Full-Rank Correlation Matrices

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3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Sep 28, 2026cs.LG

Single-Layer MeMo as a Randomized Hamming-Kernel Classifier

MeMo (Zanzotto et al., 2025) is a recent language-model architecture that stores associations between token contexts and next tokens in a correlation matrix memory. In this work, we study its single-layer form and show that its ideal retrieval rule is a multiclass classifier based on the positional Hamming kernel. The MeMo architecture represents both the sequence features and the output labels with Gaussian random codes. Its score is therefore a doubly randomized sketch of the ideal classifier. Under independent input and output codebooks, we bound the errors introduced by context sketching and output decoding, characterize their dependence on model and data parameters, and give a margin-based guarantee for recovering the ideal prediction. Controlled simulations support the trends predicted by the analysis. On a restricted WikiText-2 next-token task, we compare single-layer MeMo with classical baselines and show that it can offer a useful trade-off among predictive accuracy, memory, and throughput, particularly on a GPU, where its matrix operations can be parallelized.

Alessandro Straziota

Department of Enterprise Engineering University of Rome “Tor Vergata” Rome, Italy

Multilayer Perceptrons Language Modeling Memo Full-Rank Correlation Matrices Kernel Method

Aug 31, 2026cs.LG

How Temporal Correlations Shape Memory in Linear Recurrent Neural Networks

The linear recurrent neural network (LRNN) is a simple model for studying how much memory a network builds up as it trains. For uncorrelated inputs, earlier work found that training itself settles the network between keeping the past and reacting only to the present. Real sequences are correlated, and we solve the learning dynamics exactly for correlated inputs. In the solution, keeping the past carries a cost. The whole effect of correlation lands on that cost. This cost reduces to the earlier one when inputs are uncorrelated and grows once they are positively correlated. Three findings follow. (1) Correlation reshapes the course of learning, not only its end. Memory builds, overshoots, and is partly removed, and the settled network keeps less of the past. (2) Memory switches off at a threshold set by one number, how much each input resembles the one just before it. Neither sequence length nor longer-range correlation moves this threshold. Memory is worth keeping only when the task needs the previous input more than the current input already supplies it through correlation with the past. (3) The best network changes too. Zero error demands a feedthrough, a path that passes the current input straight to the network's output and remembers nothing, and training builds it unprompted when given one spare hidden dimension. Our work turns one property of the input into a prediction of whether a network learns memory and explains why correlated data turns recurrent networks into change detectors.

Arnol Manuel Fokam, Fasseu Sieyondji Akpevwoghene, Edem Fiifi Dawson

Independent Researcher, United Kingdom · Department of Electrical and Electronic Engineering, University of Buea, Cameroon · minoHealth AI Labs, Ghana

Recurrent Neural Networks Full-Rank Correlation Matrices Neural Network Long-Range Temporal Dependencies

Aug 31, 2026q-fin.PM

End-to-End Neural Shrinkage of Indefinite Pairwise Correlation Matrices for Small-Cap-Inclusive Portfolios

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20% and increases the Sharpe ratio by approximately 40% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9% Model Confidence Set that retains only the neural estimator.

Christian Bongiorno, Lorenzo Villassero

Université Paris-Saclay, CentraleSupélec · Mathématiques et Informatique pour la Complexité et les Systèmes · Gif-sur-Yvette, France +2

Covariance Full-Rank Correlation Matrices Portfolio Optimization Portfolio Construction

Aug 31, 2026eess.SP

Benchmarking External Generalization of SPD Matrix Learning for Resting-State fMRI Connectome Prediction

Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction, but strong performance within one cohort may not generalize to a new cohort. We ask whether within-dataset performance remains when the test data come from an entirely held-out rs-fMRI dataset. Each scan is represented as a regularized symmetric positive definite (SPD) correlation connectome, which allows methods to use the geometry of the SPD manifold. We introduce a reproducible age-prediction benchmark across six rs-fMRI datasets: COBRE, ADNIDOD, Cam-CAN, ABIDE, OASIS-3, and ADNI. The benchmark compares a vectorized correlation baseline, Tangent-Space Ridge, SPDNet, and split-wise Riemannian harmonization under within-dataset GroupKFold, pooled GroupKFold, and leave-one-dataset-out (LODO) evaluation. Within-dataset and pooled GroupKFold results are substantially more favorable than LODO results. When an entire dataset is held out, prediction error increases, differences among methods narrow, and performance is strongly affected by age-range mismatch and cohort heterogeneity. The benchmark provides common inputs, model settings, data splits, and analysis scripts so that future SPD matrix learning methods can be evaluated under the same external-validation protocol.

