arXiv subjects

Asadullah Bhuiyan

Publications and source records attributed to Asadullah Bhuiyan.

6 recordsLinked to original sources

arXiv2026

Learning from almost nothing: How neural networks survive heavy input corruption

Learning from imperfect data is a central theme in machine learning, connecting practical questions of robustness to fundamental questions of learnability. Here we examine attribute noise: learning from corrupted inputs while keeping the labels intact, a setting that has received considerably less analytical attention than its label-noise counterpart. We consider two types of corruption models: additive noise and replacement noise. Through experiments with multi-layer perceptrons (MLPs) on corrupted classification datasets, we find that neural networks remain robust, maintaining well-above-chance accuracy even when inputs are >90% corrupted -- far beyond human recognition. To understand this robustness, we analyze infinite-width networks in the heavy-corruption regime using a mean-field-inspired approach and derive a leading-order decision rule for the classification outcome: the network implements a prototype rule, the nearest-class-mean, assigning each test point to the class whose training-set average it most closely resembles. This leading-order decision rule is universal across a broad range of MLP architectures, holding for any depth, as well as a wide class of activation functions and noise distributions. The same centroid mechanism closely matches finite-width network behavior in our experiments and provides an interpretable and analytically tractable account of why learning can succeed even when individual training examples carry almost no signal.

cs.LG↗

arXiv2025

Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States

We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We introduce two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and naturally extends to interacting dynamics, and (2) the single-particle transfer matrix (sTM) symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, we show that these two frameworks are equivalent via a novel dynamical bulk-boundary correspondence: the topology of the dynamical system's spacetime bulk determines the topology of the area-law entangled steady-state ensemble living on its temporal boundary. Next, we prove that symmetry-invariant, post-selection-free Gaussian measurements are realizable in only four of the ten mEO classes (A, AI, BDI, D); the remaining six require either post-selection or interacting (non-Gaussian) measurements. Building on these results, we construct general post-selection-free topological adaptive circuits that realize topological dynamical phases in any spatial dimension for the four admissible mEO classes. These circuits simultaneously provide a protocol for preparing and stabilizing free-fermion topological states in all ten symmetry classes. As a concrete demonstration, we construct and simulate 2+1d adaptive circuits that realize mEO-class-A topological dynamics, steering toward a steady-state ensemble of Chern insulators in ${\cal O}(1)$ circuit depth. Finally, we numerically characterize topological phase transitions, dynamical domain-wall modes, and robustness to coherent noise, identifying finite error thresholds at which trajectory-resolved and trajectory-averaged quantities undergo distinct phase transitions.

quant-ph↗

arXiv2021

The bound-state solutions of the one-dimensional pseudoharmonic oscillator

We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $α$. The singular form of this potential has doubly-degenerate bound states for $-1/4\leqα<0$ and $α>0$; since the potential is symmetric, these consist of even and odd-parity states. In addition we consider a regularized form of this potential with a constant cutoff near the origin. For this regularized potential, there are also even and odd-parity eigenfunctions for $α\geq-1/4$. For attractive potentials within the range $-1/4\leqα<0$, there is an even-parity ground state with increasingly negative energy and a probability density that approaches a Dirac delta function as the cutoff parameter becomes zero. These properties are analogous to a similar ground state present in the regularized one-dimensional hydrogen atom. We solve this problem both analytically and numerically, and show how the regularized excited states approach their unregularized counterparts.

quant-ph↗

arXiv2020

Edge Localized Schrödinger Cat States in Finite Lattices via Periodic Driving

Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model, or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic systems in one dimension. A number of these studies have focused on finite systems, and results from these studies are distinct from those of infinite lattice systems as a consequence of boundary effects. In the case of a finite system, there remains a discrepancy in the results between tight-binding descriptions and continuous lattice models. Periodic driving by a time-dependent field in tight-binding models results in a collapse of all quasienergies within a band at special driving amplitudes. In the continuum model, on the other hand, a pair of nearly-degenerate edge bands emerge and remain gapped from the bulk bands as the field amplitude increases. We resolve these discrepancies and explain how these edge bands represent Schrödinger cat-like states with effective tunneling across the entire lattice. Moreover, we show that these extended cat-like states become perfectly localized at the edge sites when the external driving amplitude induces a collapse of the bulk bands.

cond-mat.mes-hall↗

arXiv2020

Landau Levels and the Issue of Gauge Invariance in Confined Spaces

We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to produce sensible results. We treat both circular and square geometries, and in the latter we explicitly demonstrate the gauge invariance of the energy levels and wave function amplitudes. Both bulk states and edge states are examined, and in the latter case, with sufficiently high quantum numbers we achieve significant differences in the square and circular geometries. Results are achieved using straightforward matrix mechanics, in a manner that is accessible to novices in the field.

cond-mat.mes-hall↗

arXiv2019

On the capacitive properties of individual microtubules and their meshworks

Microtubules are hollow cylindrical polymers composed of the highly negatively-charged (~23e), high dipole moment (1750 D) protein a,b-tubulin. While the roles of microtubules in chromosomal segregation, macromolecular transport and cell migration are relatively well-understood, studies on the electrical properties of microtubules have only recently gained strong interest. Here, we show that while microtubules at physiological concentrations increase solution capacitance, free tubulin has no appreciable effect. For a particular microtubule concentration, we were able to quantify these effects by determining the capacitance and resistance of a single 20 um-long microtubule to be 1.86 x 10^(-12) F and 1.07 x 10^12 Ohms respectively. Further, we observed a decrease in electrical resistance of solution, with charge transport peaking between 20-60 Hz in the presence of microtubules, consistent with recent findings that microtubules exhibit electric oscillations at such low frequencies. Our results show that in addition to macromolecular transport, microtubules also act as charge-storage devices through counterionic condensation across a broad frequency spectrum. We conclude with a hypothesis of an electrically-tunable cytoskeleton where the dielectric properties of tubulin are polymerization-state dependent.

physics.bio-ph↗