arXiv subjects

Vince D Calhoun

Publications and source records attributed to Vince D Calhoun.

15 recordsLinked to original sources

arXiv2026

High-Order Triadic Functional Connectivity in the Brain and Beyond

Here, we report high-order functional network connectivity as a promising way for studying the brain connectome. Traditional functional connectivity approaches capture only pairwise relationships between brain regions, overlooking complex multivariate dependencies that underlie cognition and behavior. First, we demonstrated that high-order interactions capture more information and can distinguish between resting-state and task-state brain activity. Second, we introduce a matrix-based entropy-functional method for estimating triadic interactions, which are statistical dependencies among triplets of brain regions, and apply it to large-scale functional brain networks. The resulting triadic networks revealed distinct community patterns that complement those observed in traditional pairwise functional connectivity analyses and simultaneously capture additional connection information. Despite the potential combinatorial explosion of triadic configurations, the networks exhibited constrained and hierarchical structures that allowed computation and interpretation. These findings position triadic connectivity as a promising next-step functional connectivity framework for probing brain network organization and high-order neural interactions, while also highlighting key biological and technical challenges that require careful consideration.

q-bio.NC↗

arXiv2026

Cross-Spectral Witness for Hidden Nonequilibrium Beyond the Scalar Ceiling

Partial observation is a pervasive obstacle in nonequilibrium physics: coarse graining may absorb hidden forcing into an apparently equilibrium-like reduced description, so a driven system can look reversible through the only variables one can measure. For scalar Gaussian observables of linear stochastic systems, no time-irreversibility statistic can detect the underlying drive. The Lucente--Crisanti ceiling constrains what one channel carries; what two channels carry is a different question, with a sharp closed-form answer. Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to any scalar reduction; under channel-separable multiplicative structure the observed-channel response factors cancel identically, leaving a closed-form cross-spectral witness controlled only by the hidden spectrum, the loadings, and the innovation scales, strictly positive at every nonzero cross-coupling including at exact timescale coalescence where every scalar reduction is blind. Within general CSM this certifies shared hidden-sector drive; under the additional one-way coupling assumption the witness identifies the total entropy production rate at leading order with a square-root scaling.

cond-mat.stat-mech↗

arXiv2026

Timescale Coalescence Makes Hidden Persistent Forcing Spectrally Dark

Under coarse observation, unresolved slow forcing can remain dynamically active yet locally invisible to reduced spectral inference. For a solvable driven AR$(1)$ benchmark, the local Whittle/Kullback--Leibler distance from the true spectrum to the best nearby one-pole surrogate obeys $\Dloc(λ)=Cλ^4+O(λ^6)$, even though the observed spectrum itself is perturbed at $O(λ^2)$. The quartic onset is a geometric consequence of the reduced model manifold: the $O(λ^2)$ perturbation is partially absorbed by tangent-space reparametrization, and only the normal residual survives. We obtain $C$ in closed form for an AR$(1)$ hidden driver and show that $C$ vanishes as $(a-b)^2$ at timescale coalescence, identifying a spectrally \emph{dark} regime. We then show that this dark regime is not geometrically inevitable: for a non-degenerate AR$(2)$ hidden driver (second characteristic root $z_2\neq 0$), $C>0$ for all parameter values, including single-root coalescence, because the richer spectral structure cannot be absorbed by the two-dimensional tangent space. The quartic coefficient interpolates smoothly between the two cases as $C\sim z_2^4$ when the second characteristic root vanishes. Together, the AR$(1)$ and AR$(2)$ results yield a classification within the one-pole projection class: the quartic law and the boundary $\lcpop(N)\propto(\log N/N)^{1/4}$ are universal features of the projection geometry within this class, while the dark regime requires the hidden driver's spectrum to match the null family's pole structure.

cond-mat.stat-mech↗

arXiv2026

Spectral Coherence Index: A Model-Free Metric for Protein Structural Ensemble Quality Assessment

