Search: “finite-fields”

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Efficient Branch-and-Bound Testing and Verification of zkVMs

ZEBRA verifies zkVM constraint systems via branch-and-bound cardinality counting, finding 11 zero-day bugs across five real-world zkVMs and running 51.5x faster than SMT verification.

ZEBRA reduces zkVM correctness to a solution-set cardinality problem requiring that each constraint system admit exactly one valid execution trace, eliminating redundancies like null-row padding and non-deterministic permutations before counting. It lifts analysis from finite-field witnesses to an integer interval lattice, exploiting that constraints across 5 real-world zkVMs use only 14.0% of theoretical connectivity capacity on average, enabling tight interval propagation. A parallel branch-and-bound search produces concrete counterexamples or certifies absence of violations within a bounded region. ZEBRA discovers 11 zero-day bugs (6 independently confirmed, 3 fixed), is 51.5x faster than SMT-based verification, and verifies 16.5 percentage points more instances.

arXiv cs.CR·Sep 14, 04:35 UTC · 3d agoResearch

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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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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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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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Augustinian BabyLM: What Ostensive Definition Can and Cannot Teach a Small Language Model

Study shows visually grounded token embeddings in a small masked LM persist through training and improve object-property knowledge, but escape standard BabyLM benchmarks.

The paper implements ostensive definition for a small DeBERTa masked language model trained on 10M words, seeding visually grounded tokens with embeddings derived from labeled image regions before training. Visual initialization leaves a persistent, seed-replicated advantage on object-property knowledge (COMPS) and a corpus-tailored Visual-Property Swap benchmark covering color, material, size, and shape, but has no effect on most BabyLM grammar benchmarks. Synthetic grounding of previously unseeded words causally transfers the advantage to exactly those words.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:43 UTC · 6d agoAI research

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Low-Rank Masking for Single-Server Matrix Multiplicationnew

Researchers prove rank-r additive masks for outsourced matrix multiplication achieve maximal-correlation secrecy of at most q^-r, with a matching lower bound.

An arXiv paper analyzes statistical privacy for outsourcing matrix multiplication over a finite field to a single server using additive masks of rank at most r. Uniform rank-ball masks and products of independent uniform factors yield maximal-correlation secrecy bounded by q^{-r}, with encoding and decoding costing O(n^2 r) field operations. The authors prove an asymptotically matching lower bound for r=o(n), showing these samplers are optimal among input-independent additive masks even with secret invertible transformations. They also show every such mask requires delta approaching 1 in entry-level (epsilon, delta)-differential privacy for fixed field size.

arXiv cs.CR·Sep 16, 16:12 UTC · 12h agoResearch

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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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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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Benign Loss Landscapes Can Coexist with Worst-Case Hardness

Theory paper shows tree tensor networks contain worst-case hard targets yet benign loss landscapes, with difficulty arising from degenerate saddles.

The paper studies tree tensor networks (TTNs), which generalize deep linear networks and Tucker decompositions and embed arbitrary read-once Boolean formulas. It proves that every local minimum that is minimum-norm is global for every realizable target, so bad local minima do not distinguish typical from worst-case problems. Instead, learning difficulty arises from high-order degenerate saddle points caused by rank-deficiency, illustrated via a parity function case study, linking landscape geometry to computational hardness.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:57 UTC · 5d agoAI research

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A Note on Sphere Packing Bounds for Tuple Lattice Sieving

Proves upper bounds on k-irreducible unit vector set rates, yielding nearly tight asymptotics relevant to tuple lattice sieving in cryptanalysis.

The paper bounds the maximal asymptotic rate of k-irreducible sets of unit vectors via spherical code packing bounds. It shows R_k is sandwiched between (1/2 - o(1)) log2(k)/k and (1 + o(1)) log2(k)/k for large k. These almost-tight bounds inform subexponential complexity analyses of tuple lattice sieving, which underpins security estimates for lattice-based cryptography.

arXiv cs.CR·Sep 8, 03:20 UTC · 9d agoResearch

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Witness Encryption via Prime-Order Generic Groupsnew

Unconditional witness encryption construction for NP in the generic-group model, plus first superconstant NP-hardness result for homogeneous MinRank.

