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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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Locus: A Framework for Exploring and Optimizing Point Addition Hardware for Zero-Knowledge Proofs

Locus framework automates ASIC and FPGA point-addition designs for elliptic curves, achieving 2.71x speedups and 3.11x area reductions for ZKPs.

Locus is a framework that automatically generates ASIC and FPGA implementations of elliptic curve point addition (PADD) for supported equation forms, enabling exploration of over 1,000 design points. On a 12nm technology node, its designs achieve a 2.71x geomean speedup and 3.11x geomean area reduction versus prior ASICs, plus 34.67x geomean speedup over CPU. Integrated into a prior ZKP accelerator at iso-area, it yields a 3.15x geomean speedup on end-to-end proof generation. The framework is open source on GitHub.

arXiv cs.CR·Sep 16, 15:53 UTC · 16h 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 research1

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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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Double descent is the principle of least action

A statistical mechanics analysis explains double descent: finite-time diffusion induces effective weight decay that regularizes models as parameters grow.

The paper models stochastic gradient-based training as a particle diffusing over the training-loss energy landscape at an induced temperature, sampling parameters via a Boltzmann distribution. Finite training time carries an effective weight decay, making every parameter a quadratic degree of freedom governed by the equipartition theorem. Adding parameters at fixed training loss lowers the temperature and the L2 norm of the stationary path, increasing effective regularization and explaining the double descent phenomenon.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:17 UTC · 15h 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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Fast Learning Rates for Physics-Informed Kernel Methods

Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.

The paper analyzes a physics-informed kernel estimator combining n value observations and m differential observations for a linear differential operator D, asking how much differential information improves prediction. The authors prove finite-sample bounds, supported by simulations, revealing a two-regime structure: when m is limited the rate depends jointly on n and m, and when m exceeds a problem-dependent threshold the rate saturates to the oracle rate. Examples in Sobolev spaces, including partial Laplacian constraints on the torus and gradient observations on bounded domains, illustrate improvements from the nonparametric n^-1/4 rate to the parametric n^-1/2 rate, plus physically consistent rates in a stronger norm.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 16:39 UTC · 15h agoAI research

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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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How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

Researchers show model growth via looped transformers improves scaling exponents; a 7.4B architecture matches GPT-3 13B with roughly 20x less compute.

The paper shows that architectural interventions, contrary to conventional wisdom, can modify pre-training scaling exponents and yield exponential performance gains with compute. Looped transformers with increasing loop counts provide a model growth mechanism; a 7.4B model-growth architecture matches GPT-3 13B on CORE with roughly 20x less compute, with efficiency gains that increase with scale. A boundary operator that normalizes and injects an earlier block also improves compute efficiency, and in data-constrained multi-epoch settings increasing loops with scale is compute-optimal.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:36 UTC · 14h 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 · 8d 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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Real-Time Intelligence with IBM Time Series Models on Confluent

IBM Research post on the Hugging Face blog describes running IBM time series models on Confluent for real-time intelligence.

Hugging Face's blog published an IBM Research post titled 'Real-Time Intelligence with IBM Time Series Models on Confluent.' No article body was available for classification, so details are limited to the title. The title indicates guidance on deploying IBM time series models alongside Confluent streaming infrastructure for real-time analytics.

Hugging Face Blog·Sep 2, 13:49 UTC · 14d agoAI tools & infra

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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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Google's new AI model predicts the future from sales data, weather, and discount schedules

Google Research released TimesFM-3, a 330M-parameter multivariate time series forecasting model that tops Gift-Eval, FEV-Bench, and Time benchmarks and is on Hugging Face.

Google Research released TimesFM-3, a 330-million-parameter Transformer-based time series forecasting model trained on more than one trillion real and synthetic data points. It works zero-shot and adds multivariate support, ingesting related series, historical-only covariates, and known future events such as discount schedules and weather forecasts, while filling all future time steps in a single one-shot pass. Google reports first place among pretrained forecasting models on Gift-Eval, FEV-Bench, and Time, ahead of Amazon's Chronos-2, the Toto-2.0 family, and its own TimesFM-2.5. Weights are available on GitHub and Hugging Face, with BigQuery integration planned in the coming weeks.

The Decoder·Sep 12, 09:26 UTC · 4d agoModel release2

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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 · 2d 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·Sep 16, 11:09 UTC · 21h 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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Flag Game: A Toy Model for Mechanistic Swarm Interpretability

Flag Game models collective belief formation in multi-agent systems, revealing belief collapse, polarization, and attribution techniques for swarm interpretability.

The paper introduces the Flag Game, a toy model where bounded agents observe only private crops of a hidden country flag and exchange beliefs while weighing social evidence. It reproduces non-monotonic performance scaling with population size, collective belief collapse at small populations, and polarization at large ones that drives performance decline. The authors propose social circuit attribution with causal agent-patching interventions, and a statistical-mechanical theory that matches the empirical phase diagram, as first steps toward mechanistic swarm interpretability for collective alignment.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:46 UTC · 14h agoAI safety & security

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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 · 10d 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 · 8d agoAI tools & infraHN 21↑ · 5 comments1

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