching bounds for Reed-Solomon codes. A constructed infinite family of constant-rate Gabidulin codes shows the (d-1)/(2n) bound is tight, and a counterexample establishes a lower bound on the error at the d/(3n) gap. Applications include an IOPP for interleaved Gabidulin codes adapted from the Ligero IOPP and a q-linearized polynomial commitment scheme adapted from Ligero-based PCS, reportedly the first PCS framework based on rank-metric codes.

arXiv cs.CR·Sep 9, 07:45 UTC · 7d agoResearch

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Searching for New Physics with Reinforcement Learning

Researchers apply reinforcement learning to identify SMEFT operators explaining particle physics anomalies, reproducing and improving known CDF W-mass results.

The paper introduces a reinforcement learning method to search the large Standard Model Effective Field Theory (SMEFT) operator space for explanations of measurement anomalies. It was validated on the CDF W-mass anomaly, reproducing and improving known results, then applied to a harder multi-anomaly scenario. RL efficiently navigates complex loop-level operator correlations that bias human-driven phenomenological analysis.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 16:07 UTC · 7d agoAI research

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Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science

Stellar Colosseum, a many-agent harness for long-horizon math and TCS research, solves open problems and reaches 71% on TCS-Bench with Gemini models.

Stellar Colosseum is a model-agnostic harness that allocates inference across long-horizon research in mathematics and theoretical computer science, using strategy exploration, a readiness gate, section-level decomposition, and verifier feedback routing. Integrated into Google Antigravity's Teamwork framework as the Long Proof pattern, it obtains new results on open problems from FOCS and JMLR papers using Gemini 3.1 Pro. On TCS-Bench it achieves 71.0% accuracy with Gemini 3.1 Pro and Gemini 3.7 Flash, and a Codeforces evaluation with Gemini 3.1 Pro solves 218 of 222 problems.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:58 UTC · 2d agoAI research

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Show HN: LLM Attention Visualization

A developer released a browser-based tool that visualizes which past tokens influence each LLM output token using aggregated, value-weighted attention scores.

A Show HN project presents a React application built on Transformers.js that renders per-token attention influence by aggregating attention weights scaled by value-vector magnitudes across all attention heads and layers. To expose internal tensors, the author instrumented the ONNX computation graph, hosted a modified model on Hugging Face, and pre-generated prompts to avoid long model downloads in the browser. Demos with a 600-million-parameter model show how verbatim copying draws heavily on source tokens and how single outputs blend information from multiple phrases.

Hacker News · AI·Sep 8, 16:59 UTC · 8d agoAI tools & infraHN 41↑ · 9 comments

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Caltech Mathathon – first hackathon ever devoted to research level mathematics

Caltech will host the first research-level mathematics hackathon on October 30, giving 100 teams frontier AI models to attack open conjectures.

The Caltech Mathathon runs October 30 to November 1, assembling about 100 teams that will receive frontier models and over $2 million in AI credits to work on open mathematical problems. Teams will defend their results before leading mathematicians, with prize rounds before and after community verification of the results. The announcement cites recent AI-driven math results, including the disproof of Erdos's 80-year-old planar unit-distance conjecture, the first explicit non-sofic group, and a claimed complex structure on the six-sphere (unverified).

Hacker News · security·Sep 7, 09:26 UTC · 9d agoAI industryHN 264↑ · 92 comments1

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Implementing a White-Box Undetectable Backdoor for Random Fourier Features

Researchers implement Goldwasser's CLWE-based undetectable backdoor for Random Fourier Features models in numpy/scipy, confirming practical realizability with no detectable differences from clean models.

The paper provides an end-to-end implementation of the Goldwasser et al. white-box undetectable backdoor for models trained with the Random Fourier Features algorithm, using only numpy and scipy. It derives two samplers for the core GP_d(b_k) distribution: a rejection-sampling proxy and an exact closed-form sampler verified against its analytic form. Statistical indistinguishability tests covering weight-space and functional black-box comparisons found no detectable difference between backdoored and clean models across sparsity ratios. The underlying lattice hardness reduction was not reproduced, and the work demonstrates the threat is realizable with commodity scientific-computing tools rather than specialized cryptographic infrastructure.

arXiv cs.CR·Sep 14, 22:18 UTC · 1d agoResearch

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🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing

Caltech professor Anima Anandkumar discusses Neural Operators and FourCastNet for physics modeling, arguing inductive biases beat pure token scaling.

Anima Anandkumar, Bren Professor at Caltech and co-founder of Accelerated Understanding, describes Fourier Neural Operators that learn in frequency and spherical-harmonic domains to model weather, fusion, and fluid or heat flow. Her team built FourCastNet 3, a global weather model competitive with physics-based simulations that runs on consumer-grade GPUs. She also introduced TorchLean, a framework for writing PyTorch-style networks inside the Lean proof assistant for formal verification, and was appointed to the United Nations Scientific Advisory Board. She argues physical domains resist scaling due to tiny datasets and context lengths in the hundreds of billions, so progress comes from built-in structure and physical priors.