Ce Ju, Antoine Collas, Florent Bouchard +1

Inria, CEA, Universit´e Paris-Saclay, Palaiseau, France · Universit´e Paris-Saclay, CNRS, CentraleSup´elec, L2S, France

Human Connectome Project Full-Rank Correlation Matrices Vascular Age Kernel Ridge Regression Matrix

Aug 5, 2026cs.CV

Image Classification Using CNN-QNN Hybrid Model with Optimized Correlated Features

We propose a method to optimize the correlation among convolutional neural network (CNN) features that are used as inputs to quantum neural network (QNN) to enhance image classification accuracy. Unlike prior approaches that employ orthogonal decomposition as preprocessing, we intentionally introduce correlated features that are more physically compatible with QNN. This design leverages the QNN's inherent ability to exploit quantum entanglement for representing correlated states-an advantage unavailable to classical neural networks. We hypothesize that aligning feature correlations with the entanglement structure of QNN improves binary classification performance. Based on a mathematical derivation of QNN outputs, Monte Carlo simulations indicate that an average correlation between features of 0.5 yields optimal classification accuracy. To validate this finding, we evaluate a quantum-classical hybrid model on three tasks: CIFAR-10 (automobile vs. truck), Fashion-MNIST (shirt vs. coat), and radar micro-Doppler signatures (robotic dogs vs. non-robots). To regulate feature correlations, we introduce a correlation-regularization term on the outputs of the CNN, driving the off-diagonal entries of the feature correlation matrix toward a target constant. Across all datasets, inducing intermediate correlation consistently improved accuracy compared to low, high, or unregulated correlations, while also reducing classification accuracy variance. These results demonstrate that imposing moderate feature correlations-without modifying the quantum circuit-enhances classification accuracy and stability by aligning feature statistics with the QNN's entanglement structure. This study highlights the potential of QNN to surpass the performance of classical classifiers as more qubits become available.

Minseo Seong, Youngwook Kim

Sogang University

Quantum Neural Networks Image Classification Convolutional Neural Networks Entanglement Full-Rank Correlation Matrices

Aug 1, 2026cs.CR

Explainable Hybrid Feature Selection for Intrusion Detection in Internet of Medical Things Environments

Internet of Medical Things (IoMT) networks are hard to protect: devices are heterogeneous, computing resources are scarce, and traffic must be analyzed in real time. We present an intrusion detection system that addresses these constraints through feature selection. A Pearson correlation filter first removes redundant attributes; a hybrid strategy then combines model-based feature importance with SHAP attribution to pick a compact subset, on which we train Random Forest and LightGBM classifiers. SHAP and LIME explain what each retained feature contributes to the decisions. On CIC-IoMT 2024 and CIC-IDS 2017, the method cuts the feature space by up to 88% - from 40 to as few as 5 features - and accuracy and F1-score stay within a few points of models trained on all features. Compact, interpretable detectors of this kind are practical candidates for deployment on resource-limited medical networks.

Amira Berrezzek, Hayet Djellali, Giulio Mallardi +1

Computer Science Dept. Badji Mokhtar University Annaba, Algeria · Computer Science Dept. University of Bari Bari, Italy

Intrusion Detection Feature Importance Feature Selection Random Forest Healthcare Full-Rank Correlation Matrices

Jul 24, 2026stat.ML

Graph-Based Correlation Matrix Generation: A Convex Optimization Approach

This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures. We propose a novel convex optimization framework in which an initial matrix is projected onto an elliptope under a positive semidefiniteness constraint. Several numerical schemes are implemented and compared. The problem falls within the broader class of matrix completion, where off-diagonal entries corresponding to absent edges are fixed to zero and diagonal entries are fixed to one. Beyond this structural constraint, the approach offers greater flexibility than existing methods by allowing control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that better reflect realistic data. This procedure is not designed to yield a uniform distribution over the feasible set; rather, it provides a principled and tunable way to construct correlation matrices suitable for benchmarking statistical methods for graphical model inference. Theoretical guarantees on the existence of solutions are established, both in the general setting and under the additional mean constraint. Simulation studies illustrate the properties of the generated matrices with respect to graph structure. The methodology is applied to two real-world datasets from neuroscience and finance, and a comparison with GAN-based correlation matrix generation is provided.

