Amritendu Mukherjee

Debashis Guha, Amritendu Mukherjee, Sanjay Kukreja et al.

Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This paper addresses both. We represent the reasoning state as an epistemic state graph encoding extracted claims, evidential relations, open questions, and confidence weights. We define the order-gap as the distance between the states reached by expand-then-consolidate versus consolidate-then-expand; a small order-gap suggests that the two orderings agree and further iteration is unlikely to help. Our main result gives a necessary and sufficient condition for the linearised order-gap to be non-degenerate near the fixed point, showing when the criterion is informative rather than algebraically vacuous. This is a local condition, not a global convergence guarantee. We apply the framework to recursive reasoning systems and sketch its application to agent loops, tree-of-thought reasoning, theorem proving, and continual learning.

Amritendu Mukherjee, Dipanwita Sinha Mukherjee, Parthasarathy Ramachandran

Training a neural network for pixel based classification task using low resolution Landsat images is difficult as the size of the training data is usually small due to less number of available pixels that represent a single class without any mixing with other classes. Due to this scarcity of training data, neural network may not be able to attain expected level of accuracy. This limitation could be overcome using a generative network that aims to generate synthetic data having the same distribution as the sample data with which it is trained. In this work, we have proposed a methodology for improving the performance of ANN classifier to identify built-up pixels in the Landsat$7$ image with the help of developing a simple GAN architecture that could generate synthetic training pixels when trained using original set of sample built-up pixels. To ensure that the marginal and joint distributions of all the bands corresponding to the generated and original set of pixels are indistinguishable, non-parametric Kolmogorov Smirnov Test and Ball Divergence based Equality of Distributions Test have been performed respectively. It has been observed that the overall accuracy and kappa coefficient of the ANN model for built-up classification have continuously improved from $0.9331$ to $0.9983$ and $0.8277$ to $0.9958$ respectively, with the inclusion of generated sets of built-up pixels to the original one.