Satyasaran Changdar

Rajat Khanda, Mohammad Baqar Sambuddha Chakrabarti, Satyasaran Changdar

Autonomous AI agents operating in dynamic environments face a persistent challenge: acquiring new capabilities without erasing prior knowledge. We present Adaptive Memory Crystallization (AMC), a memory architecture for progressive experience consolidation in continual reinforcement learning. AMC is conceptually inspired by the qualitative structure of synaptic tagging and capture (STC) theory, the idea that memories transition through discrete stability phases, but makes no claim to model the underlying molecular or synaptic mechanisms. AMC models memory as a continuous crystallization process in which experiences migrate from plastic to stable states according to a multi-objective utility signal. The framework introduces a three-phase memory hierarchy (Liquid--Glass--Crystal) governed by an Itô stochastic differential equation (SDE) whose population-level behavior is captured by an explicit Fokker--Planck equation admitting a closed-form Beta stationary distribution. We provide proofs of: (i) well-posedness and global convergence of the crystallization SDE to a unique Beta stationary distribution; (ii) exponential convergence of individual crystallization states to their fixed points, with explicit rates and variance bounds; and (iii) end-to-end Q-learning error bounds and matching memory-capacity lower bounds that link SDE parameters directly to agent performance. Empirical evaluation on Meta-World MT50, Atari 20-game sequential learning, and MuJoCo continual locomotion consistently shows improvements in forward transfer (+34--43\% over the strongest baseline), reductions in catastrophic forgetting (67--80\%), and a 62\% decrease in memory footprint.

Rajat Khanda, Mohammad Baqar, Sambuddha Chakrabarti et al.

Group Relative Policy Optimization (GRPO) has shown promise in discrete action spaces by eliminating value function dependencies through group-based advantage estimation. However, its application to continuous control remains unexplored, limiting its utility in robotics where continuous actions are essential. This paper presents a theoretical framework extending GRPO to continuous control environments, addressing challenges in high-dimensional action spaces, sparse rewards, and temporal dynamics. Our approach introduces trajectory-based policy clustering, state-aware advantage estimation, and regularized policy updates designed for robotic applications. We provide theoretical analysis of convergence properties and computational complexity, establishing a foundation for future empirical validation in robotic systems including locomotion and manipulation tasks.

Sumit Pandey, Satyasaran Changdar, Mathias Perslev et al.

Automated segmentation of distinct tumor regions is critical for accurate diagnosis and treatment planning in pediatric brain tumors. This study evaluates the efficacy of the Multi-Planner U-Net (MPUnet) approach in segmenting different tumor subregions across three challenging datasets: Pediatrics Tumor Challenge (PED), Brain Metastasis Challenge (MET), and Sub-Sahara-Africa Adult Glioma (SSA). These datasets represent diverse scenarios and anatomical variations, making them suitable for assessing the robustness and generalization capabilities of the MPUnet model. By utilizing multi-planar information, the MPUnet architecture aims to enhance segmentation accuracy. Our results show varying performance levels across the evaluated challenges, with the tumor core (TC) class demonstrating relatively higher segmentation accuracy. However, variability is observed in the segmentation of other classes, such as the edema and enhancing tumor (ET) regions. These findings emphasize the complexity of brain tumor segmentation and highlight the potential for further refinement of the MPUnet approach and inclusion of MRI more data and preprocessing.

Narayan S Iyer, Bivas Bhaumik, Ram S Iyer et al.

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches like Physics$-$Informed Neural Networks (PINNs) have been developed, offering a mesh$-$free, analytic type framework for efficiently solving PDEs across a wide range of applications. However, traditional PINNs often struggle with challenges such as limited precision, slow training dynamics, lack of labeled data availability, and inadequate handling of multi$-$physics interactions. To overcome these challenging issues of PINNs, we proposed a Gradient Enhanced Self$-$Training PINN (gST$-$PINN) method that specifically introduces a gradient based pseudo point self$-$learning algorithm for solving PDEs. We tested the proposed method on three different types of PDE problems from various fields, each representing distinct scenarios. The effectiveness of the proposed method is evident, as the PINN approach for solving the Burgers$'$ equation attains a mean square error (MSE) on the order of $10^{-3}$, while the diffusion$-$sorption equation achieves an MSE on the order of $10^{-4}$ after 12,500 iterations, with no further improvement as the iterations increase. In contrast, the MSE for both PDEs in the gST$-$PINN model continues to decrease, demonstrating better generalization and reaching an MSE on the order of $10^{-5}$ after 18,500 iterations. Furthermore, the results show that the proposed purely semi$-$supervised gST$-$PINN consistently outperforms the standard PINN method in all cases, even when solution of the PDEs are unavailable. It generalizes both PINN and Gradient$-$enhanced PINN (gPINN), and can be effectively applied in scenarios prone to low accuracy and convergence issues, particularly in the absence of labeled data.

Satyasaran Changdar, Snehangshu Bhattacharjee

This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a learning algorithm, be able to solve definite integrals, by minimising a well constructed error function. The proposed algorithm, with respect to existing numerical methods, is effective and precise and well-suited for purposes which require integration of higher order polynomials. The observations have been recorded and illustrated in tabular and graphical form.

Sabyasachi Mukhopadhyay, Soham Mandal, Sawon Pratiher et al.

In this paper, a comparative study between proposed hyper kurtosis based modified duo-histogram equalization (HKMDHE) algorithm and contrast limited adaptive histogram enhancement (CLAHE) has been presented for the implementation of contrast enhancement and brightness preservation of low contrast human brain CT scan images. In HKMDHE algorithm, contrast enhancement is done on the hyper-kurtosis based application. The results are very promising of proposed HKMDHE technique with improved PSNR values and lesser AMMBE values than CLAHE technique.