Search: “formal-theorem-proving”

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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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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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Thought without systematicity? Evaluating reasoning models on rule induction tasks

Study finds reasoning models often fail on structurally equivalent variants of tasks they solve, suggesting their reasoning lacks systematicity.

The paper extends rule induction tasks from cognitive science using task isomorphisms such as recombination and substitution to test systematicity in reasoning models. Despite solving tasks correctly, models frequently fail on structurally equivalent variants of the same task. The authors conclude many model behaviors lack systematicity, making it difficult to establish cognitive abilities beyond the specific evaluation contexts.

Hugging Face daily papers·Sep 11, 20:00 UTC · 5d agoAI research

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Understanding the Usability of Cryptographic Verification Tools

Survey of Tamarin and ProVerif users reveals usability barriers: debugging non-termination, model validation, and opaque proof failures hinder cryptographic protocol verification.

The paper presents an exploratory human-centered survey of researchers, graduate students, and practitioners with hands-on experience using Tamarin, ProVerif, and related cryptographic protocol verification tools. Findings reveal usability barriers across the verification workflow, including difficulties debugging non-termination and performance issues plus the lack of systematic methods for validating formal models against real protocols. When proofs fail without concrete attacks, users commonly simplify models, add helper lemmas, and revisit modeling abstractions. Participants called for actionable diagnostics, clearer explanations of results, visualization, and automation for recurring proof tasks.

arXiv cs.CR·Sep 14, 20:40 UTC · 2d agoResearch

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CertiFlash: A Formal Verification Framework for Flash Translation Layers in Computational Solid State Drives

CertiFlash provides machine-checked formal verification of SSD flash translation layers, proving isolation, integrity, and ownership invariants to prevent tenant data leaks.

CertiFlash is an open-source formal verification framework for Flash Translation Layers (FTL) in computational SSDs, mechanized in the Rocq proof assistant. It shows that a faulty FTL can corrupt device state at five surfaces (e.g., leaking data between tenants or dropping integrity tags), demonstrated on a DaisyPlus OpenSSD. Designers prove once that every operation of a general FTL model preserves a global invariant covering mapping, isolation, integrity, ownership, and allocation; new designs need only discharge five hypotheses. Across four case studies, added effort was 27-3,231 lines against a 16,489-line framework.

arXiv cs.CR·Sep 9, 15:44 UTC · 7d agoResearch1

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Scaling Verification of Cryptographic Software with Aeneas, Rust, and Lean

Microsoft SymCrypt implementations of SHA-3 and ML-KEM verified in Lean via Aeneas-extracted Rust models, with AI agents writing proofs.

The paper develops a methodology for verifying production Rust cryptographic code by using Aeneas to extract pure models into Lean, avoiding low-level pointer and aliasing reasoning. Applied to Microsoft's SymCrypt, it verifies SHA-3 and ML-KEM implementations ported from C to Rust and extends SymCrypt with FrodoKEM, ML-DSA, and HPKE. A 237 KLOC Lean development establishes safety, panic-freedom, and functional correctness of 16.7 KLOC of Rust supporting post-quantum cipher suites on x86-64 and ARM. AI agents autonomously write formal proofs verified by the Lean kernel, and evaluation shows verified Rust meets SymCrypt's performance and portability requirements.

arXiv cs.CR·Sep 14, 14:32 UTC · 2d agoResearch1

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Accountability in Certificate Transparency and Variants

Formal Dolev-Yao analysis shows plain Certificate Transparency requires an honest log, SCT Auditing removes that assumption, and Gossiping does not.

The paper analyzes accountability in Certificate Transparency and its SCT Auditing and Gossiping extensions in the Dolev-Yao model, starting from a vanilla PKI. It finds plain CT provides accountability only under the assumption of an honest log. The SCT Auditing extension can eliminate that assumption, while the Gossiping extension cannot. CT is supported by all major browsers and obliges Certificate Authorities to record issued certificates in public, monitored logs.

arXiv cs.CR·Sep 10, 13:45 UTC · 6d agoResearch

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Access Control as Verified Parse Constraints

Researchers verify a class of EverParse validators that correctly enforce access-control policies, deploying a machine-checked enforcement gate on seL4.

The paper targets enforcement-code bugs in commercial security gateways by proving that forward-only, backtrack-free EverParse validators are verified recognizers for a bounded finite-state class that includes access-control decision functions with fixed-offset fields and bounded disjunction. Encoding a bounded policy language into a fixed-size byte buffer allows an SMT solver to verify the enforcement code once, covering all byte values, policies, requests, and sessions. Editing rule content over a fixed endpoint set requires no new proof, while adding endpoints reruns the toolchain. A deployment on the seL4 microkernel ensures every request passes through the gate and unverified components cannot corrupt the enforcement chain.

arXiv cs.CR·Sep 11, 06:33 UTC · 5d agoResearch1

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Guppy: Efficient Light Clients via Recursive Zero-Knowledge Proofs

Guppy lets blockchain light clients verify full state via recursive zero-knowledge proofs without validators maintaining state commitments, processing thousands of updates per second.