Ali Fakhar, K{é}vin Polisano, Ir{è}ne Gannaz +1

UGA · Univ. Grenoble Alpes, CNRS, Grenoble INP, Inria, LJK, F-38000 Grenoble, France · G-SCOP\_GROG, G-SCOP, Grenoble INP, UGA +2

Full-Rank Correlation Matrices Matrix Probabilistic Graphical Models Convex Optimization Spurious Correlations Sparsity

Jul 17, 2026cs.LG

An Exploratory Study of Single Channel Surface Electromyography for Hand Gesture Classification

Accurate hand gesture recognition using surface electromyography (sEMG) typically relies on multichannel sensor arrays and computationally intensive models. This limits practical deployment in low-power and embedded systems. This study investigates the feasibility of classifying ten hand gestures using a single sEMG channel combined with lightweight machine learning architectures. Raw sEMG signals were transformed into a comprehensive feature-based representation, including time-domain, frequency-domain, higher-order-crossing, and relative-intensity features. Feature redundancy was reduced using Pearson correlation filtering and the removal of highly correlated features, while dimensionality-reduction techniques (LDA and PCA) were applied selectively. Three classifiers, a feed-forward neural network (NN), k-nearest neighbors (KNN), and a support vector machine (SVM), were systematically evaluated across four experiments. Results demonstrate that combining time and frequency features with Pearson filtering and a compact NN can achieve up to 90 percent accuracy, even with limited temporal and spatial information. These findings highlight the potential of single-channel sEMG systems for cost-effective, low-power gesture-recognition applications.

Daanish Hindustani

Department of Computer Science, University of Minnesota

Surface Electromyography Hand Gesture Recognition Full-Rank Correlation Matrices

Jun 23, 2026cs.CL

Towards Version-aware Operations and Transaction Memories for Multi-layer MeMo

MeMo proposes language models with explicit multi-layer correlation matrix memories (CMMs), where memorization, retrieval, and forgetting are architectural operations. This paper asks how such memories can reduce the need for retraining when knowledge changes. For changes expressible as MeMo memory associations, the model's accessible knowledge can be updated by editing explicit memories rather than retraining the whole model. We propose a version-aware operation layer in which high-level operations such as replace, obsolete, keep-history, rollback, and trace are compiled into MeMo-native primitive calls over sequences and tokens. The key observation is that a version-aware operation is rarely a single MeMo association. It is an ordered transaction of primitive edits, for example forgetting one sequence-token chain, memorizing another, preserving a historical chain, and recording an inverse program. The framework introduces two auxiliary CMMs: a Version CMM (V-CMM) for mapping version transitions to transaction handles, and a Transaction CMM (T-CMM) for storing reusable change contents and inverse programs. It supports both direct sequence-level edits and structured diff-level inputs, and outlines an evaluation route for update success, rollback, traceability, locality, and transaction reuse.

Peiran Li

Freie Universität Berlin, Kaiserswerther Str. 16-18, 14195 Berlin, Germany

Version Memo Transaction Evidence Full-Rank Correlation Matrices

Jun 16, 2026cs.CV

Neural Phase Correlation

Correspondence is fundamentally relational: it seeks the unknown transformation between two observations of a common scene, not the content of either. Yet the dominant learning-based methods do not represent the transformation as a first-class object in the architecture. They encode each image independently and let a learned similarity function or a deep decoder discover the mapping implicitly. Phase correlation is the canonical exception, measuring the inter-image relationship directly in the Fourier domain, but the rigidity of its fixed basis confines it to global translation. We introduce a learned generalization of phase correlation that lifts this restriction by learning the basis on which the transformation decomposes. The same algebraic primitive extends to dense non-rigid deformations and to unitary dynamics. On the ACDC cardiac-MRI benchmark the framework matches or exceeds prior published baselines on both registration directions. On CAMUS echocardiography it matches state-of-the-art without auxiliary scoring or adaptive-smoothness mechanisms. Applied to time-evolved wavefunction pairs of the 1-D quantum harmonic oscillator, the same framework recovers the Hermite-function eigenstates and the quantized energy levels of the unknown Hamiltonian from observation pairs alone.