A cryptography paper unconditionally constructs witness encryption for NP in the classical generic-group model using an ordinary cyclic group of prime order. For SAT instances of size n, encryption and decryption run in poly(n) time with correctness error 2^-n^Ω(1), while generic adversaries making n^Θ(log n) queries achieve at most n^-Θ(log n) distinguishing advantage. It also proves the first superconstant-factor NP-hardness of approximation for homogeneous MinRank under randomized reductions.

arXiv cs.CR·Sep 16, 07:54 UTC · 20h agoResearch

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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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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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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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OpenArch – PyTorch implementations of modern LLM architectures

OpenArch provides PyTorch reference implementations of modern LLM architectures for developers and researchers.

OpenArch is a GitHub project offering PyTorch implementations of modern large language model architectures. The repository attracted 43 points and 7 comments on Hacker News. It targets developers and researchers who want readable, runnable versions of current LLM architectures.

Hacker News · AI·Sep 14, 07:55 UTC · 2d agoAI tools & infraHN 43↑ · 7 comments

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EFI Pairs Without One-Way Puzzles: Oracle Separations from Communication Complexity

Theorists build a classical oracle where one-way puzzles fail yet EFI pairs survive, separating two candidate minimal assumptions of quantum cryptography.

The paper constructs a single classical oracle relative to which one-way puzzles do not exist, even with an unbounded verifier, while an EFI pair survives every classical-query distinguisher holding advice, making one superposition query at the end. Security is proven by reducing adversary knowledge to communication complexity for Vector-in-Subspace, with the superposition query bounded using random matrix theory. Relative to the oracle, quantum polynomial time offers no advantage on tasks with classical inputs and outputs and there is no proof of quantumness, separating the leading minimal assumptions of quantum cryptography.

arXiv cs.CR·Sep 10, 17:54 UTC · 6d 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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Differential Privacy Meets Fixed Parameter Tractability: Algorithms and Lower Bounds

Theory paper combines differential privacy with fixed-parameter tractable encoders, improving approximation guarantees for combinatorial optimization and proving new lower bounds.

The paper studies combinatorial optimization under epsilon-differential privacy within the implicit encoder-decoder framework of Gupta et al. (SODA 2010), generalizing it to allow fixed-parameter tractable encoders. This circumvents approximation barriers inherent to polynomial-time algorithms and yields improved guarantees for fundamental combinatorial optimization problems. The authors establish the first representation-independent lower bounds: assuming a non-uniform variant of the Gap Exponential Time Hypothesis, no epsilon-DP encoder-decoder pair can achieve certain approximation guarantees with a subexponential-time decoder for sufficiently small epsilon. Representation-dependent lower bounds are also provided for larger epsilon.

arXiv cs.CR·Sep 11, 07:13 UTC · 5d agoResearch

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Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks

Theory paper derives nearly tight Rademacher complexity bounds for sparsely activated one-hidden-layer ReLU networks.

Building on Awasthi et al. (COLT 2024), the authors bound statistical complexity for networks where each input activates at most k of s hidden units. A support-preserving cover and normalized chaining argument remove the explicit dimension factor, with matching lower bounds up to logarithms. They also derive agnostic minimax excess-risk bounds of order min{1, sqrt(s/(km))} for a normalized bounded loss and show bias bounds comparable to WR restore worst-case rates even on domains where sparsity holds globally.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:53 UTC · 8d agoAI research

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

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 · 12h agoResearch

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Double descent is the principle of least actionnew

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 · 11h agoAI research

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harshatheg/Qwen-2.5-1B-RLCD — new model trending #30 on Hugging Facenew

A community MLX inference engine evaluates constrained JSON schema fields in parallel on Apple Silicon, reporting 5.6-7.0x latency speedups with guaranteed schema validity.

The repository harshatheg/Qwen-2.5-1B-RLCD appeared at #30 on Hugging Face trending, but its content describes Parallel Constrained Decoding, an MLX-based inference engine for structured extraction and classification on Apple Silicon Macs. Benchmarked with mlx-community/Qwen2.5-1.5B-Instruct-4bit on an M4 Max, it reports 5.6x-7.0x latency reductions (e.g., 1,900 ms to 270 ms for a 28-field support triage task) with 100% syntactic validity and calibrated field-level probabilities. The engine prefills a single KV-cache, broadcasts it across all schema fields, and slices logits to valid candidate tokens for enum fields with up to 255 choices.

Hugging Face trending models·Sep 16, 01:35 UTC · 1d agoAI tools & infra

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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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Register Tokens for Bounded-State Reasoning in Diffusion Language Models

Register tokens let diffusion language models like LLaDA and Dream carry reasoning state across cleared chunks, gaining up to 19.5 points on code.