Guppy is a light-client protocol in which validators commit only to state updates while an off-chain, untrusted service secured by recursive zero-knowledge proofs maintains a verifiable Merkle tree over the full state. A hash-chain commitment moves validator signature verification out of the proving circuit, and a parallel recursive proving pipeline keeps latency growth logarithmic with throughput. A Plonky2-based implementation maintains a tree of size 2^30 while processing thousands of updates per second, adding only 2-4 seconds of latency without increasing block-construction complexity.

arXiv cs.CR·Sep 7, 20:41 UTC · 9d agoResearch

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Opaque recurrence, and other AI terms that you should probably know

TechCrunch updates its plain-English glossary defining common AI terms from AGI and agents to chain-of-thought reasoning.

TechCrunch maintains a regularly updated glossary of AI terminology, defining terms such as AGI, AI agents, API endpoints, chain of thought, coding agents, compute, deep learning, and diffusion. It highlights 'opaque recurrence', the reasoning technique in OpenAI's new Astra model that has drawn attention from AI safety researchers. The piece is an educational living document rather than new research or a product announcement.

TechCrunch · AI·Sep 7, 19:24 UTC · 9d agoAI industry1

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Recurrent GraphNeural NetworkswithSet-BasedAggregation

Paper proves two-directional equivalence between recurrent GNNs with set-based aggregation and Boolean closure of reachability/safety properties in modal mu-calculus, checkable from weights.

The authors study recurrent graph neural networks with set-based aggregation and identify sufficient conditions, checkable directly from network weights, for compiling networks into logical formulas and formulas into networks. They establish an effective two-directional equivalence with the Boolean closure of reachability and safety properties, the fragment BΣ°1 of the modal μ-calculus, shown to be the exact expressive level of stabilization over finite vocabulary. The correspondence needs no counting logic, external halting signal, or non-effective acceptance condition, yielding a verifiable path from weights to symbolic explanations.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:39 UTC · 2d 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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You've Got a BUD in Me: Authenticated Reads from Per-Block Write Logs

Researchers propose BUD, per-block write-log digests enabling blockchain validators to serve historical membership and exclusion proofs far cheaper than state-wide tries.

The paper introduces Block Update Digests (BUD), which authenticate each block's write log with predecessor pointers, plus a SuperBUD and exponential hierarchy to turn long unchanged intervals into short proofs. Soundness against adversarial provers and up to f Byzantine validators is proven under archive, attestation, and committee evidence assumptions. Benchmarks show a 50x state-size increase raises the base-BUD path only 1.24x versus 3.1x for in-memory and 69.5x for disk-backed Merkle Patricia tries, with read payloads below 800 bytes and p99 warm verification at 146 microseconds.

arXiv cs.CR·Sep 10, 08:46 UTC · 6d agoResearch

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Observational Indistinguishability and Integrity Blind Regions in Hybrid Quantum-Classical Workflows

Framework formalizes integrity blind regions in hybrid quantum-classical workflows, validated across 3,600 label interventions with conformal detection rules.

The paper presents a claim-relative evidence and reference framework for integrity of hybrid quantum-classical workflows, distinguishing structural blind regions caused by observational indistinguishability from finite-batch statistical misses. Experiments over 3,600 label interventions show exact label-path invariance for feature and prediction views. The geometry-aligned construction detects 343 of 2,700 conclusion-changing interventions using the conformal rule and 1,183 of 2,700 with the uncorrected union, with executed conformal clean false-action rates of 0.048-0.059.

arXiv cs.CR·Sep 15, 13:16 UTC · 1d agoResearch

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Towards Tackling Application Logic Flaws through Autonomous Formal-Logic Modeling and Automated Reasoning

LL-Verifier combines LLMs with logic model checking to automatically discover logic flaws, uncovering vulnerabilities in 27 IoT access-control protocols.

Researchers present LL-Verifier, a framework that uses LLMs to autonomously convert natural-language protocol descriptions and security goals into formal logic models in a new logic language built on Maude, then applies logic model checking for exhaustive verification. The framework targets application-logic flaws that are tied to business semantics and hard to scale with manual analysis. Evaluation on 27 access-control protocols of widely used IoT devices uncovered a range of sophisticated logic vulnerabilities with security and privacy implications.

arXiv cs.CR·Sep 9, 17:58 UTC · 7d agoResearch1

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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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Beyond Solver Verdicts: Generative Reward Models for Autoformalization

Researchers introduce Generative Verification (GenV), a generative reward model achieving 0.961 AUROC in detecting unfaithful autoformalization that preserves solver verdicts.

