arXiv subjects

Prashant Singh

Publications and source records attributed to Prashant Singh.

At least 19 recordsLinked to original sources

arXiv2026

Critical initialization destabilizes higher input derivatives in wide scalar-input networks

The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.

stat.ML↗

arXiv2026

What Fixed-Rollout pass@k Evaluations Can Identify

Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k <= n, but generic extrapolated pass@k, tail exponents, and tail constants are not identified for k > n, even with arbitrarily many exchangeable tasks at the same rollout budget. This is stronger than the observation that the usual estimator is undefined beyond n: it characterizes the information missing from the fixed-depth count-law experiment. We give exact count-law-preserving constructions with incompatible extrapolations, state the exceptional unique-extension case, and compute sharp population identified intervals through Hausdorff principal representations. On the public 10,000-rollout-per-problem release of Brown et al., counterfactual n = 16 evaluations leave failure at k = 1000 ambiguous by factors from 1.5 to over 2,600 across four MATH/GSM8K/CodeContests configurations. The calibration shows that intermediate-scale failure share alone does not determine width. Our result does not reject parametric inference-time scaling laws; it supplies the nonparametric baseline against which their assumptions can be evaluated. We give an exact, conservative one-coordinate finite-task confidence certificate and a reporting standard separating direct estimates, identified sets, and model-conditioned forecasts.

stat.ML↗

arXiv2026

Breakdown of Anomalous Hall Scaling in Dilute Kondo System

The confluence of strong electronic correlations and Berry curvature-driven transport constitutes a largely underexplored frontier in quantum materials research, particularly in systems where electronic correlations arise from flat-band physics rather than conventional $f$-electron states. Here, we report an intrinsic Berry curvature driven anomalous Hall transport in the dilute Kondo system Ru$_2$Mn$_{0.5}$Ti$_{0.5}$Ge, a non-$f$-electron Heusler alloy hosting flat bands with van Hove singularity proximate to the Fermi level. The anomalous Hall response is strikingly non-monotonic, violating the Fermi-liquid scaling relation near the magnetic transition and is restored only at low temperature, coincident with the onset of Kondo coherence. \textit{Ab initio} calculations strongly establish that the Berry curvature originates from the Kondo hybridization induced interplay of flat bands and spin-orbit coupling mediated anticrossings at the Fermi level. Our findings demonstrate that Kondo coherence of flat bands bears a profound impact on Berry curvature associated ferroic responses, mandating a rigorous theoretical understanding of anomalous transport in the regime where reciprocal space topology and strong correlations are intrinsically intertwined.

cond-mat.str-el↗

arXiv2026

Squeeze-Release: Iterative Pruning with Exact Structural Minimization

Unstructured pruning produces sparse weight tensors, but the standard implementation keeps tensor shapes unchanged so the deployed model is no smaller than before pruning. We present an exact structural rewrite, which we call minimization, that converts a masked network into a smaller dense network with the same forward function up to floating-point rounding. The Squeeze-Release cycle iterates pruning and minimization with an intermediate release step that re-enables the exact-zero positions inside the compacted tensors as small calibrated noise, turning otherwise wasted capacity back into trainable parameters. Successive cycles use that capacity to find structural redundancy a single pass cannot reach. We additionally introduce CompensatedLayerNorm, a function-preserving replacement for LayerNorm that extends minimization to channel reduction across LayerNorm-equipped residual streams. Squeeze-Release compresses the deployable network to 39x smaller than the unpruned model on a fully-connected model network and 14.8x smaller on modern CNN (ConvNeXt-Tiny), at comparable accuracy. In addition we prove that the rewrite can be extended to transformer architectures.

cs.LG↗

arXiv2026

GeoFlowVLM: Geometry-Aware Joint Uncertainty for Frozen Vision-Language Embedding

Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support). Existing post-hoc methods either recover at most one of the two uncertainty components, or ignore the hyperspherical geometry of these models' embeddings. We propose \textbf{GeoFlowVLM} as a post-hoc adapter that learns the joint distribution of paired $\ell_2$-normalised dual-encoder VLM embeddings on the product hypersphere $\mathbb{S}^{d-1} \times \mathbb{S}^{d-1}$ via Riemannian flow matching with a single masked velocity field. A consistency result shows that, in the population limit, the trained network exposes the joint flow and both cross-modal conditional flows as valid Riemannian flow-matching velocity fields on their respective domains. We derive two quantities from this single model: a conditional retrieval entropy that quantifies aleatoric ambiguity with a decision-theoretic interpretation via a Fano-type bound, and a marginal-typicality epistemic score justified by an exact chain-rule decomposition of the joint NLL. This decomposition isolates a cross-modal pointwise-mutual-information term that is structurally discriminative rather than epistemic, and is empirically the only consistently uninformative standalone component. Empirically, the entropy tracks Recall@1 with near-ideal monotonic calibration across three retrieval benchmarks in both directions, and the marginal-typicality sum yields consistently calibrated selective accuracy across four zero-shot classification benchmarks.

cs.LG↗

arXiv2026

Disagreement-Regularized Importance Sampling for Adversarial Label Corruption

Standard Importance Sampling (IS) collapses under label corruption because high-norm examples, prioritized for variance reduction, are often adversarial outliers. We formalize this misalignment using an $\varepsilon$-contamination model and propose Disagreement-Regularized Importance Sampling (DR-IS), a sub-sampling method based on loss rank-disagreement across independent proxy ensemble. We prove finite-sample concentration bounds showing that the empirical rank disagreement of bulk corrupted examples is bounded above, and that of boundary-clean examples bounded below, both at rate $O(\sqrt{\log(N/\delta)/K})$ with probability $1-\delta$; when the structural expectation gap $\Delta'$ between the two groups is positive and the boundary-clean set is at least as large as the selected subset, these bounds certify strict separation and control the contamination rate of the selected subset. Empirically, DR-IS remains robust under targeted high-norm attacks that break magnitude-based methods such as the Error $L_2$-norm (EL2N) on benchmark datasets. DR-IS complements training-dynamics approaches like Area Under the Margin ranking (AUM), offering improved robustness in the loss-aligned regime alongside explicit finite-sample concentration certificates and a contamination bound limiting noise leakage from the statistical tail of corrupted points.

cs.LG↗

arXiv2026

Insights into hydrogen-induced vacancy stability and creep in chemically complex alloys

Hydrogen (H) content modifies the creep response of Fe-based alloys by altering thermodynamics of point-defects; here we identify the electronic-structure mechanism underlying this effect. Using spin-polarized first-principles calculations combined with a cluster dynamics formulation, we establish a general framework linking H-assisted vacancy stabilization to diffusion-mediated creep in BCC Fe, FCC Fe, and chemically complex FCC Fe-Cr-Ni alloys. H-vacancy binding analysis shows that H-stabilized vacancies form at low hydrogen content in BCC Fe but require much higher chemical potentials in FCC Fe and Fe-Cr-Ni alloys due to broader d-bands, electronic screening, and chemical disorder. Consequently, plastic deformation mediated by diffusive processes is expected to be far more strongly impacted in BCC Fe than in FCC alloys. These electronic-controlled trends determine steady-state vacancy populations and provide a symmetry-resolved microscopic basis for H-assisted creep in ferritic and austenitic steels.

cond-mat.mtrl-sci↗

arXiv2026

Sokoban Random Walk: A Trapping Perspective

We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\rm P}$ number of obstacles. For $N_{\rm P}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\rm P}$. The long-time exponent matches the Balagurov--Vaks--Donsker--Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $\rho$: it is small at both low and high densities, but reaches a peak at a characteristic density $\rho_*$. We estimate $\rho_* \approx 0.55$ for the Sokoban model and $\rho_* \approx 0.675$ for the generalized Sokoban model.

cond-mat.stat-mech↗

arXiv2026

OneFlowSBI: One Model, Many Queries for Simulation-Based Inference

We introduce \textit{OneFlowSBI}, a unified framework for simulation-based inference that learns a single flow-matching generative model over the joint distribution of parameters and observations. Leveraging a query-aware masking distribution during training, the same model supports multiple inference tasks, including posterior sampling, likelihood estimation, and arbitrary conditional distributions, without task-specific retraining. We evaluate \textit{OneFlowSBI} on ten benchmark inference problems and two high-dimensional real-world inverse problems across multiple simulation budgets. \textit{OneFlowSBI} is shown to deliver competitive performance against state-of-the-art generalized inference solvers and specialized posterior estimators, while enabling efficient sampling with few ODE integration steps and remaining robust under noisy and partially observed data.

stat.ML↗

arXiv2026

Epistemic Uncertainty Quantification for Pre-trained VLMs via Riemannian Flow Matching

