arXiv subjects

Kanishka Reddy

Publications and source records attributed to Kanishka Reddy.

3 recordsLinked to original sources

arXiv2026

Diffusion Operator Geometry of Feedforward Representations

Feedforward neural networks transform data through learned representations whose geometry shapes how classes separate and relate across successive layers. We study that geometry through diffusion operators. Each feature-cloud snapshot is assigned a Gaussian-kernel Markov operator, giving a smooth description of one-step transport between classes from which spectral, boundary, and local geometric information can be read. We define the empirical class chain, state the condition under which it is an exact Markov quotient, and derive both the corresponding population transition and a simpler overlap chain based on expected class affinities. For balanced shared-covariance Gaussian class-conditional snapshots these affinities have closed forms controlled by a regularized Mahalanobis separation, which yields explicit expressions for leakage and coarse spectral behaviour. We further show that operator observables vary smoothly under feature perturbations, whereas hard neighborhood graphs are controlled by neighbor-order margins. Experiments on CIFAR-10 and CIFAR-100 ResNet-18 representations find that class transport becomes increasingly persistent with depth while retaining structured relations between classes, and that the diffusion class chain is more stable than its $k$-nearest-neighbor counterpart under matched perturbations.

cs.LG↗

arXiv2026

Finite-Lag Operator Geometry of Recurrent Representations

Recurrent representations are trajectories, but representation geometry is often measured from static snapshots. We develop finite-lag operator geometry for recurrent hidden states from observed source-successor pairs $(X_t,X_{t+Δ})$. The primitive is the conditional transport law $Q_Δ(dy\mid x)$, estimated by a dense Gaussian source-smoothing operator. From this directed finite-lag law we derive a source-centered transport tensor $G_Δ$, which decomposes exactly into conditional spread and coherent displacement, and an antisymmetric coordinate circulation $W_Δ^ρ$, which summarizes directed lagged flow. We prove affine covariance with explicit metric dependence of scalar summaries, dense estimator stability on bounded trajectory clouds, and a finite-lag separation result showing that source-centered transport detects deterministic recurrent motion not recorded by infinitesimal carre-du-champ geometry. A linear-Gaussian closed form calibrates the quantities in terms of the update $A_Δ$, source covariance, and innovation covariance. Controlled experiments validate the decomposition, circulation, covariance, and stability predictions. In performance matched repeat-copy networks, the framework reveals architecture dependent differences in total transport scale and coherent displacement trace, while coherent displacement fraction is metric and resolution dependent.

cs.LG↗

arXiv2026

Compact Dynamical Mean-Field Theory of Oscillator Networks

We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped Langevin dynamics, we build a path-integral representation that keeps the $2π$-periodicity of the phases explicit. After averaging over the disorder in the thermodynamic limit, this construction reduces to a single-oscillator stochastic equation driven by a deterministic mean field and a self-consistent colored Gaussian noise, whose covariance is fixed by a circular two-time correlator. In the limit of vanishing disorder, the formalism reproduces the Ott--Antonsen reduction and recovers standard Kuramoto and theta-neuron neural-mass equations. The same framework accommodates arbitrary $2π$-periodic coupling functions, including those obtained from infinitesimal phase response curves (iPRCs) of biophysical neuron models. As an example, we show that for adaptive exponential integrate-and-fire neurons, inserting an iPRC-fitted coupling into the compact DMFT yields quantitative predictions for synchronization thresholds, providing a direct route from single-neuron phase response data to network-level mean-field predictions for arbitrary phase-reducible oscillators.

q-bio.NC↗