Cole Reynolds

Weyl Labs

Image Registration Deformable Cnn Full-Rank Correlation Matrices Fourier Phase Space Cardiac Magnetic Resonance Imaging+1

Jun 14, 2026stat.ML

Phase Transition in Convex Relaxations for Graph Alignment

We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices

(A, B)

with correlation

1/\sqrt{1+σ^2}

. While the maximum likelihood estimator is information-theoretically optimal, its computation, which reduces to a quadratic assignment problem, is intractable. Motivated by this, we analyze convex relaxations based on minimizing

\|AX - XB\|_F

over the set of doubly stochastic matrices and the unit hypercube. We show that when the correlation parameter satisfies

σ= o(n^{-1/2}/\log^4 n)

, the solution of either relaxation

(X^\star)

concentrates around the ground-truth permutation matrix

(Π^\star)

, i.e.,

\|X^\star-Π^\star\|_F^2 = o(n)

, implying recovery of all but a vanishing fraction of vertices after simple post-processing. Combined with existing lower bounds, our results precisely characterize that

\|X^\star-Π^\star\|_F^2

transitions from

o(n)

for

σ= \tilde{o}(n^{-1/2})

to

Ω(n)

for

σ= \tildeΩ(n^{-1/2})

. In doing so, our analysis significantly tightens prior results and extends them beyond doubly stochastic relaxations.

Laurent Massoulié, Sushil Mahavir Varma, Louis Vassaux +1

INRIA, DI/ENS, PSL Research University, Paris, France · Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan, USA. · CNRS, INRIA, Universit´e Paris Dauphine, Paris, France

Convex Relaxation Full-Rank Correlation Matrices Feature Alignment Gaussian Primitives Phase Transitions

Jun 13, 2026cs.LG

LieBN: Batch Normalization over Lie Groups

Manifold-valued measurements are prevalent in various machine learning tasks. Recent advances have extended Deep Neural Networks (DNNs) to operate on manifolds, accompanied by normalization techniques tailored to different geometries, collectively referred to as Riemannian normalization. However, most existing Riemannian normalization methods are either designed for specific manifolds or fail to effectively normalize manifold-valued sample distributions. To address these limitations, we propose LieBN, a framework for Riemannian Batch Normalization (RBN) over Lie groups. Our approach leverages the theoretically convenient left- and right-invariant metrics, which naturally exist in every Lie group, and provides theoretical guarantees for controlling the Riemannian mean and variance. We instantiate LieBN across nine distinct geometries: four on the Symmetric Positive Definite (SPD) manifold, one on the group of rotation matrices, and four on the manifold of full-rank correlation matrices. Notably, among the SPD metrics, we introduce a novel right-invariant metric and extend three existing Lie group structures via matrix power deformation. Extensive experiments on different manifolds validate the effectiveness of our framework. The code is available at https://github.com/GitZH-Chen/LieBN.git.

Ziheng Chen, Yue Song, Rui Wang +2

Department of Information Engineering and Computer Science, University of Trento, Trento, Italy · Computing and Mathematical Sciences, Caltech, CA, USA · School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China

Batch Normalization Lie Group Equivariant Neural Networks Full-Rank Correlation Matrices

Jun 11, 2026cs.LG

A Stationarity-and-Coupling Criterion for Training-Free Time-Lagged Spectral Embeddings of Multivariate Time Series

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is

D(τ)

, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that

D(τ)

separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static (

τ=0

) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching

88.5\pm4.5\%

under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that

D(τ)

is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

Siddharth Pal, Viktoria Rojkova

Multivariate Time-Series Stationarity Time-Frequency Full-Rank Correlation Matrices Timestep Embeddings Discriminative+1

