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Tag: cs.LG

  • ManifoldFlow: Spectrum-Learnable Stiefel Optimization via SPD Relaxation

    ManifoldFlow: Spectrum-Learnable Stiefel Optimization via SPD Relaxation

    [Submitted on 5 Jul 2026 (v1), last revised 11 Oct 2026 (this version, v3)]

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    Abstract:Orthogonal and Stiefel constraints help control weight geometry, improve conditioning, and stabilize signal propagation in neural networks. However, standard Stiefel optimization fixes the represented singular values at one, preventing the model from learning direction-dependent amplification or attenuation. We introduce ManifoldFlow, a spectrum-learnable extension of Stiefel optimization that separates an orthonormal factor from a bounded symmetric positive-definite (SPD) spectral factor. The SPD factor equals the Gram matrix of the realized weight, providing exact spectral interpretability and recovering standard Stiefel optimization when set to the identity. ManifoldFlow uses the gradient component rejected by the Stiefel constraint to guide spectral adaptation. By aligning and accumulating this information over time, the method jointly updates the orthonormal basis and the bounded spectrum. We establish the geometry of the rejected gradient, characterize optimization on the Stiefel-SPD product space, and analyze how the learned spectrum affects conditioning, signal propagation, and spectral complexity. Across diverse tasks, ManifoldFlow consistently outperforms matched fixed-spectrum Stiefel baselines, with particularly strong gains in recurrent language modeling.

    Submission history

    From: Haiwen Yi [view email]
    [v1] Sun, 5 Jul 2026 22:46:17 UTC (7,872 KB)
    [v2] Wed, 30 Sep 2026 21:41:51 UTC (4,863 KB)
    [v3] Sun, 11 Oct 2026 22:07:12 UTC (4,897 KB)

  • SEEK: Agentic Knowledge Graph Retrieval for Secure Code Generation

    SEEK: Agentic Knowledge Graph Retrieval for Secure Code Generation

    [Submitted on 10 Oct 2026]

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    Abstract:Large Language Models (LLMs) can generate functionally correct code while introducing exploitable security weaknesses, particularly when developers specify functionality without explicit security requirements. Recent state-of-the-art approaches mitigate this problem using external security knowledge, but largely rely on flat similarity-based retrieval over independent artifacts, making it difficult to infer the relevant vulnerability space and retrieve targeted knowledge when direct matches are unavailable. We propose SEEK, an agentic Graph RAG framework for secure code generation that constructs a security knowledge graph using the Common Weakness Enumeration (CWE) taxonomy as its structural backbone and injects it with curated real-world CVE vulnerability-fix instances. At inference time, a Planner Agent predicts potential CWE weaknesses associated with the developer query, which guide Graph Scoping to restrict retrieval to relevant regions of the CWE taxonomy before deterministic multi-faceted candidate ranking. A Selection Agent subsequently validates the predicted weaknesses and retrieved candidates prior to code generation. Across five open-source LLMs, we evaluate SEEK in an out-of-distribution setting on CodeGuard+ and CyberSecEval, spanning C, C++, and Python. SEEK achieves the highest SecurePass@1 of 77.45% on CodeGuard+ and the highest aggregate ICD pass rate of 79.45% on CyberSecEval, surpassing prior approaches. Moreover, SEEK achieves 85.2% SecurePass@1 across 13 unseen CWE types with no directly linked vulnerability-fix instances, demonstrating strong generalizability, while maintaining acceptable inference latency costs.

    Submission history

    From: Varun Gadey [view email]
    [v1] Sat, 10 Oct 2026 14:37:22 UTC (321 KB)

  • Perfect Reconstruction Cannot Show Whether Two Codebooks on a VAE’s Latent Space Agree

    Perfect Reconstruction Cannot Show Whether Two Codebooks on a VAE’s Latent Space Agree

    [Submitted on 29 Sep 2026]

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    Abstract:Many systems read the latent space of a variational autoencoder (VAE) as discrete codes, and rely on each latent being read back as the code it was written as. Shannon (1948) took such a shared codebook as given; inside a VAE nothing enforces it. We prove that no item of a standard training report can reveal whether the written and read codes agree on encoded data. We construct two VAEs that reconstruct every input perfectly, infer exactly, and match on every per-example ELBO and every code histogram, yet agreement is one in the first and zero in the second. We then show that the ELBO’s own terms bound how far a measured agreement can move: the variational gap bounds the shift to exact inference, and the rate bounds the shift to generation from the prior. For Gaussian posteriors, a mean-field encoder pays an exact price in the gap that depends on its choice of axes. On probabilistic PCA the gap certifies a trained encoder in all 75 settings we test, at agreement between 0.76 and 0.97. On 240 trained VAEs, a floor set by the rate and the dataset size rules out rate-side certification in advance for 66 models, and none of them certifies. The results yield a simple protocol, Certify-or-Measure, for any pipeline that reads a VAE as codes.

