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Search: “covariance”

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Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs

Theoretical tutorial establishes equivalence between covariance neural networks and PCA, with stability and transferability bounds and brain-age applications.

The paper reviews the theory of coVariance neural networks (VNNs), graph neural networks that operate on covariance matrices as graphs. It derives a conceptual equivalence between VNNs and PCA-based information processing, refined stability bounds under finite-sample covariance perturbations, and transferability characterizations across multiscale datasets. Demonstrated applications include brain age gap estimation for neurodegenerative conditions from neuroimaging data.

arXiv cs.AI / cs.LG / cs.CL · 6d agoAI research1

General Quantification of Covariate and Concept Shifts

Paper proposes γ*-concept shifts via entropic optimal transport, deriving estimable generalization bounds unifying covariate and concept shift under distribution shift.

The authors show existing definitions of concept shift break when source and target supports mismatch and propose γ*-concept shifts grounded in entropic optimal transport. They derive a general error bound covering broad loss functions, label spaces and stochastic labeling, plus estimators with concentration guarantees. The resulting DataShifts algorithm quantifies distribution shifts and estimates the error bound in most applications, addressing learning bounds that were previously non-estimable from samples.

arXiv cs.AI / cs.LG / cs.CL · 5d agoAI research1

Algorithmic stability via ensembling

Theoretical work derives a general framework quantifying stability guarantees for averaging-based ensembles under arbitrary data perturbations via covariance operator norms.

The paper develops a framework for quantifying algorithmic stability of ensembling strategies defined via averaging, for varied types of data perturbation. The main result bounds the stability of the ensembled algorithm in terms of the norm of a covariance operator describing the ensembling process. The framework yields interpretable insights across practical perturbation examples and provides sharper guarantees than those derived from differential privacy considerations.

arXiv cs.AI / cs.LG / cs.CL · 6d agoAI research

Kalman Delta Networks: Uncertainty-aware Associative Memory

Kalman Delta Networks add uncertainty tracking to linear-attention associative memory, improving perplexity and downstream accuracy at 750M and 1.3B scales.

Kalman Delta Networks reformulate recurrent associative memory in linear-attention models as a linear-Gaussian state-space model, allowing the Kalman gain to weight each residual write by accumulated evidence and observation reliability; Delta-rule updates emerge as a special case lacking covariance tracking. Two scan-compatible approximations, Diagonal KDN (online mean-field variational inference) and Isotropic KDN (one uncertainty scalar per head), produce Mobius-map uncertainty recurrences enabling associative scans with logarithmic parallel depth. Controlled pretraining at 750M and 1.3B parameters consistently improves perplexity and mean downstream accuracy over state-of-the-art linear-attention models.

arXiv cs.AI / cs.LG / cs.CL · 8d agoAI research1

Kalman Delta Networks: Uncertainty-aware Associative Memory

Researchers propose Kalman Delta Networks, adding Kalman-filter uncertainty tracking to delta-rule linear attention, improving perplexity and accuracy at 750M and 1.3B parameters.

The paper introduces Kalman Delta Networks (KDNs), which reformulate recurrent associative memory in linear-attention models as a linear-Gaussian state-space model where the Kalman gain weights each write by accumulated evidence and observation reliability. Two scan-compatible approximations, Diagonal KDN via online mean-field variational inference and Isotropic KDN with a single uncertainty scalar per head, enable associative scans with logarithmic parallel depth. Delta-rule updates are shown to be a special case of this formulation. KDN variants consistently improve perplexity and mean downstream accuracy over state-of-the-art linear-attention baselines in controlled pretraining at 750M and 1.3B parameters.

Hugging Face daily papers · 9d agoAI research

Coupled Calibration and Learning: Mitigating Teacher Bias in LLM Distillation without Target-Domain Reward Feedback

CCL couples teacher calibration with student updates via token-level branching, provably removing teacher bias in LLM distillation.

The paper proposes Coupled Calibration and Learning (CCL), an LLM distillation algorithm that alternates teacher calibration using source-question reward feedback with student training on target questions under covariate shift. Each iteration calibrates the teacher on source feedback, trains the student on target questions, and lets the updated student inform subsequent calibration. The authors prove the student's expected KL divergence to the oracle student converges to zero at a polynomial rate, and show regularized direct matching error can remain bounded away from zero.

arXiv cs.AI / cs.LG / cs.CL · 20h agoAI research

How well do agents use test/verification techniques?

Dan Luu's eval finds coding-agent testing instructions (TDD, formal methods, PBT, skills) mostly fail to beat defaults on Zstd implementation correctness.

The author ran 26 prompt conditions plus 4 skills on a Zstd-in-Rust implementation eval using codex with GPT-5.6, testing TDD, fuzzing, property-based testing, formal methods (Lean 4, TLA+, Verus, Kani, SMT solvers) and community skills. Nothing dramatically outperformed the default no-instruction condition, which did above average; at xhigh effort, fuzzing and PBT conditions did slightly better than formal methods. Pre-registered predictions included TDD underperforming and popular test skills (ECC, Hegel, Trail of Bits) not outperforming. Results are averages of 80 runs per condition plotted against cost.

Hacker News · security · 8d agoAI researchHN 131↑ · 50 comments