Latent Space·Aug 26, 15:15 UTC · 21d agoAI research1

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[AINews] Jev: a “System One Model” that only decides/classifies/routes/scores — >100x faster, >200x cheaper than small frontier LLMs

TypeSafe launches Jev, an RLCD-trained decision model claiming 20-200x faster, 40-400x cheaper classification than frontier LLMs, alongside Gemini 3.8 Live and Neon.

TypeSafe's Jev is a 'System One' decision model trained with RLCD, claiming 20-200x faster and 40-400x cheaper classification and routing than frontier LLMs with free output tokens and no hallucinated text. Google launched Gemini 3.8 Live and 3.8 Live Extended Thinking, supporting 97 languages and async tool calls, debuting #1 on Artificial Analysis' speech-to-speech index at 82.6. Periodic Labs' Neon is a ~1T-parameter XRD analysis model trained with RL on proprietary lab data using 1,300 H200s, lifting FrontierXRD success from 2.7% to 55.3% and beating GPT-6 Astra at lower inference cost.

Latent Space·11:09 UTC · 10h agoModel release1

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Embedded Graph Flows for Categorical Graph Generation

Researchers propose Embedded Graph Flows, a generative model with learned categorical embeddings that beats DiGress and GruM on molecular graph benchmarks.

Embedded Graph Flows (EGF) learns continuous embeddings for node and unordered-edge categories and transports Gaussian noise toward these endpoints using a permutation-equivariant graph transformer. On QM9 it achieves the best result on all four reported metrics, with a Fréchet ChemNet Distance of 0.150 versus 0.717 for DiGress and 0.812 for GruM. On ZINC250k it retains the lowest NSPDK MMD, indicating close agreement with local substructures of reference molecules. Code is released on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 16:26 UTC · 12d agoAI research1

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Graph Machine: Towards Better Pretraining via Edges

Researchers propose Graph Machine, an O(n)-state sparse architecture that replaces 75% of Qwen3-0.6B dense layers with only slight loss change.

The paper introduces the Graph Machine (GM), an architecture that maintains an O(n)-sized state accessed through sparse, dynamic routing via pointer-like edges updated differentiably by a referral mechanism resembling pointer chasing. The authors replaced 75% of dense Transformer layers in Qwen3-0.6B with GM sparse layers and pretrained from scratch on 15.7B tokens. Retrieving 2 of 4,096 tokens per KV head in each sparse layer degrades loss only slightly, while retrieving 4 marginally improves loss over the dense baseline.

Hugging Face daily papers·Sep 1, 20:00 UTC · 15d agoAI research

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MathKernel: An evidence-aware multi-engine mathematics kernel and MCP server

MathKernel is an open-source, evidence-aware multi-engine mathematics kernel that exposes verification workflows to AI agents via an MCP server.

MathKernel, published on GitHub, is a mathematics kernel that combines multiple computation engines with evidence-aware outputs. It ships as an MCP server, enabling AI agents and coding assistants to perform and verify calculations. The project drew moderate attention on Hacker News.

Hacker News · security·Sep 7, 00:21 UTC · 9d agoAI tools & infraHN 36↑ · 5 comments

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Show HN: MultiMatte, a Promptable Image Background Removal Model

Feyn releases MultiMatte, a promptable background-removal model fine-tuned from Meta's SAM 3 via LoRA, outputting alpha mattes that beat SAM 3 on segmentation benchmarks.

Feyn introduced MultiMatte, a promptable image background-removal model built on Meta's SAM 3 (860M parameters). It modifies only 19.49M parameters (2.27%) using a rank-16 LoRA adapter and replaces binary masks with alpha mattes to handle fuzzy boundaries like hair. On the DIS-VD benchmark it scores 0.901 S-measure versus SAM 3's 0.667, and it improves on SAM 3 across all twelve evaluated splits. Training used 19,953 images for 14,000 steps with focal and Dice loss, and the merged weights are available via the nobg library and a web demo.

Hacker News · security·Sep 10, 15:50 UTC · 6d agoModel releaseHN 21↑ · 4 comments1

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27.5KB language-agnostic WebGPU syntax highlighter

A developer released gpu-lexer, a 27.5KB language-agnostic syntax highlighter that uses a tiny WebGPU model to label code tokens in the browser.

gpu-lexer splits source into words, whitespace, and symbols, then a small WebGPU model uses local and whole-file context to assign nine token classes, working on languages never seen in training. On held-out files, 12.57% of token labels differ from Shiki, though this measures agreement with Shiki rather than objective correctness. In benchmarks against Shiki 4.4.3, Prism.js, Highlight.js, Sugar High, and Starry Night, it highlighted 10 concatenated copies of three.min.js (5.56M characters) about 10x faster on an Apple M4 Pro in Chrome 152. The author frames it as an experiment, not a grammar-equivalent highlighter.

Hacker News · security·Sep 9, 01:14 UTC · 7d agoAI tools & infraHN 21↑ · 5 comments1

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Reduced-Space Multi-Fidelity Bayesian Optimization of Process Simulation Models

RS-MFBO couples global sensitivity analysis with fidelity-augmented Gaussian processes to slash costly high-fidelity simulation runs in industrial flowsheet optimization.

