Search: “complexity-theory”

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Discovery Foundation Models: Toward Open-Ended Discovery Intelligence

Proposes Discovery Foundation Models that participate in creating new problems and knowledge, instantiated in Zetema and the GALILEO therapeutic-discovery system.

The paper formulates Discovery Foundation Models (DFMs) as general-purpose systems for open-ended discovery, supporting seven coupled capabilities from problem discovery through evidence-grounded revision and continual improvement. It instantiates the framework with Zetema, combining explicit research-state dynamics, verification gating, external grounding, and cross-task Discovery Skill evolution. GALILEO, a real therapeutic-discovery system, closes the loop between Dry-Lab reasoning, robotic and hands-on Wet-Lab experimentation, and iterative hypothesis revision. The authors also define process-centered evaluation so discovery behavior can be trained and measured beyond final answers.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:56 UTC · 2d agoAI research 2 sources

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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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Diffusion Models and Concept Formation

Paper argues diffusion models implicitly form Cobweb-like concept hierarchies, with a basic level emerging at intermediate noise levels.

The authors draw a formal correspondence between diffusion models and Cobweb, a classic incremental concept-hierarchy learner, noting both are hierarchical Bayesian density models with Gaussian prototypes. Modes of the diffusion model's noisy marginals form a hierarchy whose basic level sits at intermediate noise, where class identity commits. The correspondence is tested on MNIST and Fashion-MNIST via mode-finding. Diffusion is reframed as a cognitive model of concept formation.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:43 UTC · 5d agoAI research

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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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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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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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Convergent Emergence of In-Context Learning Across Modalities

Controlled experiments show few-shot in-context learning emerges across six modalities including language, genomes, images, and proteins, partially supporting a convergence hypothesis.

The paper tests the Convergent Emergence Hypothesis: that few-shot in-context learning, when it emerges, shares a common cross-modality difficulty profile. A controlled framework instantiated the same task suite across six modalities: language, genome, integer sequences, time series, images, and proteins. Paired-mapping ICL emerged in all six modalities, surpassed controlled baselines, and showed correlated per-task effects in five of them, providing partial support for the hypothesis.

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

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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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Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start

Thin-shell stability proof along the Gaussian cooling path improves cold-start logconcave sampling complexity to near n^2.5 from n^2.75.

The authors prove that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This yields improved complexity for sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions the complexity is nearly n^2.5, improving the previous n^2.75 bound and matching the abstract Speedy walk.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:10 UTC · 2d 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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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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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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I wrote an AI textbook — how long until AI can do it better?

AI researcher Nathan Lambert argues LLMs remain weak at long-form technical writing, questioning whether models can autonomously organize scientific knowledge for breakthroughs.

Nathan Lambert describes writing a post-training textbook, Reinforcement Learning from Human Feedback, and finds today's LLMs weak at organizing long-form technical content despite becoming superhuman at coding and math. He notes GPT 5.5 Pro found deep typos across a 200-300 page manuscript while Claude models proved more useful as editors. He argues that compressing knowledge through writing is a prerequisite for autonomous scientific insight and tempers expectations for near-term AI-driven open science.

Interconnects·Aug 12, 13:01 UTC · Aug 12, 2026AI research

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Type Diversity Enables Transformers to Generalise Compositionally

Researchers show lexical-versus-structural compositional generalization gaps in Transformers stem from type diversity imbalance in datasets, not architectural limits.

The paper argues that Transformers' difficulty with structural compositional generalization is an artifact of low structural type diversity in prior benchmark datasets rather than an architectural limitation. Using Grammatical Framework, the authors create linguistically diverse variants of COGS and SLOG. They find type diversity correlates with compositional generalization equally in lexical and structural test cases, contradicting previous claims that compound divergence explains task difficulty.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:59 UTC · 5d agoAI research

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Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Procedural Graph framework stores procedural knowledge as triplets and self-evolves via LLM refinement, beating memory-based baselines across datasets, tasks, and LLMs.