Protein structural ensembles from NMR spectroscopy capture biologically important conformational heterogeneity, but it remains difficult to determine whether observed variation reflects coordinated motion or noise-like artifacts. We evaluate the Spectral Coherence Index (SCI), a model-free, rotation-invariant summary derived from the participation-ratio effective rank of the inter-model pairwise distance-variance matrix. Under grouped primary analysis of a Main110 cohort of 110 NMR ensembles (30--403 residues; 10--30 models per entry), SCI separated experimental ensembles from matched synthetic incoherent controls with AUC-ROC $= 0.973$ and Cliff's $δ= -0.945$. Relative to an internal 27-protein pilot, discrimination softened modestly, showing that pilot-era thresholds do not transfer perfectly to a larger, more heterogeneous cohort: the primary operating point $τ= 0.811$ yielded 95.5\% sensitivity and 89.1\% specificity. PDB-level sensitivity remained nearly unchanged (AUC $= 0.972$), and an independent 11-protein holdout reached AUC $= 0.983$. Across 5-fold grouped stratified cross-validation and leave-one-function-class-out testing, SCI remained strong (AUC $= 0.968$ and $0.971$), although $σ_{R_g}$ was the stronger single-feature discriminator and a QC-augmented multifeature model generalized best (AUC $= 0.989$ and $0.990$). Residue-level validation linked SCI-derived contributions to experimental RMSF across 110 proteins and showed broad concordance with GNM-based flexibility patterns. Rescue analyses showed that Main110 softening arose mainly from size and ensemble normalization rather than from loss of spectral signal. Together, these results establish SCI as an interpretable, bounded coherence summary that is most useful when embedded in a multimetric QC workflow for heterogeneous protein ensembles.

q-bio.QM↗

arXiv2026

Grokking as a Falsifiable Finite-Size Transition

Grokking -- the delayed onset of generalization after early memorization -- is often described with phase-transition language, but that claim has lacked falsifiable finite-size inputs. Here we supply those inputs by treating the group order $p$ of $\mathbb{Z}_p$ as an admissible extensive variable and a held-out spectral head-tail contrast as a representation-level order parameter, then apply a condensed-matter-style diagnostic chain to coarse-grid sweeps and a dense near-critical addition audit. Binder-like crossings reveal a shared finite-size boundary, and susceptibility comparison strongly disfavors a smooth-crossover interpretation ($Δ\mathrm{AIC}=16.8$ in the near-critical audit). Phase-transition language in grokking can therefore be tested as a quantitative finite-size claim rather than invoked as analogy alone, although the transition order remains unresolved at present.

cs.LG↗

arXiv2026

The Financial Connectome: A Brain-Inspired Framework for Modeling Latent Market Dynamics

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, but as high-dimensional dynamic systems composed of latent market modules. Treating stocks as functional nodes and their co-fluctuations as expressions of collective cognition, we introduce dynamic Market Network Connectivity (dMNC), the financial analogue of dynamic functional connectivity (dFNC). This biologically inspired framework reveals structurally persistent market subnetworks, captures regime shifts, and uncovers systemic early warning signals all without reliance on predictive labels. Our results suggest that markets, like brains, exhibit modular, self-organizing, and temporally evolving architectures. This work inaugurates the field of financial connectomics, a principled synthesis of systems neuroscience and quantitative finance aimed at uncovering the hidden logic of complex economies.

q-fin.CP↗

arXiv2026

Scaling Laws are Redundancy Laws

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s / (2s + 1/beta), where beta controls the spectral tail and 1/beta measures redundancy. This reveals that the learning curve's slope is not universal but depends on data redundancy, with steeper spectra accelerating returns to scale. We establish the law's universality across boundedly invertible transformations, multi-modal mixtures, finite-width approximations, and Transformer architectures in both linearized (NTK) and feature-learning regimes. This work delivers the first rigorous mathematical explanation of scaling laws as finite-sample redundancy laws, unifying empirical observations with theoretical foundations.

cs.LG↗

arXiv2026

Conditioning on a Volatility Proxy Compresses the Apparent Timescale of Collective Market Correlation

We address the attribution problem for apparent slow collective dynamics: is the observed persistence intrinsic, or inherited from a persistent driver? For the leading eigenvalue fraction $ψ_1=λ_{\max}/N$ of S\&P 500 60-day rolling correlation matrices ($237$ stocks, 2004--2023), a VIX-coupled Ornstein--Uhlenbeck model reduces the effective relaxation time from $298$ to $61$ trading days and improves the fit over bare mean reversion by $Δ$BIC$=109$. On the decomposition sample, an informational residual of $\log(\mathrm{VIX})$ alone retains most of that gain ($Δ$BIC$=78.6$), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail ($Δ$BIC$_{\max}=2.7$), disjoint weekly reconstructions still favor the field-coupled model ($Δ$BIC$=140$--$151$), and six anchored chronological holdouts preserve the out-of-sample advantage. Quiet-regime and field-stripped residual autocorrelation controls show the same collapse of persistence. Stronger hidden-variable extensions remain only partially supported. Within the tested stochastic class, conditioning on the observed VIX proxy absorbs most of the apparent slow dynamics.

