arXiv subjects

Santanu Das

Publications and source records attributed to Santanu Das.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Linear and Overcomplete Regimes: A Mean-Field Analysis of Bottleneck Autoencoders

Autoencoders (AEs) learn low-dimensional representations by mapping data into a latent space while minimizing reconstruction error. Despite their empirical success, theoretical understanding remains limited and largely restricted to linear models or settings without a bottleneck. In this work, we study nonlinear AEs with a fixed finite-dimensional bottleneck in the mean-field (MF) regime. We derive explicit MF learning dynamics for both encoder and decoder, providing a tractable characterization of training in the nonlinear setting. We show that, over finite time horizons, the empirical risk of finite-width networks trained with stochastic gradient descent closely tracks the MF risk trajectory with high probability. At optimality, we further establish that the finite-width risk converges to the MF optimum, demonstrating that finite networks are sufficiently expressive to approximate the infinite-width solution.

cs.LG↗

arXiv2026

Convex Basins in Single-Index Model Loss Landscapes: Applications to Robust Recovery under Strong Adversarial Corruption

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 $O(\sigma\sqrt{\epsilon})$ in $\tilde{O}(nd)$ time with $\tilde{O}(d)$ samples, where $\epsilon$ is the contamination fraction.

cs.LG↗

arXiv2026

Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexity

Phase retrieval is the classical problem of recovering a signal $x^* \in \mathbb{R}^n$ from its noisy phaseless measurements $y_i = \langle a_i, x^* \rangle^2 + \zeta_i$ (where $\zeta_i$ 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.

cs.LG↗

arXiv2025

Deep Learning for CMB Foreground Removal and Beam Deconvolution: A U-Net GAN Approach

Extracting cosmological information from microwave sky observations requires accurate estimation of the underlying Cosmic Microwave Background (CMB) by removing foreground contamination, instrumental noise, and the effects of beam convolution. In this work, we develop a machine learning-based approach for CMB reconstruction using a generative adversarial network (GAN) architecture, where the generator is modeled as a U-Net-based convolutional neural network. To train the network, we generate realistic microwave sky maps by simulating Planck-like observations: scanning HEALPix-simulated skies with real Planck beam profile, actual scan patterns, and anisotropic noise consistent with Planck data. Our method achieves high-fidelity reconstruction, with the difference between the input and recovered maps being less than $1\%$ (approximately $2\mu\mathrm{K}$ for temperature and less than $0.5\mu\mathrm{K}$ for polarization) outside the Galactic region. Even within the Galactic plane, the reconstruction error stays below $2$-$3\%$ for temperature maps across most regions, and is even smaller for polarization, apart from a few isolated pixels.. Most importantly, we demonstrate, for the first time, that a GAN-based method can effectively correct for foreground contamination, the systematic effects of non-circular beams and the asymmetric Planck scan pattern for both T and E-mode skymaps. Our results demonstrate the effectiveness of our method for robust and accurate recovery of the CMB signal, even in the presence of strong astrophysical foregrounds and instrumental systematics.

astro-ph.IM↗

arXiv2025

Phase space analysis of R\'enyi Holographic dark energy model

Recent observational evidences point out towards a late time acceleration of the universe. In order to study the accelerated expansion, scientists have incorporated the existence of an exotic matter with negative pressure, termed as dark energy. Afterwards a new idea of dark energy have been studied depending on the holographic principle of quantum gravity, called as the Holographic Dark Energy(HDE). Later on modifying Bekestein-Hawking entropy, different generalized entropies have been proposed, one of them being R\'enyi entropy which leads to R\'enyi holographic dark energy model (RHDE). We have considered RHDE model with Hubble horizon as the IR cut off and have studied the cosmological behaviour under non interacting, linear and non-linear interacting scenarios with the help of dynamical systems analysis. We have also investigated the stability of the system around hyperbolic critical points along with the type of fluid description, evolution of equation of state parameter as well as matter and energy density parameters.

gr-qc↗

arXiv2025

Machine Learning-Based Anomaly Detection of Correlated Sensor Data: An Integrated Principal Component Analysis-Autoencoder Approach

The growing adoption of IoT systems in industries like transportation, banking, healthcare, and smart energy has increased reliance on sensor networks. However, anomalies in sensor readings can undermine system reliability, making real-time anomaly detection essential. While a large body of research addresses anomaly detection in IoT networks, few studies focus on correlated sensor data streams, such as temperature and pressure within a shared space, especially in resource-constrained environments. To address this, we propose a novel hybrid machine learning approach combining Principal Component Analysis (PCA) and Autoencoders. In this method, PCA continuously monitors sensor data and triggers the Autoencoder when significant variations are detected. This hybrid approach, validated with real-world and simulated data, shows faster response times and fewer false positives. The F1 score of the hybrid method is comparable to Autoencoder, with much faster response time which is driven by PCA.