Researchers propose register tokens: dedicated fixed-position tokens whose continuous hidden states are trained to carry reasoning progress across generation chunks in masked diffusion language models. After decoding and clearing a chunk, the model continues from the prompt and the carried register state instead of retaining earlier text. On LLaDA and Dream, registers outperform discrete-text carry on every benchmark, with gains up to 8.5 points on math and 19.5 points on code. Registers are especially effective for bounded code generation and can be further refined with reinforcement learning on long-horizon reasoning tasks.

Hugging Face daily papers·Sep 13, 20:00 UTC · 3d agoAI research

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Data Scarcity and Model Sparsity: Mixtures-of-Experts Overfit More to Repeated Data

Study finds Mixture-of-Experts models overfit faster than dense Transformers under repeated training data, with degradation tied to total parameter sparsity.

Across models from 80M to 1B active parameters (8.5B total), MoE architectures degrade more rapidly than dense models when training data is repeated, with the effect increasing with sparsity as dictated by total parameters. Dense 80M models tolerate 8x repetition with minimal loss while MoEs suffer at 4x and underperform dense models beyond 32x. Masking-based regularization such as dropout mitigates overfitting, letting MoEs beat dense models even at over 64x repetition, though no method matches all-unique training data. Routing stabilizes early and expert specialization correlates with overfitting to repeated data.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:57 UTC · 6d 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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Distance generalization in transformers: why bother with positional encoding?

arXiv study uses synthetic delay-copy tasks to show how RoPE, ALiBi, NoPE and training data diversity affect transformers' distance generalization.

The paper studies distance generalization in transformers: extrapolating when inter-token distances change between training and inference while context length stays fixed. Using two synthetic delay-copy tasks with finite source-recall distances, the authors test models on unseen delays. They investigate whether positional encodings such as RoPE and ALiBi outperform no positional encoding (NoPE), how the diversity of training distances affects performance, and when distance transfer learning is positive or negative.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:57 UTC · 6d agoAI research2

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Unfold The World: Factorize 4D Properties in Reinforcing Spatial Reasoning

FactoSR factorizes 4D spatial reasoning into XY, Z, and T reinforcement-learning sub-objectives, boosting VLM performance on VSI-Bench by 5.9% and All-Angles-Bench by 4.5%.

Researchers present FactoSR, a factorized reinforcement learning framework that decomposes world-consistent reasoning into planar correspondence, depth consistency, and temporal reversibility sub-objectives. Optimizing these verifiable constraints turns the ill-posed projection recovery problem into tangible reasoning steps. Evaluations show gains of 5.9% on VSI-Bench and 4.5% on All-Angles-Bench for 3D and 4D reasoning, arguing VLMs' spatial bottleneck stems from training on 2D projections versus latent 3D geometry and temporal continuity.

Hugging Face daily papers·Sep 2, 20:00 UTC · 14d agoAI research

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Large Universe Subset Predicate Encryption with IND-CCA Security (with Constant-size Ciphertext and Keys)

New construction achieves first large-universe subset predicate encryption with IND-CCA security and constant-size ciphertexts and keys under subgroup decision assumptions.

The paper proposes the first large-universe subset predicate encryption scheme achieving IND-CCA security with both constant-size ciphertexts and constant-size secret keys. Prior large-universe constructions by Chatterjee and Mukherjee either achieved only restricted selective security with constant sizes or adaptive security with attribute-dependent ciphertext size, and none achieved CCA security. The new construction is proven selectively secure under standard subgroup decision problems. Black-box transformations yield the first CCA-secure WIBE and WKD-IBE with constant-size ciphertexts and keys.

arXiv cs.CR·Sep 14, 10:02 UTC · 2d agoResearch

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Kaininja: Extending Native 3D Generators to the Part Level

KaiNinja extends TRELLIS.2 native 3D generation to part-level assets via a dual-volume O-Voxel representation, cutting whole-object Chamfer distance by 40%.

KaiNinja extends the TRELLIS.2 native 3D generator to produce part-level assets instead of one fused mesh, enabling downstream editing, rigging, and simulation. A dual-volume form of the O-Voxel representation solves the problem that a single volume cannot represent interfaces where two parts touch. The model needs no segmentation network, is partly trained on LLM-agent-authored part data, lowers whole-object Chamfer distance by 40%, and raises strict part F-score by 16% versus other part-generation pipelines.

Hugging Face daily papers·Sep 13, 20:00 UTC · 3d 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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