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Akshit Nanda

Publications and source records attributed to Akshit Nanda.

2 recordsLinked to original sources

Positive Pair Geometry Matters: Optimal Transport for Contrastive Learning of Visual Representations

Contrastive self-supervised learning has achieved strong performance by learning representations from multiple augmented views of the same image. However, most existing methods construct positive pairs using independently sampled stochastic augmentations, which may alter semantic content and ignore the intrinsic geometry of the data distribution. In this work, we propose OTCLR, an optimal transport-aware framework for contrastive learning representations that generates geometry-consistent positive samples. Instead of directly contrasting two randomly augmented views, we construct intermediate views between the original image and its augmented variants through entropic optimal-transport displacement interpolation. These transport-interpolated samples serve as positive views that better preserve image structure while explicitly modeling spatial distributional geometry. To further promote smooth representation learning, we evaluate auxiliary Sinkhorn regularization terms that encourage transport-interpolated views to remain consistent with their endpoint images. The proposed method can be incorporated into standard contrastive learning pipelines without modifying the encoder architecture. Experiments on multiple benchmark datasets show that our approach improves representation quality and transfer learning performance compared with conventional augmentation-based contrastive learning baselines.

cs.CV↗

Symmetry-Constrained Exact Coherent Structures in Plane Poiseuille Flow

Turbulence in wall-bounded shear flows is increasingly understood through exact coherent structures (ECS) -- invariant solutions of the Navier-Stokes equations that act as organising centres in the high-dimensional state space. Here we report five new ECS of plane Poiseuille flow: two relative periodic orbits (RPOs) and three travelling waves (TWs), that are computed in four distinct symmetry-invariant subspaces using a Newton-Krylov-hookstep solver initialised from direct numerical simulations. We trace each state through one-parameter continuations in both the Reynolds number $Re$ and the spanwise period $L_z$. All five states are organised around counter-rotating rolls sustaining streamwise velocity streaks, yet they exhibit qualitatively different stability properties: the two RPOs are linearly stable within their symmetry subspace, while the three TWs are saddle-type solutions whose instabilities are, respectively, mixed oscillatory-and-monotone, purely monotone and purely oscillatory. The continuation diagrams reveal their bifurcation geometry, from simple saddle-node folds for the RPOs to a pronounced S-shaped multi-branch structure with three coexisting dissipation levels for one of the travelling waves. Along each branch, the roll-streak topology is preserved across the folds, with the different branches distinguished by their amplitude and gradient intensity rather than by a change in spatial organisation. Floquet spectra evaluated at multiple points along each branch shows that folds generically act as sites of reduced instability for the travelling waves, while upper branches develop stronger and sometimes qualitatively different unstable modes. These include the emergence of linearly stable segments on the intermediate and upper branches of the multi-branch travelling wave, despite the solution being unstable at its reference parameters.

physics.flu-dyn↗