    Submission history

    From: Yusuke Hayashi [view email]
    [v1] Tue, 29 Sep 2026 05:58:53 UTC (1,819 KB)

  • Splicing Hints into Reasoning Traces: Learning from Demonstrator Failures

    Splicing Hints into Reasoning Traces: Learning from Demonstrator Failures

    [Submitted on 26 Sep 2026]

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    Abstract:Reinforcement learning with verifiable rewards improves mathematical reasoning when a final answer can be checked, but a correct answer does not certify the derivation behind it, and proof problems offer no answer to check. Replacing the check with a reasoning model as an in-loop verifier faces a fundamental obstacle: the policy must already produce occasional correct attempts for any reward to exist, which it may never do at olympiad level. We instead move verification and repair out of the training loop and into offline data generation with SPLICE, a workflow in which a second model, given only a reference solution, edits a reasoning model’s traces as they are generated: it verifies progress, truncates a failed trace at its last verified step, and splices in an adaptively strengthened hint until progress resumes. The resulting dataset includes repaired examples whose sampled unaided trajectory failed, with failed continuations removed and progress repeatedly checked against the reference solution. A model finetuned on SPLICE traces outperforms the same model distilled from the reasoning model’s unedited traces on AIME and, under a grading protocol validated against human grades, on olympiad proofs. The trained model’s own traces show a corresponding behavioral signature: at difficult points it announces a branch in the style of the spliced hints and takes riskier steps, with predictive entropy rising there and just after, a pattern absent from the model trained on unedited traces.

    Submission history

    From: Hamed Mahdavi [view email]
    [v1] Sat, 26 Sep 2026 23:28:04 UTC (149 KB)

  • Enhanced Trading Systems with Intelligent Market Analysis

    Enhanced Trading Systems with Intelligent Market Analysis

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  • What Can Language Models Inherit from Solomonoff Induction? Limits, Attainable Properties, and What Served Conditionals Reveal

    What Can Language Models Inherit from Solomonoff Induction? Limits, Attainable Properties, and What Served Conditionals Reveal

    [Submitted on 28 Sep 2026]

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    Abstract:A familiar line of reasoning runs as follows: language models are flexible approximators trained under a strictly proper loss, so scale brings them closer to Solomonoff induction, and their predictive success is evidence of that approach. We apply known results from algorithmic information theory, universal prediction and Bayesian consistency. In its uniform form the conclusion holds for no computable model: each has cheap environments it never learns, and every uniformly computable family of total predictors shares one on which each member fails beyond a horizon growing with its index, so “closer” can hold only pointwise, one environment at a time. Nor could the offered routes certify even that: finite evaluation cannot certify agreement on rarely reached contexts, perfect corpus fit selects the corpus law as prior, and asymptotic criteria cannot see the constants that carry Solomonoff’s guarantee. Our lens is the Kraft inequality read for predictors. Every model has at most the same budget of predictive success, so Solomonoff’s predictor, which leaves part of it unspent, differs from a language model not in having more of it but in where it spends it; on mutually singular families this is exact, and only full-mass Bayes mixtures reach the frontier. We then discuss what is inheritable, including in-context learning as amortised Bayesian inference; what survives within a context window; which Solomonoff-like properties a deployed system should have or avoid; and what served conditionals determine. A closing table states what common practices certify and what to report. Tests are developed in a companion paper.

    Submission history

    From: Luan Carlos De Sena Monteiro Ozelim [view email]
    [v1] Mon, 28 Sep 2026 19:01:50 UTC (176 KB)

  • Mode Collapse of Mean-Field Variational Inference

    Mode Collapse of Mean-Field Variational Inference

    [Submitted on 20 Oct 2025 (v1), last revised 12 Oct 2026 (this version, v2)]

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    Abstract:Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. It has been empirically observed that MFVI optimizers often suffer from emph{mode collapse}. For example, when the target measure $pi$ is a mixture $pi = w P_0 + (1 – w) P_1$, the MFVI optimizer tends to place most of its mass near a single component of the mixture. This work provides the first emph{theoretical} explanation of mode collapse in MFVI. Starting from two-component mixtures, we introduce the notion of emph{$varepsilon$-separateness} to quantify the separation of the mixture components. We derive explicit bounds on the mass that any MFVI optimizer assigns to each component, when $P_0$ and $P_1$ are $varepsilon$-separated for sufficiently small $varepsilon$. We further extend this analysis to mixture target distributions with multiple components. Our results reveal that the occurrence of mode collapse crucially depends on the relative position of the components. To address this issue, we propose emph{rotational variational inference (RoVI)}, which augments MFVI with a rotation matrix. The numerical studies support our theoretical findings and illustrate improved mode coverage with RoVI in Bayesian mixture posteriors, including a real-data example.

