arXiv subjects

Yuda Bi

Publications and source records attributed to Yuda Bi.

14 recordsLinked to original sources

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

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 $\delta = -0.945$. 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 $\tau = 0.811$ 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 $\sigma_{R_g}$ 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 ($\Delta\mathrm{AIC}=16.8$ 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

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 $\Dloc(\lambda)=C\lambda^4+O(\lambda^6)$, even though the observed spectrum itself is perturbed at $O(\lambda^2)$. The quartic onset is a geometric consequence of the reduced model manifold: the $O(\lambda^2)$ 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

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 $\psi_1=\lambda_{\max}/N$ 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 $\Delta$BIC$=109$. On the decomposition sample, an informational residual of $\log(\mathrm{VIX})$ alone retains most of that gain ($\Delta$BIC$=78.6$), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail ($\Delta$BIC$_{\max}=2.7$), disjoint weekly reconstructions still favor the field-coupled model ($\Delta$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, $\rho_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($\rho_x: 1.00\!\rightarrow\!0.77$), 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 $|\kappa(y)|=O(\kappa_{\max}/R_{\mathrm{eff}})$, yielding the order-tight $O(c_b\kappa_{\max}/R)$ 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 $R\lesssim \kappa_{\max}\sqrt{T}$. We also show that \emph{purification} -- selecting $m\!\ll\!R$ sign-consistent sources -- restores $R$-independent contrast $\Omega(1/m)$, 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

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↗

arXiv2025

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↗

arXiv2023

Cross-Modal Synthesis of Structural MRI and Functional Connectivity Networks via Conditional ViT-GANs

The cross-modal synthesis between structural magnetic resonance imaging (sMRI) and functional network connectivity (FNC) is a relatively unexplored area in medical imaging, especially with respect to schizophrenia. This study employs conditional Vision Transformer Generative Adversarial Networks (cViT-GANs) to generate FNC data based on sMRI inputs. After training on a comprehensive dataset that included both individuals with schizophrenia and healthy control subjects, our cViT-GAN model effectively synthesized the FNC matrix for each subject, and then formed a group difference FNC matrix, obtaining a Pearson correlation of 0.73 with the actual FNC matrix. In addition, our FNC visualization results demonstrate significant correlations in particular subcortical brain regions, highlighting the model's capability of capturing detailed structural-functional associations. This performance distinguishes our model from conditional CNN-based GAN alternatives such as Pix2Pix. Our research is one of the first attempts to link sMRI and FNC synthesis, setting it apart from other cross-modal studies that concentrate on T1- and T2-weighted MR images or the fusion of MRI and CT scans.

eess.IV↗

arXiv2023

Exploring the Power of Generative Deep Learning for Image-to-Image Translation and MRI Reconstruction: A Cross-Domain Review

Deep learning has become a prominent computational modeling tool in the areas of computer vision and image processing in recent years. This research comprehensively analyzes the different deep-learning methods used for image-to-image translation and reconstruction in the natural and medical imaging domains. We examine the famous deep learning frameworks, such as convolutional neural networks and generative adversarial networks, and their variants, delving into the fundamental principles and difficulties of each. In the field of natural computer vision, we investigate the development and extension of various deep-learning generative models. In comparison, we investigate the possible applications of deep learning to generative medical imaging problems, including medical image translation, MRI reconstruction, and multi-contrast MRI synthesis. This thorough review provides scholars and practitioners in the areas of generative computer vision and medical imaging with useful insights for summarizing past works and getting insight into future research paths.

eess.IV↗

arXiv2022

MultiCrossViT: Multimodal Vision Transformer for Schizophrenia Prediction using Structural MRI and Functional Network Connectivity Data

Vision Transformer (ViT) is a pioneering deep learning framework that can address real-world computer vision issues, such as image classification and object recognition. Importantly, ViTs are proven to outperform traditional deep learning models, such as convolutional neural networks (CNNs). Relatively recently, a number of ViT mutations have been transplanted into the field of medical imaging, thereby resolving a variety of critical classification and segmentation challenges, especially in terms of brain imaging data. In this work, we provide a novel multimodal deep learning pipeline, MultiCrossViT, which is capable of analyzing both structural MRI (sMRI) and static functional network connectivity (sFNC) data for the prediction of schizophrenia disease. On a dataset with minimal training subjects, our novel model can achieve an AUC of 0.832. Finally, we visualize multiple brain regions and covariance patterns most relevant to schizophrenia based on the resulting ViT attention maps by extracting features from transformer encoders.

cs.CV↗

arXiv2022

Prediction of Gender from Longitudinal MRI data via Deep Learning on Adolescent Data Reveals Unique Patterns Associated with Brain Structure and Change over a Two-year Period

Deep learning algorithms for predicting neuroimaging data have shown considerable promise in various applications. Prior work has demonstrated that deep learning models that take advantage of the data's 3D structure can outperform standard machine learning on several learning tasks. However, most prior research in this area has focused on neuroimaging data from adults. Within the Adolescent Brain and Cognitive Development (ABCD) dataset, a large longitudinal development study, we examine structural MRI data to predict gender and identify gender-related changes in brain structure. Results demonstrate that gender prediction accuracy is exceptionally high (>97%) with training epochs >200 and that this accuracy increases with age. Brain regions identified as the most discriminative in the task under study include predominantly frontal areas and the temporal lobe. When evaluating gender predictive changes specific to a two-year increase in age, a broader set of visual, cingulate, and insular regions are revealed. Our findings show a robust gender-related structural brain change pattern, even over a small age range. This suggests that it might be possible to study how the brain changes during adolescence by looking at how these changes are related to different behavioral and environmental factors.

eess.IV↗