Sohom Mukherjee

Sohom Mukherjee, Nicolas Loizou, Sebastian U. Stich

Federated learning is a paradigm of distributed machine learning in which multiple clients coordinate with a central server to learn a model, without sharing their own training data. Standard federated optimization methods such as Federated Averaging (FedAvg) ensure balance among the clients by using the same stepsize for local updates on all clients. However, this means that all clients need to respect the global geometry of the function which could yield slow convergence. In this work, we propose locally adaptive federated learning algorithms, that leverage the local geometric information for each client function. We show that such locally adaptive methods with uncoordinated stepsizes across all clients can be particularly efficient in interpolated (overparameterized) settings, and analyze their convergence in the presence of heterogeneous data for convex and strongly convex settings. We validate our theoretical claims by performing illustrative experiments for both i.i.d. non-i.i.d. cases. Our proposed algorithms match the optimization performance of tuned FedAvg in the convex setting, outperform FedAvg as well as state-of-the-art adaptive federated algorithms like FedAMS for non-convex experiments, and come with superior generalization performance.

Advait Gadhikar, Sohom Mukherjee, Rebekka Burkholz

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity $1 / \log(1/\text{sparsity})$. This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

Sohom Mukherjee, Anh-Duy Pham, Richard Pibernik et al.

We study inventory control with decision-dependent censoring, focusing on the censored or repeated newsvendor (R-NV), where each order quantity determines whether demand is fully observed or censored by sales. Existing approaches based on parametric Thompson sampling (TS) can be brittle under prior mismatch, while offline imputation methods need not transfer to online learning. Motivated by the predictive view of decision making, we combine these ideas by taking oracle actions on learned completions of latent demand. We propose in-context generative posterior sampling (ICGPS), which uses modern generative models that are meta-trained offline and deployed online by in-context autoregressive generation. Theoretically, we show that the Bayesian regret of ICGPS with a learned completion kernel is bounded by the Bayesian regret of a TS benchmark with the ideal completion kernel plus a deployment penalty scaling as $\sqrt{T}$ times the square root of the completion mismatch. This yields a plug-in template for operational problems with known TS regret bounds. For R-NV, we derive sublinear Bayesian regret by reducing censored feedback to bandit convex optimization feedback. We also show that, under reasonable coverage and stability assumptions, the online completion mismatch is controlled by the offline censored predictive mismatch, so offline predictive quality transfers to online performance. Practically, we instantiate ICGPS with ChronosFlow, which combines a frozen time-series transformer backbone with a trainable conditional normalizing-flow head for fast censoring-consistent sampling. In benchmark experiments, ChronosFlow-ICGPS matches correctly specified TS, outperforms myopic and UCB-style baselines, and is robust to prior mismatch and distribution shift. ChronosFlow-ICGPS also performs well for the real-world SuperStore dataset, especially under heavy censoring.

Sohom Mukherjee, Arif Ahmed, Debi Prosad Dogra et al.

Air-writing is the process of writing characters or words in free space using finger or hand movements without the aid of any hand-held device. In this work, we address the problem of mid-air finger writing using web-cam video as input. In spite of recent advances in object detection and tracking, accurate and robust detection and tracking of the fingertip remains a challenging task, primarily due to small dimension of the fingertip. Moreover, the initialization and termination of mid-air finger writing is also challenging due to the absence of any standard delimiting criterion. To solve these problems, we propose a new writing hand pose detection algorithm for initialization of air-writing using the Faster R-CNN framework for accurate hand detection followed by hand segmentation and finally counting the number of raised fingers based on geometrical properties of the hand. Further, we propose a robust fingertip detection and tracking approach using a new signature function called distance-weighted curvature entropy. Finally, a fingertip velocity-based termination criterion is used as a delimiter to mark the completion of the air-writing gesture. Experiments show the superiority of the proposed fingertip detection and tracking algorithm over state-of-the-art approaches giving a mean precision of 73.1 % while achieving real-time performance at 18.5 fps, a condition which is of vital importance to air-writing. Character recognition experiments give a mean accuracy of 96.11 % using the proposed air-writing system, a result which is comparable to that of existing handwritten character recognition systems.