Vision-Language Models (VLMs) are typically deterministic in nature and lack intrinsic mechanisms to quantify epistemic uncertainty, which reflects the model's lack of knowledge or ignorance of its own representations. We theoretically motivate negative log-density of an embedding as a proxy for the epistemic uncertainty, where low-density regions signify model ignorance. The proposed method REPVLM computes the probability density on the hyperspherical manifold of the VLM embeddings using Riemannian Flow Matching. We empirically demonstrate that REPVLM achieves near-perfect correlation between uncertainty and prediction error, significantly outperforming existing baselines. Beyond classification, we also demonstrate that the model also provides a scalable metric for out-of-distribution detection and automated data curation.

cs.LG↗

arXiv2026

Transition in Splitting Probabilities of Quantum Walks

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. For large systems and sampling times smaller than a critical value $\tau_c = 2\pi/\Delta E$, where $\Delta E$ is the energy bandwidth, the splitting probability is universal and equal to $1/2$, independent of the initial condition and the sampling time. Above the critical sampling time, a nonuniversal regime emerges in which the splitting probability deviates from $1/2$ and develops a fluctuating pattern of pronounced peaks and dips dependent on both the sampling time and the initial condition. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle.

cond-mat.stat-mech↗

arXiv2025

From Complex Magnetic Ground States to Magnetocaloric Effects: A Review of Rare Earth R$_2$In Intermetallic Compounds

R2In (R = rare earth) intermetallics exhibit unusual magnetic and magnetocaloric properties, driven by subtle electronic effects, lattice distortions, and spin-lattice coupling. Most of these binary compounds adopt the hexagonal Ni2In-type structure at room temperature, with Eu2In and Yb2In stabilizing in the orthorhombic Co2Si-type lattice. Lighter lanthanide compounds Eu2In, Nd2In, and Pr2In undergo first-order magnetic transitions with negligible hysteresis and minimal lattice volume change and exhibit giant cryogenic magnetocaloric effects, while heavy lanthanide R2In compounds including Gd2In show second-order transitions with moderate magnetocaloric effect. No lanthanide-based R2In compound exhibits symmetry-breaking structural transition, while Y2In transforms from hexagonal to orthorhombic structure near 250 K. Secondary low-temperature transitions, including spin reorientation or antiferromagnetic ordering, further enrich the magnetic phase landscape in these compounds. Integrating theoretical descriptors such as charge-induced strain and electronic structure provides predictive insight into phase stability and magnetocaloric performance, guiding the design of rare-earth intermetallics with tunable magnetic properties for cryogenic applications

cond-mat.mtrl-sci↗

arXiv2025

Sokoban Random Walk: From Environment Reshaping to Trapping Crossover

We study the dynamics of a Sokoban random walker moving in a disordered medium with obstacle density $\rho$. In contrast to the classic model of de Gennes with static obstacles that exhibits a percolation transition, the Sokoban walker is capable of modifying its environment by pushing a few surrounding obstacles. Surprisingly, even a limited pushing ability leads to a loss of the percolation transition. Through a combination of a rigorous large-deviation calculation and extensive numerical simulations, we demonstrate that the Sokoban model belongs to the Balagurov-Vaks-Donsker-Varadhan trapping universality class. The survival probability that the walker has not yet been trapped inside a cage exhibits stretched-exponential relaxation at late times. Furthermore, using the average trap size as a proxy, we identify the emergence of a dynamical crossover at a density $\rho_* \approx 0.55$ between two qualitatively different trapping mechanisms: a self-trapping mechanism at low density, where the walker becomes dynamically localized within a self-formed trap, and a pre-existing trapping mechanism at high density, where confinement arises from the initial arrangement of obstacles. This crossover is responsible for the loss of the classical percolation transition.

cond-mat.stat-mech↗

arXiv2025

Doping Induced Magnetic and Electronic phase Transition in Ferrimagnetic Half-metallic Mn$_{4}$Al$_{11}$ Compound

