arXiv subjects

Vedanta Thapar

Publications and source records attributed to Vedanta Thapar.

5 recordsLinked to original sources

arXiv2026

Parameter-Level Attribution of Symmetry in Trained Networks Though Parameter-Wise Functional Sensitivity

When a network has learned a function with a known symmetry, can that symmetry be moved through the parametrisation---is there a motion in parameter space realising the group action in function space? We formulate this as a lifting problem for the realisation map $\Phi:\theta\mapsto f_\theta$, and show that a smooth parameter-space action exists only if the tangent space to the function's symmetry orbit lies within the image of $\mathrm d\Phi_\theta$, whose columns are the \emph{functional sensitivities} of individual parameters. This condition is also sufficient for pointwise first-order lifting. Relaxing it in least squares yields two local parameter directions: one following the symmetry orbit, one descending towards the equivariant subspace, with residuals measuring what the parametrisation cannot reach. On a rotationally invariant classifier we find these directions induce their predicted function-space motion, but only locally: recomputed directions track the orbit and reduce the equivariance defect, while directions held fixed depart from both after training. The same holds for Hamiltonian neural networks trained on a rotationally symmetric potential, even though the architecture does not explicitly enforce the symmetry.

cs.LG↗

arXiv2026

Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we address the problem of learning symbolic representations of nonlinear Hamiltonian dynamical systems under extreme data scarcity by explicitly incorporating physical structure into the learning architecture. We introduce Adaptable Symplectic Recurrent Neural Networks (ASRNNs), a parameter-cognizant, structure-preserving model that combines Hamiltonian learning with symplectic recurrent integration, avoiding time derivative estimation, and enabling stable learning under noise. We demonstrate that ASRNNs can accurately predict long-term dynamics even when each training trajectory consists of only two irregularly spaced time points, possibly corrupted by correlated noise. Leveraging ASRNNs as structure-preserving data generators, we further enable symbolic discovery using independent regression methods (SINDy and PySR), recovering exact symbolic equations for polynomial systems and consistent polynomial approximations for non-polynomial Hamiltonians. Our results show that such architectures can provide a robust pathway to interpretable discovery of Hamiltonian dynamics from sparse and noisy data.

cs.LG↗

arXiv2025

Embedding networks with the random walk first return time distribution

We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any pair of nodes using standard metrics for discrete distributions. We present several arguments to motivate the FRTD embedding. First, we show that FRTDs are strictly more informative than eigenvalue spectra, yet insufficient for complete graph identification, thus placing FRTD equivalence between cospectrality and isomorphism. Second, we argue that FRTD equivalence between nodes captures structural similarity. Third, we empirically demonstrate that the FRTD embedding outperforms manually designed graph metrics in network alignment tasks. Finally, we show that random networks that approximately match the FRTD of a desired target also preserve other salient features. Together these results demonstrate the FRTD as a simple and mathematically principled embedding for complex networks.

cs.SI↗

arXiv2023

Applications of Machine Learning to Modelling and Analysing Dynamical Systems

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network structures into Adaptable Symplectic Recurrent Neural Networks which preserve Hamilton's equations as well as the symplectic structure of phase space while predicting dynamics for the entire parameter space. This architecture is found to significantly outperform previously proposed neural networks when predicting Hamiltonian dynamics especially in potentials which contain multiple parameters. We demonstrate its robustness using the nonlinear Henon-Heiles potential under chaotic, quasiperiodic and periodic conditions. The second problem we tackle is whether we can use the high dimensional nonlinear capabilities of neural networks to predict the dynamics of a Hamiltonian system given only partial information of the same. Hence we attempt to take advantage of Long Short Term Memory networks to implement Takens' embedding theorem and construct a delay embedding of the system followed by mapping the topologically invariant attractor to the true form. This architecture is then layered with Adaptable Symplectic nets to allow for predictions which preserve the structure of Hamilton's equations. We show that this method works efficiently for single parameter potentials and provides accurate predictions even over long periods of time.

cs.LG↗

arXiv2023

Examining Temporal Variation of the Fermi Coupling Constant using SNe Ia Light Curves

In standard model, the Fermi coupling constant, $G_F$, sets the strength of electroweak decay. We attempt an approach to constrain the temporal variation of the Fermi coupling constant $G_F$. To probe it, Type Ia supernovae (SNe Ia) light curves are being used as a source of reliable primordial nucleosynthesis events across the redshifts. We utilized studies suggesting that in the initial phase after the SNe Ia explosion, the electroweak decay of $^{56}Ni \rightarrow ^{56}Co \rightarrow ^{56}Fe$ is the key contributor to powering the SNe Ia light curve. We hence used the Pan-STARRS supernovae catalog having 1169 supernovae light curves in $g$, $r$, $i$, and $z$ spectral filters. The post-peak decrease in the apparent magnitude of light curves (in the rest frame of SNe) was related to the electroweak decay rate of primordial nucleosynthesis. Further, the decay rate relates to $G_F$. To keep the analysis independent of the cosmological model, we used the Hubble parameter measurement and a non-parametric statistical method, the Gaussian Process. Our study suggests a small yet finite temporal variation of $G_F$ and puts a strong upper bound on the present value of the fractional change in the Fermi coupling constant i.e; $\dfrac{\dot G_F}{G_F}\big\rvert_{z=0} \approx 10^{-11} yr^{-1}$ using datasets spread over a redshift range $0<z<0.75$.

astro-ph.CO↗