eess.SP↗

arXiv2025

Fault-Tolerant IoT System Using Software-Based "Digital Twin"

In this article, we present a novel redundancy scheme to realize a fault-tolerant IoT structure for application in high-reliability systems. The proposed fault-tolerant structure uses a centralized data fusion block and triplicated IoT devices, along with software-based "digital twins", that duplicate the function of each of the sensors. In case of a fault in one of the IoT devices, the pertinent digital twin takes over the function of the actual IoT device for some time in the triplicated structure till the faulty device is either replaced or repaired when possible. The use of software-based digital twins as a duplicate for each physical sensor improves the reliability of the operation with minimal increase in the overall system cost.

eess.SP↗

arXiv2024

Cosmological implications of non-minimally coupled f(Q) gravity

We experience some challenges in general gravitational theory owing to Einstein to explain late time acceleration of universe. To address this issue, geometric components of gravity have been modified in quite a few occasions to have a more general structure with some freedom. One such approach is to change the geometric components of gravity where gravitational interaction is denoted by Q,Q being the non-metricity. In our work, we have considered symmetric teleparallel gravity i.e, modified the geometry with the help of non-metricity Q or f(Q) gravity. We have considered a specific form of f(Q) which is nothing but the linear combination of Q and \alpha Q^{n}, n\neq 1, where Q is coupled with Lagrangian matter. Forming the autonomous system from governing equations and then solving it, we have tried to analyze the nature of universe using dynamical system analysis. We have studied the behavior of the universe under several circumstances. Then, we have studied the stability around critical points and considering the recent observational data available for some cosmological parameters, feasible solutions are noted which depict late time acceleration. We can see that f(Q) gravity model can be considered as an alternative model to \lambda CDM model.

gr-qc↗

arXiv2024

A direct proof of a unified law of robustness for Bregman divergence losses

In contemporary deep learning practice, models are often trained to near zero loss i.e. to nearly interpolate the training data. However, the number of parameters in the model is usually far more than the number of data points n, the theoretical minimum needed for interpolation: a phenomenon referred to as overparameterization. In an interesting piece of work, Bubeck and Sellke considered a natural notion of interpolation: the model is said to interpolate when the model's training loss goes below the loss of the conditional expectation of the response given the covariate. For this notion of interpolation and for a broad class of covariate distributions (specifically those satisfying a natural notion of concentration of measure), they showed that overparameterization is necessary for robust interpolation i.e. if the interpolating function is required to be Lipschitz. Their main proof technique applies to regression with square loss against a scalar response, but they remark that via a connection to Rademacher complexity and using tools such as the Ledoux-Talagrand contraction inequality, their result can be extended to more general losses, at least in the case of scalar response variables. In this work, we recast the original proof technique of Bubeck and Sellke in terms of a bias-variance type decomposition, and show that this view directly unlocks a generalization to Bregman divergence losses (even for vector-valued responses), without the use of tools such as Rademacher complexity or the Ledoux-Talagrand contraction principle. Bregman divergences are a natural class of losses since for these, the best estimator is the conditional expectation of the response given the covariate, and include other practical losses such as the cross entropy loss. Our work thus gives a more general understanding of the main proof technique of Bubeck and Sellke and demonstrates its broad utility.

cs.LG↗

arXiv2023

Machian Gravity: Confronting Galaxy Cluster Mass Profiles

The general theory of relativity (GR) has excelled in explaining gravitational phenomena at the scale of the solar system with remarkable precision. However, when extended to the galactic or cosmological scale, it requires dark matter and dark energy to explain observations. In our previous article (arXiv:2308.04503), we've formulated a gravity theory based in Mach's principle, known as Machian gravity. We demonstrated that the theory successfully explains galactic velocity profiles without requiring additional dark matter components. In previous studies, for a selected set of galaxy clusters, we also showed its ability to explain the velocity dispersion in the clusters without extra unseen matter components. This paper primarily explores the mass profiles of galaxy clusters. We test the Machian Gravity acceleration law on two distinct sets comprising galaxy clusters sourced from various studies. We fitted the dynamic mass profiles using the Machian gravity model. The outcomes of our study show good agreement between the theory and observational results.

astro-ph.CO↗

arXiv2023

Inverse transitions and disappearance of the {\lambda}-line in the asymmetric random field Ising and Blume-Capel models

