Sayan Banerjee

Akshay Janardan Bankar, Ankita Chatterjee, Sayan Banerjee et al.

Blind image restoration requires recovering clean images from observations corrupted by unknown and potentially mixed degradations. While recent deterministic flow-based methods model restoration as transport processes that map degraded images to clean ones, they typically rely on Euclidean interpolation, implicitly assuming linear degradation geometry. In this paper, we explicitly model degradations as points on a low-dimensional Riemannian manifold and formulate restoration as geodesic transport on the joint image-manifold space. Using a geodesic flow matching objective, we learn intrinsic transport dynamics that respect the curvature of degradation space. This framework generalizes linear flow matching, provides a principled treatment of mixed degradations as geodesic compositions, and yields a clean theoretical interpretation for generalization beyond observed degradations.

Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the relative entropy between the joint density of $N$ particle locations and the $N$-fold product target measure, starting from a regular initial distribution, splits into a dominant `negative part' proportional to $N$ times the expected $\mathsf{KSD}^2$ and a smaller `positive part'. This observation leads to $\mathsf{KSD}$ rates of order $1/\sqrt{N}$, in both continuous and discrete time, providing a near optimal (in the sense of matching the corresponding i.i.d. rates) double exponential improvement over the recent result by Shi and Mackey (2024). Under mild assumptions on the kernel and potential, these bounds also grow polynomially in the dimension $d$. By adding a bilinear component to the kernel, the above approach is used to further obtain Wasserstein-2 convergence in continuous time. For the case of `bilinear + Matérn' kernels, we derive Wasserstein-2 rates that exhibit a curse-of-dimensionality similar to the i.i.d. setting. We also obtain marginal convergence and long-time propagation of chaos results for the time-averaged particle laws.

Ye He, Krishnakumar Balasubramanian, Sayan Banerjee et al.

We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the kernelized Wasserstein gradient. For the resulting interacting $N$-particle system, we establish explicit non-asymptotic bounds for time-averaged (annealed) empirical measures, illustrating convergence in the \emph{true} (non-kernelized) Fisher information and, under a $\mathrm{W}_1\mathrm{I}$ condition on the target, corresponding $\mathrm{W}_1$ convergence for a large class of smooth kernels. Our analysis covers both continuous- and discrete-time dynamics and yields principled tuning rules for the regularization parameter, step size, and averaging horizon that quantify the trade-off between approximating the Wasserstein gradient flow and controlling finite-particle estimation error.

Sayan Banerjee, Aniruddha Mukherjee, Suket Kamboj

With the help of a digital twin structure, Agriculture 4.0 technologies like weather APIs (Application programming interface), GPS (Global Positioning System) modules, and NPK (Nitrogen, Phosphorus and Potassium) soil sensors and machine learning recommendation models, we seek to revolutionize agricultural production through this concept. In addition to providing precise crop growth forecasts, the combination of real-time data on soil composition, meteorological dynamics, and geographic coordinates aims to support crop recommendation models and simulate predictive scenarios for improved water and pesticide management.

Krishnakumar Balasubramanian, Sayan Banerjee, Philippe Rigollet

We study stationary solutions of McKean-Vlasov equations on the circle. Our main contributions stem from observing an exact equivalence between solutions of the stationary McKean-Vlasov equation and an infinite-dimensional quadratic system of equations over Fourier coefficients, which allows explicit characterization of the stationary states in a sequence space rather than a function space. This framework provides a transparent description of local bifurcations, characterizing their periodicity, and resonance structures, while accommodating singular potentials. We derive analytic expressions that characterize the emergence, form and shape (supercritical, critical, subcritical or transcritical) of bifurcations involving possibly multiple Fourier modes and connect them with discontinuous phase transitions. We also characterize, under suitable assumptions, the detailed structure of the stationary bifurcating solutions that are accurate upto an arbitrary number of Fourier modes. At the global level, we establish regularity and concavity properties of the free energy landscape, proving existence, compactness, and coexistence of globally minimizing stationary measures, further identifying discontinuous phase transitions with points of non-differentiability of the minimum free energy map. As an application, we specialize the theory to the Noisy Mean-Field Transformer model, where we show how changing the inverse temperature parameter $β$ affects the geometry of the infinitely many bifurcations from the uniform measure. We also explain how increasing $β$ can lead to a rich class of approximate multi-mode stationary solutions which can be seen as `metastable states'. Further, a sharp transition from continuous to discontinuous (first-order) phase behavior is observed as $β$ increases.

Sayan Banerjee, S Divakar Bhat, Subhasis Chaudhuri et al.

In this paper, we propose a novel framework for multi-image co-segmentation using class agnostic meta-learning strategy by generalizing to new classes given only a small number of training samples for each new class. We have developed a novel encoder-decoder network termed as DVICE (Directed Variational Inference Cross Encoder), which learns a continuous embedding space to ensure better similarity learning. We employ a combination of the proposed DVICE network and a novel few-shot learning approach to tackle the small sample size problem encountered in co-segmentation with small datasets like iCoseg and MSRC. Furthermore, the proposed framework does not use any semantic class labels and is entirely class agnostic. Through exhaustive experimentation over multiple datasets using only a small volume of training data, we have demonstrated that our approach outperforms all existing state-of-the-art techniques.

Mayank Kumar Singh, Sayan Banerjee, Shubhasis Chaudhuri

Text detection in scenes based on deep neural networks have shown promising results. Instead of using word bounding box regression, recent state-of-the-art methods have started focusing on character bounding box and pixel-level prediction. This necessitates the need to link adjacent characters, which we propose in this paper using a novel Graph Neural Network (GNN) architecture that allows us to learn both node and edge features as opposed to only the node features under the typical GNN. The main advantage of using GNN for link prediction lies in its ability to connect characters which are spatially separated and have an arbitrary orientation. We show our concept on the well known SynthText dataset, achieving top results as compared to state-of-the-art methods.

B. V. S Anusha, Sayan Banerjee, Subhasis Chaudhuri

In recent years, fingerprint recognition systems have made remarkable advancements in the field of biometric security as it plays an important role in personal, national and global security. In spite of all these notable advancements, the fingerprint recognition technology is still susceptible to spoof attacks which can significantly jeopardize the user security. The cross sensor and cross material spoof detection still pose a challenge with a myriad of spoof materials emerging every day, compromising sensor interoperability and robustness. This paper proposes a novel method for fingerprint spoof detection using both global and local fingerprint feature descriptors. These descriptors are extracted using DenseNet which significantly improves cross-sensor, cross-material and cross-dataset performance. A novel patch attention network is used for finding the most discriminative patches and also for network fusion. We evaluate our method on four publicly available datasets:LivDet 2011, 2013, 2015 and 2017. A set of comprehensive experiments are carried out to evaluate cross-sensor, cross-material and cross-dataset performance over these datasets. The proposed approach achieves an average accuracy of 99.52%, 99.16% and 99.72% on LivDet 2017,2015 and 2011 respectively outperforming the current state-of-the-art results by 3% and 4% for LivDet 2015 and 2011 respectively.