Jun 4, 2026cs.LG

A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding

Electroencephalography (EEG) offers noninvasive, millisecond resolution recordings of neuronal activity and is widely used in neuroscience and healthcare. Many EEG decoding pipelines rely on covariance descriptors for their robustness to noise, but such representations are sensitive to channel-wise scaling. Recent studies have therefore advocated full-rank correlation matrices as a scale-invariant alternative for EEG decoding. In this paper, we study Sliced-Wasserstein (SW) discrepancies for probability distributions on the manifold of full-rank correlation matrices. We adopt the pullback-Euclidean formulation of SW, referred to as Pullback Euclidean Metric Sliced-Wasserstein (PEMSW), and instantiate it under two recently introduced correlation geometries, \textit{i.e.}, the Off-Log Metric (OLM) and Log-Scaled Metric (LSM). This yields two Correlation Sliced-Wasserstein (CorSW) discrepancies with closed-form slicing coordinates and efficient computation through one-dimensional Wasserstein distances. Building on CorSW, we further develop a domain generalization (DG) framework for EEG decoding. Experiments on three EEG datasets demonstrate improved generalization under distribution shifts, with low training overhead and no additional inference cost. The source code is available at github.com/ChenHu-ML/CorSW.

Chen Hu, Rui Wang, Jiale Zhou +4

Westlake University Hangzhou, China · School of Artificial Intelligence and Computer Science Jiangnan University Wuxi, China · Zhejiang University Hangzhou, China +1

Electroencephalography Full-Rank Correlation Matrices Wasserstein Distance Riemannian Manifolds Spatio-Temporal Correlations

May 26, 2026stat.ML

Gaussian Process-based learning with new MCMC-based implementation of Wishart prior on correlation matrix

In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the GP, where the induced covariance matrix of the (resulting multivariate Normal) likelihood, governs the learning and prediction. When the sought function is highly multivariate, multiple lengthscale parameters must be learnt simultaneously, making inference difficult. We develop a ``self-assembled'' Wishart prior for the covariance matrix, while undertaking Bayesian inference on the kernel hyperparameters using MCMC. The construction uses a look-back window over recent MCMC iterations to define a time-step dependent scale matrix, thereby introducing adaptiveness to the chain. Results suggest that direct prior specification on the covariance matrix can be useful for diagnosing weakly informative inputs within the GP-based learning paradigm. We support our prior development with two distinct empirical illustrations - one on synthetic data, and another on a real-world dataset.

Kane Warrior, Dalia Chakrabarty

Department of Mathematics University of York

Gaussian Process Covariance Full-Rank Correlation Matrices

May 21, 2026cs.LG

Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form operations or depend on arbitrary region ordering, limiting scalability. We introduce a scalable geometric framework with two components: (i) the Off-log metric, a smooth transformation mapping correlation matrices to symmetric zero-diagonal matrices. This enables closed-form expressions for distances, Frechet means, and linear models, allowing standard statistical modeling without complex manifold optimization. (ii) Grassmannian subspace discrimination, which compares subjects via principal-angle distances between eigenvector subspaces, resolving inherent sign and basis ambiguities. Both components integrate into standard machine-learning workflows for inference, regression, and classification. Validated across two clinical cohorts (Parkinson's and psychosis) and three ageing fMRI datasets, the Off-log metric increased sensitivity in permutation tests and matched or exceeded Riemannian and Euclidean baselines in classification. Brain-age prediction performance was comparable, with Riemannian metrics excelling in two of three cohorts. The Grassmannian method consistently outperformed Euclidean baselines, highlighting disease-relevant networks. Overall, geometry-aware representations improve sensitivity and predictive performance while remaining straightforward to deploy at scale.

Mario Severino, Manuela Moretto, Robert A. McCutcheon +1

Department of Information Engineering, University of Padova, Padova, Italy · Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience (IoPPN), King’s College London, London, United Kingdom · Department of Psychiatry, University of Oxford, Warneford Hospital, Warneford Ln, Headington, Oxford OX3 7JX, United Kingdom +2

Full-Rank Correlation Matrices Human Brain Networks Riemannian Manifolds Data Manifold Spectral Decomposition Geometry-Aware+1

May 18, 2026cs.LG

Riemannian Networks over Full-Rank Correlation Matrices

Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.