    Submission history

    From: Shunan Sheng [view email]
    [v1] Mon, 20 Oct 2025 00:36:13 UTC (1,166 KB)
    [v2] Mon, 12 Oct 2026 00:40:12 UTC (1,199 KB)

  • Predict Before You Modify: Learning Improvement Dynamics for Self-Evolving Agents

    Predict Before You Modify: Learning Improvement Dynamics for Self-Evolving Agents

    [Submitted on 26 Sep 2026]

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    Abstract:Self-evolving agents improve through repeated cycles of modification and evaluation. However, existing methods receive feedback on modifications only after costly evaluations, and aggregate scores may obscure distinctions between failures that require different repairs. We introduce predictive self-evolution through an editable Improvement Dynamics Model (IDM). Before evaluation, the IDM predicts task-level outcomes of a proposed modification and guides an optional revision. After evaluation, past modifications and their observed outcomes are used to improve the IDM, allowing predictive knowledge to accumulate across generations. The system can thus improve how it solves tasks, proposes modifications, and predicts their effects. Building on HyperAgents, we evaluate this approach across multilingual coding, paper review, robotics reward design, and Olympiad-level mathematical grading. Our approach outperforms HyperAgents across all four domains, with up to 46% higher average performance over generations. Gains also persist under matched token budgets that include both agent evolution and task evaluation, and extend to held-out tasks. Forecast accuracy improves as the IDM evolves, and the learned predictive knowledge transfers to improve evolution in a new domain.

    Submission history

    From: Zixuan Xie [view email]
    [v1] Sat, 26 Sep 2026 18:59:47 UTC (2,245 KB)

  • When Post-Processing Fairness Constraints Help and When They Harm: Evidence from Eight Cross-Domain Evaluations

    When Post-Processing Fairness Constraints Help and When They Harm: Evidence from Eight Cross-Domain Evaluations

    [Submitted on 22 Sep 2026 (v1), last revised 10 Oct 2026 (this version, v4)]

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    Abstract:Fairness audits in production ML typically occur once, at deployment, on a single domain. Both fail in practice: fairness can shift after retraining or a changing user base, and interventions validated on one dataset are rarely tested across the heterogeneous domains an organization deploys. We present FAPE (Fairness Auditing for Production Environments), a four-stage framework evaluating a single post-processing intervention, Fairlearn’s ThresholdOptimizer, across eight domain evaluations: criminal justice, income prediction, legal admissions, credit lending, agricultural lending, a multi-domain benchmark corpus, healthcare, and education. Each is scored on demographic parity and equalized odds difference, plus disparate impact ratio and accuracy cost where computable. Intervention effectiveness tracks baseline disparity magnitude: across model-domain pairs the constraint improved disparity in 9 of 14 high-disparity cases and worsened it in 3 of 4 near-fair ones. Each of the five high-disparity exceptions reverses under one of two measurement checks, a minimum group size or thresholds fit on held-out data. A CUSUM monitor started at deployment, tested on a simulated shift, separates constrained models that never met a 0.1 parity convention from those that met it and later regressed. A single deployment-time audit is therefore an unreliable guide, which argues for baseline-disparity screening and continuous monitoring

    Submission history

    From: Nithin Raghava Ramachandra Narla [view email]
    [v1] Tue, 22 Sep 2026 18:46:00 UTC (1,657 KB)
    [v2] Tue, 29 Sep 2026 07:09:28 UTC (1,657 KB)
    [v3] Wed, 7 Oct 2026 21:33:20 UTC (1,647 KB)
    [v4] Sat, 10 Oct 2026 04:22:05 UTC (1,657 KB)

  • Notes on Uniform Policy Score Bounds and Lipschitz Continuity for Truncated Gaussian, Product Cauchy, Boltzmann, and Softmax Policies

    Notes on Uniform Policy Score Bounds and Lipschitz Continuity for Truncated Gaussian, Product Cauchy, Boltzmann, and Softmax Policies

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    arXivLabs: experimental projects with community collaborators

    arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

    Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

    Have an idea for a project that will add value for arXiv’s community? Learn more about arXivLabs.