The Procedural Graph organizes procedural knowledge into (procedure, relation, procedure) triplets; at each decision step the framework localizes the agent's active node and a guidance model translates the surrounding subgraph into step-level guidance that biases the solver's next action. An LLM refiner contrasts failed with successful trajectories and edits the graph's topology and attributes, retaining rejected edits to discourage repetition. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones and can repair flawed expert priors, delivering consistent gains over memory-based baselines across multiple datasets, task types, and LLMs.

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

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Generalized Agent Iteration: One Formal Framework for Iterative Policy Improvement and Recursive Self-Improvement

Generalized Agent Iteration formally unifies iterative policy improvement and recursive self-improvement, defining axes that distinguish anchored, goal-drifting, and self-referential agents.

The paper proposes Generalized Agent Iteration (GAI), a formal framework that models learning as a cycle of agent evaluation and agent improvement, defining the agent as a configuration of modifiable components. Two dials—whether the improving mechanism is part of the agent and whether the evaluation standard is grounded outside it—separate generalized policy iteration (GPI) from recursive self-improvement (RSI) and classify systems as anchored, goal drift, or fully self-referential. The framework places existing systems on shared axes and makes defects of recursive self-improvement statable one condition at a time.

Hugging Face daily papers·Sep 10, 20:00 UTC · 6d agoAI research

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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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Decomposition Buys Integrity, Not Yield

Study of 600 production deep-research traces finds agent-tree decomposition loses findings at rate N^(1-δ); flat architectures maximize yield.

The paper models multi-agent decomposition as a tree where an agent holding b items retains each with probability r(b); with r(b)=1/b every tree delivers exactly one finding regardless of shape. Analysis of 600 production deep-research traces estimates delta=0.34 retention decay, and 1,012 annotated traces show one brief in sixteen goes off-target per tier, giving an alignment penalty of 0.536. Depth still cuts root context exposure from N to N^(1/k) and is cheaper at scale, with a hazard model over 743,819 production tool calls showing delegation is an opening move rather than a response to filling context.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 17:04 UTC · 1d agoAI research

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A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM

A*-Thought-V2 compresses chain-of-thought into latent tokens using geometric hidden-state dynamics, cutting computation while improving accuracy on Qwen models.

A*-Thought-V2 models chain-of-thought as a hidden-state trajectory and interleaves explicit text with continuous latent tokens, compressing steps whose transitions deviate from the question-to-solution direction. Trained via stepwise embedding forcing and label forcing with soft multi-modal supervision, it was evaluated on Qwen3.5-9B and Qwen3.6-27B across six benchmarks. Reported results include up to 2.6% average accuracy gain, up to 50% shorter responses, 2.29x higher Accuracy per Computation Unit, 94.6% faster preprocessing, and up to 80.3% faster training.

Hugging Face daily papers·Sep 7, 13:56 UTC · 9d agoAI research

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A Generalization of Amari's Bayesian Duality

Paper generalizes Amari's Bayesian duality by connecting it to a convex duality of Bayes' rule.

The authors revisit Amari's less-known work on Bayesian duality from information geometry. They connect Bayesian duality to a convex duality formulation of Bayes' rule and present a generalization of it. The paper is purely theoretical and discusses relevance for modern AI, with no experiments or model releases.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:51 UTC · 8d agoAI research

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Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Researchers introduce Procedural Graphs, self-evolving (procedure, relation, procedure) structures guiding LLM agent tool use and planning.

Procedural Graphs organize procedural knowledge into (procedure, relation, procedure) triplets to guide LLM agent actions, addressing drift such as lost objectives, out-of-order tool calls, and repeated unproductive steps. At each decision step the framework localizes the active node and a guidance model translates the surrounding subgraph into step-level situational guidance. An LLM refiner edits graph topology by contrasting failed with successful trajectories, and across datasets, task types and LLMs the approach outperforms memory-based baselines and matches or surpasses hand-designed graphs.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:59 UTC · 8d agoAI research1

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Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning

Review connects control theory, optimal transport, probabilistic inference, thermodynamics, and machine learning via free-energy optimization under constraints.