We report on reentrance in the random field Ising and Blume-Capel models, induced by an asymmetric bimodal random field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the {\lambda}-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first order transition lines that always end at ordered critical points. We find that while for symmetric random field distributions there was no reentrance, the asymmetry in the random field results in a range of temperatures for which magnetisation shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first order inverse phase transitions that ends at an inverse ordered critical point. We show that the location of the inverse transitions can be inferred from the ground state phase diagram of the model.

cond-mat.stat-mech↗

arXiv2023

Machian Gravity: Modeling Rotation Curves and Radial Acceleration in the SPARC Galaxy Sample

This paper investigates the potential of Machian Gravity (MG), a five-dimensional theory of gravity, to explain the acceleration law governing rotationally bound systems, in particular spiral galaxies. MG was proposed as a framework capable of accounting for a range of astrophysical and cosmological phenomena -- including galactic rotation curves, mass distributions in galaxy clusters, and cosmic expansion -- without invoking additional dark components. In this study, we apply the MG acceleration law to a large sample of galaxies drawn from the SPARC database. Through a detailed analysis, we determine the optimal MG parameters for each individual galaxy, successfully fitting their observed rotation curves. Similar to Modified Newtonian Dynamics (MOND), our results indicate the existence of a characteristic acceleration scale associated with galactic dynamics, which regulates rotational behavior in the outer regions. Notably, this acceleration scale varies from galaxy to galaxy, but typically remains of order $10^{-8} {\rm cm/s^2}$.

astro-ph.CO↗

arXiv2023

Machian Gravity: A mathematical formulation for Mach's Principle

The general theory of relativity (GR) was proposed with an aim of incorporating Mach's principle mathematically. Despite early hopes, it became evident that GR did not follow Mach's principle. Over time, multiple researchers attempted to develop gravity theories aligned with Machian idea. Although these theories successfully explained various aspects of Mach's principle, each of these theories possessed its own strengths and weaknesses. In this paper, we discuss some of these theories and then try to combine these theories into a single framework that can fully embrace Mach's principle. This new theory, termed Machian Gravity (MG) is a metric-based theory, and can be derived from the action principle, ensuring compliance with all conservation laws. The theory converges to GR at solar system scales, but at larger scales, it diverges from GR and aligns with various modified gravity models proposed to explain dark sectors of the Universe. We have tested our theory against multiple observational data. It explains the galactic rotation curve without requiring additional dark matter (DM). The theory also resolves the discrepancy between dynamic mass and photometric mass in galaxy clusters without resorting to DM, but it introduces two additional parameters. It can also explain the expansion history of the Universe without requiring dark components.

gr-qc↗

arXiv2023

Aspects of Everpresent $\Lambda$ (II): Cosmological Tests of Current Models

This paper investigates Everpresent $\Lambda$, a stochastic dark energy model motivated by causal set theory and unimodular gravity, and confronts it with two key observational data sets, Supernova Ia (SN Ia) and Cosmic Microwave Background (CMB) data. A key feature of this model is that $\Lambda$ fluctuates over time and on average the magnitude of its fluctuations is of the order of the dominant energy density (be it radiation or matter) for the given epoch. In particular, we focus on a phenomenological implementation of Everpresent $\Lambda$ known as Model 1. The random fluctuations in Everpresent $\Lambda$ realizations are generated using seed numbers, and we find that for a small fraction of seeds Model 1 is capable of producing realizations that fit SN Ia data better than $\Lambda$CDM. We further investigate what features distinguish these realizations from the more general behaviour, and find that the "good'' realizations have relatively small fluctuations at low redshifts ($z<1.5$), which do not closely track the matter density. We find that Model 1 struggles to improve on $\Lambda$CDM at describing the CMB data. However, by suppressing the values of $\Lambda$ near the last scattering surface, as suggested in arXiv:1703.06265, we find a large improvement in the best fit of the model, though still with a $\chi^2$ value much larger than that of $\Lambda$CDM. We also study the allowed variation of the dark energy density by the CMB constraints in a more model-independent manner, and find that some variation (especially prior to recombination) is possible and in fact can lead to improvement over $\Lambda$CDM and reduce the Hubble tension, in line with some early dark energy proposals. However, for the kinds of variations considered, the favoured fluctuations are smaller in magnitude than is typical in current Everpresent $\Lambda$ models.

