arXiv subjects

Md Shahriar Rahim Siddiqui

Publications and source records attributed to Md Shahriar Rahim Siddiqui.

9 recordsLinked to original sources

arXiv2026

Preconditioned Flow Matching

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $Σ_t$ of $p_t$ is ill-conditioned, gradient-based training rapidly fits high-variance directions while making slow progress along low-variance ones. In an exactly solvable Gaussian setting, we prove that the excess risk is weighted by $Σ_t$, and that both gradient descent and stochastic gradient descent inherit condition-number-dependent convergence. We then extend the analysis to Gaussian mixtures, showing that multimodality does not average away this effect; instead, the slowest and worst-conditioned component can control optimization. Motivated by this analysis, we propose \emph{preconditioned flow matching}, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning. Across controlled Gaussian and Gaussian-mixture experiments, latent MNIST and other high resolution image datasets up to $512{\times}512$ resolution, preconditioning improves path-conditioning diagnostics, low-eigenvalue recovery, FID, MMD, precision, and recall. Compute-matched baselines and preconditioner-quality ablations further show that the gains are not explained merely by additional preconditioner parameters, but by improved geometry of the downstream flow matching problem.

cs.LG↗

arXiv2026

Conservative Flows: A New Paradigm of Generative Models

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

cs.LG↗

arXiv2025

Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fields

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fréchet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at $256\times256$), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

cs.LG↗

arXiv2025

Learning Regularization for Graph Inverse Problems

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph directly; instead, noisy and indirect measurements of these properties are available. These scenarios are coined as Graph Inverse Problems (GRIP). In this work, we introduce a framework leveraging GNNs to solve GRIPs. The framework is based on a combination of likelihood and prior terms, which are used to find a solution that fits the data while adhering to learned prior information. Specifically, we propose to combine recent deep learning techniques that were developed for inverse problems, together with GNN architectures, to formulate and solve GRIP. We study our approach on a number of representative problems that demonstrate the effectiveness of the framework.

cs.LG↗

arXiv2024

Deep Optimal Experimental Design for Parameter Estimation Problems

Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.

stat.ML↗

arXiv2022

X-ray annual modulation observed by XMM-Newton and Axion Quark Nugget Dark Matter

The XMM-Newton observatory shows evidence, with a 11$σ$ confidence level, for seasonal variation of the X-ray background in the near-Earth environment in the 2-6 keV energy range (Fraser et al. 2014). The authors argue that the observed seasonal variation suggests a possible link with dark matter. We propose an explanation which involves the Axion Quark Nugget (AQN) dark matter model. In our proposal, AQNs can cross the Earth and emit high energy photons at their exit. We show that the emitted spectrum is consistent with (Fraser et al. 2014), and that our calculation is not sensitive to the specific details of the model. Our proposal predicts a large seasonal variation, on the level of 20-25%, much larger than conventional dark matter models (1-10%). Since the AQN emission spectrum extends up to $\sim $ 100 keV, well beyond the keV sensitivity of XMM-Newton, we predict the AQN contribution to the hard X-ray and $γ$-ray backgrounds in the Earth's environment. The Gamma-Ray Burst Monitor (GBM) instrument, aboard the FERMI telescope, is sensitive to the 8 keV-40 MeV energy band. The NuSTAR (Nuclear Spectroscopic Telescope Array) is a NASA space based X ray telescope which operates in the range 3 to 79 keV is also sensitive to higher energy bands. We suggest that the multi-year archival data from the GBM or NuSTAR could be used to search for a seasonal variation in the near-Earth environment up to 100 keV as a future test of the AQN framework.

astro-ph.HE↗

arXiv2020

Radio impulsive events in quiet solar corona and Axion Quark Nugget Dark Matter

The Murchison Widefield Array (MWA) recorded \cite{Mondal-2020} impulsive radio events in the quiet solar corona at frequencies 98, 120, 132, and 160 MHz. We propose that these radio events are the direct manifestation of dark matter annihilation events within the axion quark nugget (AQN) framework. It has been argued \cite{Zhitnitsky:2017rop,Raza:2018gpb} that the AQN annihilation events in the quiet solar corona can be identified with the nanoflares conjectured by Parker \cite{Parker-1983}. We further support this claim by demonstrating that observed impulsive radio events \cite{Mondal-2020}, including their rate of appearance, their temporal and spatial distributions and their energetics, are matching the generic consequences of AQN annihilations in the quiet corona. We propose to test this idea by analyzing the correlated clustering of impulsive radio events in different frequency bands. These correlations are expressed in terms of the time delays between radio events in different frequency bands, measured in seconds. We also make generic predictions for low (80 and 89 MHz) and high (179, 196, 217 and 240 MHz) frequency bands, that have been recorded, but not published, by \cite{Mondal-2020}. We finally suggest to test our proposal by studying possible cross-correlation between MWA radio signals and Solar Orbiter recording of extreme UV photons (a.k.a. "campfires").

astro-ph.HE↗

arXiv2020

Axion Quark Nugget Dark Matter: Time Modulations and Amplifications

We study the new mechanism of the axion production suggested recently in [1,2]. This mechanism is based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented to explain the similarity of the dark and visible cosmological matter densities. We perform numerical simulations to evaluate the axion flux on the Earth's surface. We examine annual and daily modulations, which have been studied previously and are known to occur for any type of dark matter. We also discuss a novel type of short time enhancements which are unique to the AQN model: the statistical fluctuations and burst-like amplification, both of which can drastically amplify the axion signal, up to a factor $\sim10^2-10^3$ for a very short period of time. The present work studies the AQN-induced axions within the mass window $10^{-6}{\rm\,eV}\lesssim m_a\lesssim10^{-3}\rm\,eV$ with typical velocities $\langle v_a\rangle\sim0.6c$. We also comment on the broadband detection strategy to search for such relativistic axions by studying the daily and annual time modulations as well as random burst-like amplifications.

astro-ph.CO↗

arXiv2019

Gravitationally trapped axions on Earth

We advocate for the idea that there is a fundamentally new mechanism for axion production on Earth, as recently suggested in Fischer et al. (2018) and Liang & Zhitnitsky (2018). We specifically focus on production of axions within Earth, with low velocities such that they will be trapped in the gravitational field. Our computations are based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented to explain the similarity of the dark and visible cosmological matter densities. This occurs in the model irrespective of the axion mass $m_\mathrm{a}$ or initial misalignment angle $θ_0$. Annihilation of antimatter AQNs with visible matter inevitably produce axions when AQNs hit Earth. The emission rate of axions with velocities below escape velocity is very tiny compared to the overall emission, however these axions will be accumulated over the 4.5 billion year life time of the Earth, which greatly enhances the discovery potential. We perform numerical simulations with a realistically modeled incoming AQN velocity and mass distribution, and explore how AQNs interact as they travel through the interior of the Earth. We use this to estimate the axion flux on the surface of the Earth, the velocity-spectral features of trapped axions, the typical annihilation pattern of AQN, and the density profile of the axion halo around the Earth. Knowledge of these properties is necessary to make predictions for the observability of trapped axions using CAST, ADMX, MADMAX, CULTASK, ORPHEUS, ARIADNE, CASPEr, ABRACADABRA, QUAX, DM Radio.

astro-ph.CO↗