The paper formalizes Verdict-Preserving-Unfaithfulness (VPU), a failure mode in neurosymbolic autoformalization where an incorrect encoding executes successfully and matches the expected solver verdict, and proves verdict-only verification is bounded to chance-level detection. The proposed Generative Verification (GenV) distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score within the language model's vocabulary space. The oracle-mined verifier (GenV+HN) achieves 0.961 AUROC, generalizes zero-shot across unseen translators and formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation. Mechanistic analysis with decision-projected logit lenses and sparse autoencoders shows the generative readout extracts precise spatial error coordinates without explicit localization training.

Hugging Face daily papers·Sep 9, 20:00 UTC · 7d agoAI research1

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One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation

A review paper frames on-policy self-distillation collapse as governed by three levers: token weighting, privileged information, and guidance decay.

The paper critically reviews On-Policy Self-Distillation (OPSD), where a language model trains on its own generations scored token-by-token by a teacher conditioned on privileged information such as reference solutions or environment feedback. It identifies collapse, the progressive narrowing of producible reasoning paths, as the dominant failure mode and analyzes it through three levers: signal weighting, the nature of privileged information, and teacher dynamics. The review is restricted to mathematical reasoning, reports no new experiments, and offers a shared vocabulary separating settled findings from disputed ones.

Hugging Face daily papers·Aug 25, 20:00 UTC · 22d agoAI research

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An Evidence Model for Agentic Processes: Evidence Claims, Trust Assumptions, and Policy Assessment

Researchers propose an evidence claim model defining which trust and audit claims agentic AI systems can support, mapping claims to mechanisms, assumptions, and threats.

The paper proposes an evidence claim model for agentic AI processes that exchange messages, invoke tools, request approvals, and modify shared artifacts. It distinguishes claim types such as artifact integrity, provenance, approval evidence, and policy assessment, mapping each to mechanisms, assumptions, limitations, and threats. It stresses that hashes, signatures, and external anchors do not establish semantic truth, authorization, or capture completeness. The contribution is conceptual, offering vocabulary for what an agentic black box can and cannot evidence and which controls must surround it.

arXiv cs.CR·Sep 8, 09:25 UTC · 8d agoAI safety & security

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An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics

Open post-training pipeline turns Nemotron 3 Ultra checkpoints into an IMO 2026 gold-medal system, scoring 30/42 without formal provers or external tools.

Starting from Nemotron 3 Ultra, researchers trained two specialist checkpoints using supervised fine-tuning and reinforcement learning for natural-language olympiad proof generation. Three checkpoints power an iterative generate-verify-refine search plus a separate high-compute selection stage, operating entirely in natural language with no formal prover, external tools, or internet access. The system scored 30 of 42 points at IMO 2026, reaching the gold-medal threshold. The release includes the post-trained checkpoints, training data, training and inference code, submitted solutions, and Nemotron-IMO-Bench with 200 novel olympiad-level problems.

Hugging Face daily papers·Sep 8, 20:00 UTC · 8d agoModel release

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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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τ^τ-Bench: An Environment for End-To-End, Realistic Agent Construction

New τ^τ-bench tasks coding agents with building deployable customer-service agents; best config, Claude Opus 5, passes only 23.9% of simulations.

Researchers introduce τ^τ-bench, an end-to-end benchmark where a developer agent must build a complete customer-service agent from real business records, a client with requirements, a production API, an inherited codebase, and cost/model limits, then is scored by deploying it against held-out simulated users. Across 53 tasks in four domains, the strongest configuration, Claude Opus 5 under Claude Code, passes just 23.9% of evaluation simulations versus an 82.2% expert-authored reference ceiling. Failure modes mirror those of human developers: shallow queries instead of deep record comprehension, almost no client communication, and shipping the first architecture that runs rather than experimenting.

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

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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 · 2d agoResearch

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Fresh-Challenge VDF Attestations for Model-Relative Response Latency

Fresh-Challenge VDF Attestations bind verifiable delay functions to unpredictable public challenges, yielding succinct evidence of model-relative response latency.

The paper specifies FCLA, a protocol composition that binds a VDF to an unpredictable public challenge, a message, and independently auditable release/receipt records. Under explicit assumptions about VDF sequentiality and a calibrated bound on an adversary's sequential evaluation rate, an accepted transcript is inconsistent with post-challenge generation. A benchmark of the public reference implementation confirms the expected evaluation-versus-verification separation on one documented machine. The contribution is a protocol design analysis, not a new VDF construction.

arXiv cs.CR·Sep 11, 11:25 UTC · 5d agoResearch

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Embodied-BenchForge: A Closed-Loop Agentic Workflow for Embodied Benchmark Construction

Embodied-BenchForge automates embodied benchmark construction via closed-loop synthesis with verification and repair, yielding seven benchmarks for MLLM evaluation.