The paper presents RS-MFBO, a reduced-space multi-fidelity Bayesian optimization framework for high-dimensional, expensive black-box functions. It integrates Global Sensitivity Analysis for dimensionality reduction with a fidelity-augmented Gaussian process and a cost-aware acquisition strategy featuring cooldown and promotion mechanisms. Validation on a plasmid DNA bioprocess (SuperPro Designer) and a green fuel synthesis plant (Aspen HYSYS) shows substantial reductions in high-fidelity evaluations while remaining competitive with single-fidelity baselines.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 16:46 UTC · 1d agoAI research

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Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

Mathematical paper constructs counterexamples on c0 and l1 disproving Rockafellar's conjecture that sums of maximally monotone operators remain maximally monotone.

The authors build counterexamples where two maximally monotone operators satisfy the interior-domain condition yet their sum is not maximally monotone, refuting Rockafellar's sum conjecture. One counterexample is constructed on c0 and another on l1 with its usual norm. A general construction theorem computes the monotone polar of a class of graphs, gives necessary and sufficient conditions for maximal monotonicity, and shows how a positive rank-one perturbation yields a nonmaximal sum.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:26 UTC · 7d agoAI research

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On the Navier–Stokes Millennium Prize Problem

OpenAI says an unreleased model produced a claimed solution to the Navier-Stokes existence and smoothness problem, disputed by an NYU mathematician.

OpenAI used an unreleased model to produce a claimed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1,000,000 prize since May 24, 2000. The result is contested: NYU mathematics professor Tristan Buckmaster accused collaborators of skulduggery and rushed out his own competing results with mathematician Levent Alpoge, who works at Anthropic. The dispute is documented in a published PDF describing the competing claims.

Simon Willison·Sep 8, 23:39 UTC · 7d agoAI research

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AI models' written reasoning steps correspond to distinct internal patterns, a new study finds

KAIST and Naver AI Lab researchers show LLM reasoning steps like extraction and computation map to distinct activation patterns, strongest in middle layers.

Researchers at KAIST and Naver AI Lab defined eight recurring reasoning operations, including extraction, decomposition, formula recall, deduction, and computation, and showed they correspond to separable activation patterns in Qwen2.5-7B, Qwen3-8B, and Gemma4-31B on math tasks, with GPT-5 labeling solution segments. The separation peaks in middle layers, holds even when a computation step produces a wrong answer, and goes beyond surface-level token choice. Findings replicated on Llama-3-8B, and classifiers trained on Qwen3-8B transferred to GPQA-Diamond and MATH-500. The authors note that using internal states for error detection or mid-generation steering remains future work.

The Decoder·Sep 12, 13:39 UTC · 4d agoAI research2

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Feyospace-v1: How the Cyber Mercury Seven Trained Frontier Cyber Models

A seven-person independent team trained open-weight agentic cyber models via a data-centric post-training framework, ranking 10th on CyberGym and first at comparable scale.

The paper presents Feyospace-v1, a data-centric post-training framework combining five systems: Choulea (hidden reasoning analysis), SkyReal (teacher-sampling cost reduction), Hongzwang (bypassing teacher API restrictions), PSBreakup (restoring capabilities weakened by model merging), and Kreator (converting expert interventions into trainable reasoning). The data engine builds resettable coding, vulnerability, CTF, kernel-history, full-exploit, firmware, and device-backed environments, retaining only execution-verified and evidence-audited trajectories, yielding 164,269 trajectories for long-context supervised fine-tuning. Three checkpoints improve over their starting models by an average of 23.76% on the full CyberGym suite and 10.49% across pooled CTF suites. As of September 1, 2026, Feyospace-s1 achieves a 63.24% verified success rate, ranks 10th on the official CyberGym leaderboard, and all three checkpoints rank 1st among models at comparable parameter scales.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research

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Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarch

New work characterizes language generation in the limit via finite witnesses, proves a full separation-width hierarchy, and formalizes all results in Lean.

The paper fully characterizes when language generation in the limit is possible for arbitrary families over a countable universe: each target must admit a finite positive witness such that targets activated by any finite sample share an infinite common intersection. It defines positive separation width and proves every level of the resulting hierarchy occurs, with countable families admitting singleton witnesses and unions of families with infinite common cores requiring unbounded finite witnesses. The characterization, a universal normalization, and a diagonal capture lemma are machine-checked in the Lean proof assistant, with the development maintained on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:54 UTC · 7d agoAI research1

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The Pelican comparison grid for Astra is pretty interesting

Simon Willison's pelican SVG comparison shows GPT-6 Astra producing markedly better images than GPT-5.6 Sol, Terra, and Luna across reasoning levels.

Willison generated pelicans-riding-bicycles SVGs with newly accessed GPT-6 Astra at low through max reasoning levels and rendered them in a comparison grid against GPT-5.6 Sol, Terra, and Luna. Astra's outputs were markedly more coherent, while even the best GPT-5.6-Sol images remained largely abstract shapes. Astra does not support a reasoning=none setting, so all comparisons involved reasoning-enabled runs.

Simon Willison·Sep 4, 23:59 UTC · 11d agoAI research

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