Ziheng Chen, Xiaojun Wu, Bernhard Schölkopf +1

Department of Information Engineering and Computer Science, University of Trento, Trento, Italy · Max Planck Institute for Intelligent Systems, Tübingen, Germany · School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China

Full-Rank Correlation Matrices High-Order Correlations Rectified Linear Unit Networks Backpropagation

May 13, 2026cs.LG

Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization

This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.

Jannis Lübsen, Annika Eichler

Institute of Control Systems, Hamburg University of Technology, Hamburg, Germany · Institute of Control Systems, Hamburg University of Technology · Deutsches Elektronen-Synchrotron, Hamburg, Germany

Bayesian Optimization Gaussian Process Full-Rank Correlation Matrices Robust Optimization

May 6, 2026stat.ML

Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval

How many key-value associations can a

d\times d

linear memory store? We show that the answer depends not only on the

d^2

degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for the stored pairs, we show that top-1 retrieval, where every signal must beat its largest distractor, requires the logarithmic model-size scale

d^2\asymp n\log n

. We prove that the correlation matrix memory construction, which stores associations by superposing key-target outer products, achieves this scale through a sharp phase transition, and that the same scaling is necessary for any linear memory. Thus the logarithm is the intrinsic extreme-value price of winner-take-all decoding. We next consider listwise retrieval, where the correct target need not be the unique top-scoring item but should remain among the strongest candidates. To formalize this regime, we propose the Tail-Average Margin (TAM), a convex upper-tail criterion that certifies inclusion of the correct target in a controlled candidate list. Under this listwise retrieval criterion, the capacity follows the quadratic scale

d^2\asymp n

. At load

n/d^2\toα

, we develop an exact asymptotic theory for the TAM empirical-risk minimizer through a two-parameter scalar variational principle. The theory has a rich phenomenology: in the ridgeless limit it yields a closed-form critical load separating satisfiable and unsatisfiable phases, and it predicts the limiting laws of true scores, competitor scores, margins, and percentile profiles. Finally, a small-tail extrapolation further leads to the conjectural sharp top-1 threshold

d^2\sim 2n\log n

.

Nicholas Barnfield, Juno Kim, Eshaan Nichani +2

Harvard University · University of California, Berkeley · Princeton University

Dense Associative Memory Full-Rank Correlation Matrices Capacity Keys And Value

Apr 19, 2026cs.CY

PsychBench: Auditing Epidemiological Fidelity in Large Language Model Mental Health Simulations

Large language models are increasingly deployed to simulate patients for clinical training, research, and mental health tools, yet population-level validity remains largely untested. We introduce PsychBench, the first epidemiological audit of LLM patient simulation: 28,800 profiles from four frontier models (GPT-4o-mini, DeepSeek-V3, Gemini-3-Flash, GLM-4.7) evaluated against NHANES and NESARC-III baselines across 120 intersectional cohorts. The central finding is a coherence-fidelity dissociation: models produce clinically plausible individuals while misrepresenting the populations they are drawn from. Variance compression ranges from 14 percent (GLM-4.7) to 62 percent (DeepSeek-V3), eliminating the distributional tails of clinical reality. Despite test-retest correlations above r = 0.90, 36.66 percent of cases cross diagnostic thresholds between runs. Symptom correlation matrices diverge across demographic groups beyond split-half noise, with transgender populations diverging three to five times more than racial differences. Calibration bias is systematic and asymmetric. Models overestimate depression severity for most groups by 3.6 to 6.1 points (Cohen d = 1.13 to 1.91), consistent with training on clinical corpora with elevated base rates. For transgender women the direction inverts: models capture only 8 to 46 percent of documented minority stress elevation, yielding a -5.42 residual (d = -1.55). Models also attribute irritability to Black men and fatigue to women beyond matched controls, encoding racialized and gendered assumptions. Patterns replicate across US and Chinese architectures, indicating failures tied to current training paradigms rather than isolated implementations. For most users, LLM mental health tools risk pathologizing ordinary distress; for transgender users, algorithmic erasure of genuine need. The patients look right. They do not represent real populations.

Patrick Keough

Independent Researcher Bremerton, Washington, USA

Mental Health Simulated Patients Epidemiological Models Full-Rank Correlation Matrices