q-fin.CP↗

arXiv2026

Reservoir Subspace Injection for Online ICA under Top-n Whitening

Reservoir expansion can improve online independent component analysis (ICA) under nonlinear mixing, yet top-$n$ whitening may discard injected features. We formalize this bottleneck as \emph{reservoir subspace injection} (RSI): injected features help only if they enter the retained eigenspace without displacing passthrough directions. RSI diagnostics (IER, SSO, $ρ_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($ρ_x: 1.00\!\rightarrow\!0.77$), degrading SI-SDR by up to $2.2$\,dB. A guarded RSI controller preserves passthrough retention and recovers mean performance to within $0.1$\,dB of baseline $1/N$ scaling. With passthrough preserved, RE-OICA improves over vanilla online ICA by $+1.7$\,dB under nonlinear mixing and achieves positive SI-SDR$_{\mathrm{sc}}$ on the tested super-Gaussian benchmark ($+0.6$\,dB).

cs.LG↗

arXiv2026

A 1/R Law for Kurtosis Contrast in Balanced Mixtures

Kurtosis-based Independent Component Analysis (ICA) weakens in wide, balanced mixtures. We prove a sharp redundancy law: for a standardized projection with effective width $R_{\mathrm{eff}}$ (participation ratio), the population excess kurtosis obeys $|κ(y)|=O(κ_{\max}/R_{\mathrm{eff}})$, yielding the order-tight $O(c_bκ_{\max}/R)$ under balance (typically $c_b=O(\log R)$). As an impossibility screen, under standard finite-moment conditions for sample kurtosis estimation, surpassing the $O(1/\sqrt{T})$ estimation scale requires $R\lesssim κ_{\max}\sqrt{T}$. We also show that \emph{purification} -- selecting $m\!\ll\!R$ sign-consistent sources -- restores $R$-independent contrast $Ω(1/m)$, with a simple data-driven heuristic. Synthetic experiments validate the predicted decay, the $\sqrt{T}$ crossover, and contrast recovery.

cs.LG↗

arXiv2025

Redundancy as a Structural Information Principle for Learning and Generalization

We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework, redundancy is expressed as a general family of informational divergences that unifies multiple classical measures, such as mutual information, chi-squared dependence, and spectral redundancy, under a single geometric principle. This reveals that these traditional quantities are not isolated heuristics but projections of a shared redundancy geometry. The theory further predicts that redundancy is bounded both above and below, giving rise to an optimal equilibrium that balances over-compression (loss of structure) and over-coupling (collapse). While classical communication theory favors minimal redundancy for transmission efficiency, finite and structured systems, such as those underlying real-world learning, achieve maximal stability and generalization near this equilibrium. Experiments with masked autoencoders are used to illustrate and verify this principle: the model exhibits a stable redundancy level where generalization peaks. Together, these results establish redundancy as a measurable and tunable quantity that bridges the asymptotic world of communication and the finite world of learning.

cs.LG↗

arXiv2025

BRIEF: BRain-Inspired network connection search with Extensive temporal feature Fusion enhances disease classification

Existing deep learning models for functional MRI-based classification have limitations in network architecture determination (relying on experience) and feature space fusion (mostly simple concatenation, lacking mutual learning). Inspired by the human brain's mechanism of updating neural connections through learning and decision-making, we proposed a novel BRain-Inspired feature Fusion (BRIEF) framework, which is able to optimize network architecture automatically by incorporating an improved neural network connection search (NCS) strategy and a Transformer-based multi-feature fusion module. Specifically, we first extracted 4 types of fMRI temporal representations, i.e., time series (TCs), static/dynamic functional connection (FNC/dFNC), and multi-scale dispersion entropy (MsDE), to construct four encoders. Within each encoder, we employed a modified Q-learning to dynamically optimize the NCS to extract high-level feature vectors, where the NCS is formulated as a Markov Decision Process. Then, all feature vectors were fused via a Transformer, leveraging both stable/time-varying connections and multi-scale dependencies across different brain regions to achieve the final classification. Additionally, an attention module was embedded to improve interpretability. The classification performance of our proposed BRIEF was compared with 21 state-of-the-art models by discriminating two mental disorders from healthy controls: schizophrenia (SZ, n=1100) and autism spectrum disorder (ASD, n=1550). BRIEF demonstrated significant improvements of 2.2% to 12.1% compared to 21 algorithms, reaching an AUC of 91.5% - 0.6% for SZ and 78.4% - 0.5% for ASD, respectively. This is the first attempt to incorporate a brain-inspired, reinforcement learning strategy to optimize fMRI-based mental disorder classification, showing significant potential for identifying precise neuroimaging biomarkers.