The future of spintronic and semiconductor applications demands materials with tailored electronic and magnetic properties. This study uses density functional theory to investigate the electronic structure of the half-metallic compound Mn$_{4}$Al$_{11}$ under uniaxial strain and in its Ge-substituted derivatives. Strain analysis shows that although the half-metallic band-gap collapses under strain beyond $-2\%$, the ferrimagnetic character remains stable. Ge substitution at six inequivalent Al-sites in Mn$_{4}$Al$_{11}$ results in varying degrees of metallicity and magnetic properties. Substitution at Al$=(000)$ induces a metal-to-insulator transition with an indirect semiconducting gap of $0.14~ eV$. Bonding and hybridization analysis reveals that local Mn-Al interactions due to Ge substitution significantly modify the local electronic structure, causing both electronic and magnetic phase transitions. This work highlights the effectiveness of substitutional doping in tuning half-metallicity and magnetic properties in inorganic solids, enabling the design of materials for future technological applications.

cond-mat.mtrl-sci↗

arXiv2025

Exploiting the Asymmetric Uncertainty Structure of Pre-trained VLMs on the Unit Hypersphere

Vision-language models (VLMs) as foundation models have significantly enhanced performance across a wide range of visual and textual tasks, without requiring large-scale training from scratch for downstream tasks. However, these deterministic VLMs fail to capture the inherent ambiguity and uncertainty in natural language and visual data. Recent probabilistic post-hoc adaptation methods address this by mapping deterministic embeddings onto probability distributions; however, existing approaches do not account for the asymmetric uncertainty structure of the modalities, and the constraint that meaningful deterministic embeddings reside on a unit hypersphere, potentially leading to suboptimal performance. In this paper, we address the asymmetric uncertainty structure inherent in textual and visual data, and propose AsymVLM to build probabilistic embeddings from pre-trained VLMs on the unit hypersphere, enabling uncertainty quantification. We validate the effectiveness of the probabilistic embeddings on established benchmarks, and present comprehensive ablation studies demonstrating the inherent nature of asymmetry in the uncertainty structure of textual and visual data.

cs.LG↗

arXiv2025

ConDiSim: Conditional Diffusion Models for Simulation Based Inference

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions, consisting of a forward process that adds Gaussian noise to parameters, and a reverse process learning to denoise, conditioned on observed data. This approach effectively captures complex dependencies and multi-modalities within posteriors. ConDiSim is evaluated across ten benchmark problems and two real-world test problems, where it demonstrates effective posterior approximation accuracy while maintaining computational efficiency and stability in model training. ConDiSim offers a robust and extensible framework for simulation-based inference, particularly suitable for parameter inference workflows requiring fast inference methods.

cs.LG↗

arXiv2025

Bayesian Robust Aggregation for Federated Learning

Federated Learning enables collaborative training of machine learning models on decentralized data. This scheme, however, is vulnerable to adversarial attacks, when some of the clients submit corrupted model updates. In real-world scenarios, the total number of compromised clients is typically unknown, with the extent of attacks potentially varying over time. To address these challenges, we propose an adaptive approach for robust aggregation of model updates based on Bayesian inference. The mean update is defined by the maximum of the likelihood marginalized over probabilities of each client to be `honest'. As a result, the method shares the simplicity of the classical average estimators (e.g., sample mean or geometric median), being independent of the number of compromised clients. At the same time, it is as effective against attacks as methods specifically tailored to Federated Learning, such as Krum. We compare our approach with other aggregation schemes in federated setting on three benchmark image classification data sets. The proposed method consistently achieves state-of-the-art performance across various attack types with static and varying number of malicious clients.

cs.LG↗

arXiv2025

Fermi surface nesting driven anomalous Hall effect in magnetically frustrated Mn_2PdIn

Noncollinear magnets with near-zero net magnetization and nontrivial bulk electronic topology hold significant promise for spintronic applications, though their scarcity necessitates purposeful design strategies. In this work, we report a topologically nontrivial electronic structure in metallic Mn_2PdIn, which crystallizes in the inverse Heusler structure and exhibits a spin-glassy ground state with quenched magnetization. The system features Weyl-type band crossings near the Fermi level and reveals a novel interplay among momentum-space nesting, orbital hybridization, and spin-orbit coupling. Comprehensive transport measurements uncover a pronounced anomalous Hall effect (AHE) in Mn_2PdIn. The observed quadratic relationship between the longitudinal and anomalous Hall resistivities highlights the intrinsic Berry curvature contribution to AHE. These findings establish inverse Heusler alloys as compelling platforms for realizing noncollinear magnets that host Weyl-type semimetallic or metallic phases-combining suppressed magnetization with robust electronic transport-thereby offering a promising route toward their seamless integration into next-generation spintronic devices.

cond-mat.mtrl-sci↗