Jatin Batra

Santanu Das, Sagnik Chatterjee, Jatin Batra

We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses. Prior work on robust recovery has considered settings such as linear regression (Pensia et al., JASA 2024), strictly monotonic link functions (Awasthi et al., NeurIPS 2022), and phase retrieval (Buna and Rebeschini, AISTATS 2025). However, these techniques do not extend to generic asymmetric non-monotonic link functions such as \textsc{GeLU} and \textsc{Swish}, which arise naturally as scalar primitives in modern gated neural architectures. We close this gap by giving the first robust recovery algorithm with near-linear sample and time complexity for generic non-monotonic link functions, thereby establishing the first robust recovery guarantees for a broad family of nonlinear SIMs for which \textit{no guarantees were previously known}. Our central contribution is a new structural understanding of the Gaussian squared-loss landscape under adversarial contamination. Crucially, we prove that for a broad class of nonlinear non-monotonic SIMs, a dimension-independent, constant-radius convex basin exists around the ground truth and is efficiently reachable via robust spectral initialization even under adversarial contamination. Prior works fail to establish both guarantees simultaneously, thereby either breaking down under adversarial contamination or failing to handle generic non-monotonic link functions. Together, these structural insights yield a principled warm start for robust gradient descent that provably converges to a final estimation error of $O(σ\sqrtε)$ in $\tilde{O}(nd)$ time with $\tilde{O}(d)$ samples, where $ε$ is the contamination fraction.

Depen Morwani, Jatin Batra, Prateek Jain et al.

Recent works have demonstrated that neural networks exhibit extreme simplicity bias(SB). That is, they learn only the simplest features to solve a task at hand, even in the presence of other, more robust but more complex features. Due to the lack of a general and rigorous definition of features, these works showcase SB on semi-synthetic datasets such as Color-MNIST, MNIST-CIFAR where defining features is relatively easier. In this work, we rigorously define as well as thoroughly establish SB for one hidden layer neural networks. More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, we show that when the data is linearly separable, the network primarily depends on only the linearly separable ($1$-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenette and Waterbirds-Landbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

Santanu Das, Jatin Batra

Phase retrieval is the classical problem of recovering a signal $x^* \in \mathbb{R}^n$ from its noisy phaseless measurements $y_i = \langle a_i, x^* \rangle^2 + ζ_i$ (where $ζ_i$ denotes noise, and $a_i$ is the sensing vector) for $i \in [m]$. The problem of phase retrieval has a rich history, with a variety of applications such as optics, crystallography, heteroscedastic regression, astrophysics, etc. A major consideration in algorithms for phase retrieval is robustness against measurement errors. In recent breakthroughs in algorithmic robust statistics, efficient algorithms have been developed for several parameter estimation tasks such as mean estimation, covariance estimation, robust principal component analysis (PCA), etc. in the presence of heavy-tailed noise and adversarial corruptions. In this paper, we study efficient algorithms for robust phase retrieval with heavy-tailed noise when a constant fraction of both the measurements $y_i$ and the sensing vectors $a_i$ may be arbitrarily adversarially corrupted. For this problem, Buna and Rebeschini (AISTATS 2025) very recently gave an exponential time algorithm with sample complexity $O(n \log n)$. Their algorithm needs a robust spectral initialization, specifically, a robust estimate of the top eigenvector of a covariance matrix, which they deemed to be beyond known efficient algorithmic techniques (similar spectral initializations are a key ingredient of a large family of phase retrieval algorithms). In this work, we make a connection between robust spectral initialization and recent algorithmic advances in robust PCA, yielding the first polynomial-time algorithms for robust phase retrieval with both heavy-tailed noise and adversarial corruptions, in fact with near-linear (in $n$) sample complexity.

Apoorva Narula, Aastha Jain, Jatin Batra et al.

The Indian summer monsoon is a highly complex and critical weather system that directly affects the livelihoods of over a billion people across the Indian subcontinent. Accurate short-term forecasting remains a major scientific challenge due to the monsoon's intrinsic nonlinearity and its sensitivity to multi-scale drivers, including local land-atmosphere interactions and large-scale ocean-atmosphere phenomena. In this study, we address the problem of forecasting daily rainfall across India during the summer months, focusing on both one-day and three-day lead times. We use Autoformers - deep learning transformer-based architectures designed for time series forecasting. These are trained on historical gridded precipitation data from the Indian Meteorological Department (1901--2023) at spatial resolutions of $0.25^\circ \times 0.25^\circ$, as well as $1^\circ \times 1^\circ$. The models also incorporate auxiliary meteorological variables from ECMWFs reanalysis datasets, namely, cloud cover, humidity, temperature, soil moisture, vorticity, and wind speed. Forecasts at $0.25^\circ \times 0.25^\circ$ are benchmarked against ECMWFs High-Resolution Ensemble System (HRES), widely regarded as the most accurate numerical weather predictor, and at $1^\circ \times 1^\circ $ with those from National Centre for Environmental Prediction (NCEP). We conduct both nationwide evaluations and localized analyses for major Indian cities. Our results indicate that transformer-based deep learning models consistently outperform both HRES and NCEP, as well as other climatological baselines. Specifically, compared to our model, forecasts from HRES and NCEP model have about 22\% and 43\% higher error, respectively, for a single day prediction, and over 27\% and 66\% higher error respectively, for a three day prediction.