astro-ph.CO↗

arXiv2023

On Geometrization of Spinors in a Complex Spacetime

While general relativity provides a complete geometric theory of gravity, it fails to explain the other three forces of nature, i.e., electromagnetism and weak and strong interactions. We require the quantum field theory (QFT) to explain them. Therefore, in this article, we try to geometrize the spinor fields. We define a parametric coordinate system in the tangent space of a null manifold and show that these parametric coordinates behave as spinors. By introducing a complex internal hyperspace on a tangent space of a null manifold, we show that we can get eight sets of such parametric coordinate systems that can behave as eight spinor fields. These spinor fields contain two triplets that can rotate among themselves under SU(3). Seven of these spinor fields also couple with a U(1) field with different strengths. We also show that while these spinors can be assigned a tensor weight $1/2$ or $-1/2$, in a $L^p$ space where the coordinates, instead of adding up in quadrature, add up in $p$th power, we can get a parametric space that contains similar spinors of tensor weight $1/p$.

gr-qc↗

arXiv2023

Aspects of Everpresent $\Lambda$ (I): A Fluctuating Cosmological Constant from Spacetime Discreteness

We provide a comprehensive discussion of the Everpresent $\Lambda$ cosmological model arising from fundamental principles in causal set theory and unimodular gravity. In this framework the value of the cosmological constant ($\Lambda$) fluctuates, in magnitude and in sign, over cosmic history. At each epoch, $\Lambda$ stays statistically close to the inverse square root of the spacetime volume. Since the latter is of the order of $H^2$ today, this provides a way out of the cosmological constant puzzle without fine tuning. Our discussion includes a review of what is known about the topic as well as new motivations and insights supplementing the original arguments. We also study features of a phenomenological implementation of this model, and investigate the statistics of simulations based on it. Our results show that while the observed values of $H_0$ and $\Omega_\Lambda^0$ are not typical outcomes of the model, they can be achieved through a modest number of simulations. We also confirm some expected features of $\Lambda$ based on this model, such as the fact that it stays statistically close to the value of the total ambient energy density (be it matter or radiation dominated), and that it is likely to change sign roughly every Hubble timescale.

gr-qc↗

arXiv2023

Chirality Reversing Active Brownian Motion in Two Dimensions

We study the dynamics of a chirality reversing active Brownian particle, which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two time-scales set by the chirality reversing rate $γ$ and rotational diffusion constant $D_R$ gives rise to four dynamical regimes, namely, (I) $t \ll \text{min}(γ^{-1}, D_R^{-1})$, (II) $γ^{-1} \ll t \ll D_R^{-1}$, (III) $D_R^{-1} \ll t \ll γ^{-1}$ and (IV) $t \gg \text{max}(γ^{-1}, D_R^{-1})$, each showing different behaviour. The short-time regime (I) is characterized by a strongly anisotropic and non-Gaussian position distribution, which crosses over to a diffusive Gaussian behaviour in the long-time regime (IV) via an intermediate regime (II) or (III), depending on the relative strength of $γ$ and $D_R$. In regime (II), the chirality reversing active Brownian motion reduces to that of an ordinary active Brownian particle, with an effective rotation diffusion coefficient which depends on the angular velocity. Finally, we find that, the regime (III) is characterized by an effective chiral active Brownian motion.

cond-mat.stat-mech↗

arXiv2022

The Tianlai dish array low-z surveys forecasts

We present the science case for surveys with the Tianlai dish array interferometer tuned to the $\left[ 1300, 1400 \right] \mathrm{MHz}$ frequency range. Starting from a realistic generation of mock visibility data according to the survey strategy, we reconstruct a map of the sky and perform a foreground subtraction. We show that a survey of the North Celestial Polar cap during a year of observing time and covering an area of $150 \, \mathrm{deg^2}$ would reach a sensitivity of $ 1.5-2 \, \mathrm{mK} $ per $1 \, \mathrm{MHz} \times 0.25^2 \, \mathrm{deg^2 }$ voxel and be marginally impacted by mode-mixing. Tianlai would be able to detect a handful $(\sim 10)$ of nearby massive \HI clumps as well as a very strong cross-correlation signal of 21\,cm intensity maps with the North Celestial Cap Survey optical galaxies. We have also studied the performance of a mid-latitude survey, covering $\sim 1500 \, \mathrm{deg^2}$ centered on a declination of $δ=55^\circ$, which overlaps the Sloan Digital Sky Survey footprint. Despite a higher noise level for the mid-latitude survey, as well as significant distortions due to mode mixing, Tianlai would be able to detect a highly significant cross-correlation between the 21\,cm signal and the Sloan spectroscopic galaxy sample. Using the extragalactic signals from either or both of these surveys, it will be possible to assess the impact of calibration uncertainties, antenna pattern uncertainties, sources of noise, and mode mixing for future surveys requiring higher sensitivity.

astro-ph.CO↗