Embodied-BenchForge is an agentic framework that transforms user-specified evaluation intents into complete embodied benchmark artifacts via Closed-Loop Benchmark Synthesis. Skill-Orchestrated Artifact Synthesis composes typed reusable skills while an artifact dependency graph records intermediate outputs; Requirement-Guided Verification and Repair triggers local re-execution or upstream rollback on failures. It constructs six Offline EQA benchmarks plus one interactive benchmark with 220 executable tasks, distinguishing MLLM and embodied agent capabilities in observation-based understanding and closed-loop execution.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:16 UTC · 5d agoAI research

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LexFlip: A Dissociation Diagnostic for Legal Meaning Preservation Metrics

LexFlip releases 373 minimal perturbations of Quebec statutory French that reverse legal force while preserving tokens, exposing weaknesses in embedding-based meaning preservation metrics.

LexFlip provides 373 minimal perturbations of Quebec statutory French that reverse legal force while preserving 0.93 of tokens, creating dissociation items that break monotone token-overlap metric validation. The seven embedding and BERTScore metrics tested register only 0.022-0.039 of their identical-to-unrelated range on these edits, versus 0.670 for bidirectional NLI. Against FrJudge, with a measured human ceiling of r=0.597, a bare length feature outscores every semantic metric tested.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 15:49 UTC · 12d agoAI research

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ReCite: Agentic Reasoning for Faithful Citation

ReCite is an agentic citation framework using claim-level reasoning and verification, outperforming large generative models in strict citation accuracy.

ReCite is a decoupled agentic framework that orchestrates location perception, intent-aware query planning, and reflective verification for citation recommendation. Trained on synthesized reasoning trajectories, the agent verifies claim-evidence consistency and triggers self-correction loops when retrieved candidates lack logical support. Experiments show the lightweight framework outperforms state-of-the-art massive generative models in strict citation accuracy, addressing misattribution where cited papers are real but logically unsupportive.

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

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Beneath the Surface of Chains-of-Thought: A Mechanistic Interpretation of Reasoning Operations in LLMs

Study shows LLM reasoning operations like planning and deduction are geometrically separable in hidden states, with separability peaking in middle layers.

Researchers investigate whether functional reasoning operations — problem formulation, goal decomposition, deduction — have corresponding geometric structure in LLM hidden representations. They find operations are separable in held-out representations with separability peaking in middle layers, ruling out lexical and positional confounds; token-wise operation alignment becomes more distributed across layers, and identical surface tokens are represented differently depending on their surrounding chunk. Attention-masking interventions show chunk-onset operation-aligned representations depend on preceding reasoning context; code is released on GitHub (naver-ai/beneath-cot).

Hugging Face daily papers·Sep 3, 20:00 UTC · 13d agoAI research1

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Sound Debloating of Redundant Checks in Zero-Knowledge Machine-Learning Circuits

Automated framework soundly removes up to 48.7% of redundant constraints in ezkl and zkml ZK-ML circuits, cutting prover time by up to 72.8%.

The framework uses whole-circuit abstract interpretation and a provenance graph to verify that each removed redundant check (range proofs, sign lookups, bit decompositions) remains entailed by the rest of the circuit, provably preserving soundness. It was evaluated on MLP, CNN, RNN, and transformer circuits generated by ezkl and zkml, with up to 25.3 million constraints. It removes up to 48.7% of constraints and reduces prover time by up to 72.8% without weakening security. Under-constrained circuits in deployed ZK systems have previously enabled attackers to forge transactions and bypass verification.

arXiv cs.CR·Sep 9, 13:27 UTC · 7d agoResearch1

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Safety for Whom? Boundary-Aware Self-Distillation for Controlled LLM Safety Refusal

A self-distillation safety framework tunes narrow-boundary refusals in Qwen3-8B, raising target-domain refusal to 84.75% while cutting over-refusal from 15.20% to 5.20%.

The paper formulates narrow-boundary safety, where deployments need refusals within specific topics rather than whole subjects, and proposes an offline self-generated framework with controlled topic generation, escalating retries, and harmful-benign boundary pairs. On political persuasion with Qwen3-8B, the method raised target-domain refusal from 9.47% to 84.75% and cut the mean unsafe-response rate across three broader benchmarks from 26.26% to 0.14%. Verified target-model responses reduced over-refusal from 15.20% to 5.20%, and boundary-pair data cut comply-side over-refusal on held-out pairs from 32.94% to 4.16%. Results show data composition controls the safety-usability trade-off and alignment should be evaluated on both sides of the refusal boundary.

Hugging Face daily papers·Sep 2, 20:00 UTC · 14d agoAI safety & security1

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