cs.LG↗

arXiv2024

Optimizing Brain-Computer Interface Performance: Advancing EEG Signals Channel Selection through Regularized CSP and SPEA II Multi-Objective Optimization

Brain-computer interface systems and the recording of brain activity has garnered significant attention across a diverse spectrum of applications. EEG signals have emerged as a modality for recording neural electrical activity. Among the methodologies designed for feature extraction from EEG data, the method of RCSP has proven to be an approach, particularly in the context of MI tasks. RCSP exhibits efficacy in the discrimination and classification of EEG signals. In optimizing the performance of this method, our research extends to a comparative analysis with conventional CSP techniques, as well as optimized methodologies designed for similar applications. Notably, we employ the meta-heuristic multi-objective Strength Pareto Evolutionary Algorithm II (SPEA-II) as a pivotal component of our research paradigm. This is a state-of-the-art approach in the selection of an subset of channels from a multichannel EEG signal with MI tasks. Our main objective is to formulate an optimum channel selection strategy aimed at identifying the most pertinent subset of channels from the multi-dimensional electroencephalogram (EEG) signals. One of the primary objectives inherent to channel selection in the EEG signal analysis pertains to the reduction of the channel count, an approach that enhances user comfort when utilizing gel-based EEG electrodes. Additionally, within this research, we took benefit of ensemble learning models as a component of our decision-making. This technique serves to mitigate the challenges associated with overfitting, especially when confronted with an extensive array of potentially redundant EEG channels and data noise. Our findings not only affirm the performance of RCSP in MI-based BCI systems, but also underscore the significance of channel selection strategies and ensemble learning techniques in optimizing the performance of EEG signal classification.

eess.SP↗

arXiv2024

An Interpretable Cross-Attentive Multi-modal MRI Fusion Framework for Schizophrenia Diagnosis

Both functional and structural magnetic resonance imaging (fMRI and sMRI) are widely used for the diagnosis of mental disorder. However, combining complementary information from these two modalities is challenging due to their heterogeneity. Many existing methods fall short of capturing the interaction between these modalities, frequently defaulting to a simple combination of latent features. In this paper, we propose a novel Cross-Attentive Multi-modal Fusion framework (CAMF), which aims to capture both intra-modal and inter-modal relationships between fMRI and sMRI, enhancing multi-modal data representation. Specifically, our CAMF framework employs self-attention modules to identify interactions within each modality while cross-attention modules identify interactions between modalities. Subsequently, our approach optimizes the integration of latent features from both modalities. This approach significantly improves classification accuracy, as demonstrated by our evaluations on two extensive multi-modal brain imaging datasets, where CAMF consistently outperforms existing methods. Furthermore, the gradient-guided Score-CAM is applied to interpret critical functional networks and brain regions involved in schizophrenia. The bio-markers identified by CAMF align with established research, potentially offering new insights into the diagnosis and pathological endophenotypes of schizophrenia.

eess.IV↗

arXiv2023

Higher-order Organization in the Human Brain from Matrix-Based Rényi's Entropy

Pairwise metrics are often employed to estimate statistical dependencies between brain regions, however they do not capture higher-order information interactions. It is critical to explore higher-order interactions that go beyond paired brain areas in order to better understand information processing in the human brain. To address this problem, we applied multivariate mutual information, specifically, Total Correlation and Dual Total Correlation to reveal higher-order information in the brain. In this paper, we estimate these metrics using matrix-based Rényi's entropy, which offers a direct and easily interpretable approach that is not limited by direct assumptions about probability distribution functions of multivariate time series. We applied these metrics to resting-state fMRI data in order to examine higher-order interactions in the brain. Our results showed that the higher-order information interactions captured increase gradually as the interaction order increases. Furthermore, we observed a gradual increase in the correlation between the Total Correlation and Dual Total Correlation as the interaction order increased. In addition, the significance of Dual Total Correlation values compared to Total Correlation values also indicate that the human brain exhibits synergy dominance during the resting state.

q-bio.NC↗