Vince D Calhoun

Yuda Bi, Wenjun Xiao, Linhao Bai et al.

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.

Yuda Bi, Vince D Calhoun

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.

Yuda Bi, Chenyu Zhang, Qiheng Wang et al.

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.

Yuda Bi, Huaiwen Zhang, Jingnan Sun et al.

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.

Wenjun Xiao, Yuda Bi, Vince D Calhoun

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).

Ziyu Zhou, Anton Orlichenko, Gang Qu et al.

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.

M. Moein Esfahani, Hossein Sadati, Vince D Calhoun

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.

Yuda Bi, Vince D Calhoun

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.

Yuda Bi, Ying Zhu, Vince D Calhoun

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.

Xiangxiang Cui, Min Zhao, Dongmei Zhi et al.

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.