arXiv subjects

Arkaprabha Ganguli

Publications and source records attributed to Arkaprabha Ganguli.

8 recordsLinked to original sources

arXiv2026

A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel

A persistent empirical observation is that trained neural networks outperform their neural tangent kernel (NTK) limit on tasks with compositional structure, yet a quantitative account of $\textbf{when}$ and $\textbf{by how much}$ has been lacking. Working on the unit circle, we give such an account through a dichotomy between two complexity measures of the target: its $\textbf{Fourier complexity}$, which controls NTK kernel regression, and its $\textbf{architectural complexity}$, which controls learning over depth-$L$, width-$w$ ReLU networks with the variation norm of the weights bounded by $R$. We first characterize the minimax rate of the architecture class $\mathcal{C}_{L,w,R}$, pinning it down up to a single factor of $L$: between $\Omega(Lw^2R^2/n)$ and $\tilde{O}(L^2w^2R^2/n)$. We then show the NTK estimator sits $\textbf{exponentially}$ above this floor whenever the two complexities decouple: for the depth-$L$ iterated sawtooth, NTK regression needs $\Omega(4^L)$ samples while the minimax floor is polynomial in $L$. Numerical experiments confirm the theoretical claims: on bandlimited smooth targets, the NTK is competitive or better, while on the hypercube sparse-parity model, a standard two-layer network beats the NTK by four to six orders of magnitude in test error. The gap is thus a function-space property, a mismatch between the kernel's smoothness bias and the target's compositional structure, rather than a generic kernel-versus-network phenomenon.

stat.ML↗

arXiv2026

High-Resolution Flood Mapping With Sentinel-1 and Sentinel-2 via Misalignment-Robust Cross-Sensor Learning and Generative Despeckling

Reliable high-resolution flood extent mapping from satellite imagery remains constrained by limited data fidelity and sensor-specific artifacts. Multispectral optical imagery is degraded by clouds, shadows, and urban confounders, while synthetic aperture radar (SAR) imagery is affected by speckle noise and sensor co-registration uncertainty. This work presents an integrated flood mapping framework that jointly addresses these limitations through curated datasets and novel learning strategies. We introduce a new Sentinel-2 (S2) and Sentinel-1 (S1) dataset covering the contiguous United States, featuring pixel-accurate 10 m water masks with emphasis on challenging weather conditions and urban environments that are underrepresented in existing benchmarks. High-quality S2 annotations are manually produced using rigorous geospatial labeling protocols and transferred to SAR imagery through weakly labeled temporally coincident acquisitions. To address SAR-specific artifacts, a shift-invariant loss function is employed to tolerate residual geolocation uncertainty between SAR imagery and optical-derived labels, and a Conditional Variational Autoencoder (CVAE) is trained on multitemporal SAR composites to suppress speckle while preserving flood-relevant spatial structure. Experiments using UNet and UNet++ architectures demonstrate strong multispectral performance (AUPRC up to 0.956) and statistically significant improvements in SAR flood mapping when using shift-invariant loss and CVAE-based despeckling compared to classical filters. These results underscore the importance of dataset fidelity, misalignment-robust training, and demonstrate the viability of generative despeckling for operational flood mapping.

cs.CV↗

arXiv2026

Event-Level QCD Inference Framework for Quark-Gluon Imaging

We introduce and demonstrate an event-level analysis framework for quark-gluon imaging. For a first application we use it for the inference of parton distribution functions from synthetic deep inelastic scattering data. This framework removes the need for unfolding of detector effects and the binning of events, and therefore eliminates two key sources of information loss. We contrast this event-level framework with the traditional histogram approach by performing a closure test for parton distribution functions from event data obtained from a known ground truth. In this study we assume a perfect detector, which makes unfolding straightforward. The elimination of binning in the event-level framework is demonstrated to have important benefits over the traditional histogram approach, and performs better in the closure test, particularly for a smaller number of events. For example, defining a mean-squared error distance metric, we find that the event-level framework performs around $35\%$ better than the traditional approach for a moderate number of events. The benefits of an event-level framework should increase for inference associated with 3D quark-gluon imaging, because these differential cross sections are of higher dimension and the comparative number of measured events is significantly reduced.

hep-ph↗

arXiv2026

Disentangled Deep Priors for Bayesian Inverse Problems

We propose a structured prior for high-dimensional Bayesian inverse problems based on a disentangled deep generative model whose latent space is partitioned into auxiliary variables aligned with known and interpretable physical parameters and residual variables capturing remaining unknown variability. This yields a hierarchical prior in which interpretable coordinates carry domain-relevant uncertainty while the residual coordinates retain the flexibility of deep generative models. By linearizing the generator, we characterize the induced prior covariance and derive conditions under which the posterior exhibits approximate block-diagonal structure in the latent variables, clarifying when representation-level disentanglement translates into a separation of uncertainty in the inverse problem. We formulate the resulting latent-space inverse problem and solve it using MAP estimation and Markov chain Monte Carlo (MCMC) sampling. On elliptic PDE inverse problems, such as conductivity identification and source identification, the approach matches an oracle Gaussian process prior under correct specification and provides substantial improvement under prior misspecification, while recovering interpretable physical parameters and producing spatially calibrated uncertainty estimates.

stat.CO↗

arXiv2026

Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models

Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.

stat.ML↗

arXiv2025

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

stat.ML↗

arXiv2022

Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning

In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultra-high dimensional and highly correlated features, in addition to the high noise level. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.

stat.ML↗

arXiv2021

Nonparametric Scanning For Nonrandom Missing Data With Continuous Instrumental Variables

This article introduces a new instrumental variable approach for estimating unknown population parameters with data having nonrandom missing values. With coarse and discrete instruments, Shao and Wang (2016) proposed a semiparametric method that uses the added information to identify the tilting parameter from the missing data propensity model. A naive application of this idea to continuous instruments through arbitrary discretizations is apt to be inefficient, and maybe questionable in some settings. We propose a nonparametric method not requiring arbitrary discretizations but involves scanning over continuous dichotomizations of the instrument; and combining scan statistics to estimate the unknown parameters via weighted integration. We establish the asymptotic normality of the proposed integrated estimator and that of the underlying scan processes uniformly across the instrument sample space. Simulation studies and the analysis of a real data set demonstrate the gains of the methodology over procedures that rely either on arbitrary discretizations or moments of the instrument.

stat.ME↗