The review unifies five fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. The common conceptual thread is optimization of free-energy-like functionals under dynamical or statistical constraints. Selected applications are presented in reinforcement learning, variational inference, and generative modeling. The tutorial-style text assumes no prior familiarity and begins from physics principles.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:16 UTC · 2d 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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Why don't machine learning research agents overfit?

Amazon researchers explain why ML research agents avoid benchmark overfitting, attributing generalization to compressibility of successful strategies.

Amazon Science summarizes the paper "What fits (into few tokens) doesn't overfit: Compression and generalization in ML research agents," which investigates why benchmark hill-climbing loops, whether run by human communities or LLM research agents, do not produce rampant overfitting. The explanation formalizes Occam's razor via a counting argument: successful ML strategies are highly compressible, so short descriptions lack room to memorize benchmark data and must capture real structure. LLM-based agents, being resettable and controllable, allow this hypothesis to be tested empirically.

Hacker News · security·Sep 14, 16:32 UTC · 2d agoAI researchHN 21↑ · 3 comments

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Dream-RSI: Recursive Self-Improvement through Evolving Worlds

Dream-RSI refines exploration policies by dreaming in replay simulators built from discovery history, cutting discovery costs across coding tasks.

Dream-RSI is a framework for scalable recursive self-improvement in autonomous coding agents, where a lightweight orchestration layer makes exploration explicit and programmable while leaving the underlying agent unchanged. Its core insight is that accumulated discovery history can serve as a replay simulator over the realized search space, providing immediate, low-cost off-policy feedback to evaluate and refine exploration policies without expensive online evaluations. Across algorithm engineering, mathematical optimization, and GPU kernel engineering, Dream-RSI achieves competitive or improved discovery quality at substantially reduced cost.

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

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OpenAI fought dirty on career-making math problem, says NYU mathematician

NYU mathematician Tristan Buckmaster alleges OpenAI learned of his team's Navier-Stokes approach and raced ahead using massive compute to claim a full proof first.

NYU mathematics professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced preliminary proofs toward the Navier-Stokes existence and smoothness problem, a $1 million Clay Millennium Prize problem, developed using OpenAI's Codex and Claude. They allege OpenAI learned of their progress and that an OpenAI team then used an 'insane amount of compute' to announce a full proof first. OpenAI research lead Sebastian Bubeck denies the claims as 'false and inflammatory'. Buckmaster also raised concerns that OpenAI could have learned from his Codex interactions, which the company may use for model training.

TechCrunch · AI·Sep 8, 17:32 UTC · 8d agoAI industry

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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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ScienceBuddy: Recursive-in-Recursive Self-Improvement for Interactive Scientific Agents

ScienceBuddy couples harness evolution with model reinforcement learning so scientific agents continually self-improve from researcher feedback in an interactive workspace.

The authors release ScienceBuddy, an interactive scientific research workspace that transforms researcher requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. Its recursive-in-recursive self-improvement paradigm couples harness evolution (inner recursion, model fixed) with model reinforcement learning under the improved harness (outer recursion). Case studies span four scientific task families, and the system is released to the scientific community as a research product.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 17:55 UTC · 1d agoAI research 2 sources

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CodeTD: Topology of Attention Detects Hallucinations in Code LLMs

CodeTD detects hallucinations in code LLMs before execution by analyzing topological patterns of attention maps, outperforming recent baselines.

CodeTD applies topological data analysis (TDA) to code LLM attention maps to quantify prompt-generation mismatch as a pre-execution correctness signal. Experiments cover HumanEval, MBPP, BigCodeBench, and MultiPL-E across 5 programming languages and 10 code LLMs up to 34B parameters. The method outperforms recent baselines and transfers between coding benchmarks, helping catch code that fails the task or embeds security vulnerabilities.

arXiv cs.AI / cs.LG / cs.CL·Sep 7, 17:26 UTC · 9d agoAI research1

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