Charanjit S. Jutla

Charanjit S. Jutla, Vimal Sharma

We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions. To ground this claim, we trace the history of the Fourier transform and relevant mathematics, from the vibrating string controversy to the hear equation and subsequent formalisms prevalent in mathematics. At each critical juncture, a physics problem forced the acceptance or creation of a mathematical tool that pure formal reasoning failed to anticipate or, worse, human reasoning had resisted. We further survey the landscape of logical complexity, from NP-hard propositional satisfiability to the non-elementary decision-procedures for monadic second-order theories, to demonstrate that even when a logic is decidable, the resources required for worst-case deduction are astronomically prohibitive. We argue that these barriers make physics-inspired pattern matching not just a historical accident but a cognitive necessity. Finally, we draw the consequence for artificial intelligence: if pure reasoning is constitutively insufficient, then any system aiming at human-level mathematical creativity must embed a vast store of cross-domain patterns rather than rely on deduction alone. This furnishes a principled justification for the enormous scale of contemporary large language models.

Aditya Malik, Nalini Ratha, Bharat Yalavarthi et al.

With the rapid surge in the prevalence of Large Language Models (LLMs), individuals are increasingly turning to conversational AI for initial insights across various domains, including health-related inquiries such as disease diagnosis. Many users seek potential causes on platforms like ChatGPT or Bard before consulting a medical professional for their ailment. These platforms offer valuable benefits by streamlining the diagnosis process, alleviating the significant workload of healthcare practitioners, and saving users both time and money by avoiding unnecessary doctor visits. However, Despite the convenience of such platforms, sharing personal medical data online poses risks, including the presence of malicious platforms or potential eavesdropping by attackers. To address privacy concerns, we propose a novel framework combining FHE and Deep Learning for a secure and private diagnosis system. Operating on a question-and-answer-based model akin to an interaction with a medical practitioner, this end-to-end secure system employs Fully Homomorphic Encryption (FHE) to handle encrypted input data. Given FHE's computational constraints, we adapt deep neural networks and activation functions to the encryted domain. Further, we also propose a faster algorithm to compute summation of ciphertext elements. Through rigorous experiments, we demonstrate the efficacy of our approach. The proposed framework achieves strict security and privacy with minimal loss in performance.

Vatsal Aggarwal, Arjun Ramesh Kaushik, Charanjit Jutla et al.

Autonomous Unmanned Aerial Vehicles (UAVs) have become essential tools in defense, law enforcement, disaster response, and product delivery. These autonomous navigation systems require a wireless communication network, and of late are deep learning based. In critical scenarios such as border protection or disaster response, ensuring the secure navigation of autonomous UAVs is paramount. But, these autonomous UAVs are susceptible to adversarial attacks through the communication network or the deep learning models - eavesdropping / man-in-the-middle / membership inference / reconstruction. To address this susceptibility, we propose an innovative approach that combines Reinforcement Learning (RL) and Fully Homomorphic Encryption (FHE) for secure autonomous UAV navigation. This end-to-end secure framework is designed for real-time video feeds captured by UAV cameras and utilizes FHE to perform inference on encrypted input images. While FHE allows computations on encrypted data, certain computational operators are yet to be implemented. Convolutional neural networks, fully connected neural networks, activation functions and OpenAI Gym Library are meticulously adapted to the FHE domain to enable encrypted data processing. We demonstrate the efficacy of our proposed approach through extensive experimentation. Our proposed approach ensures security and privacy in autonomous UAV navigation with negligible loss in performance.

Arjun Ramesh Kaushik, Charanjit Jutla, Nalini Ratha

In safeguarding mission-critical systems, such as Unmanned Aerial Vehicles (UAVs), preserving the privacy of path trajectories during navigation is paramount. While the combination of Reinforcement Learning (RL) and Fully Homomorphic Encryption (FHE) holds promise, the computational overhead of FHE presents a significant challenge. This paper proposes an innovative approach that leverages Knowledge Distillation to enhance the practicality of secure UAV navigation. By integrating RL and FHE, our framework addresses vulnerabilities to adversarial attacks while enabling real-time processing of encrypted UAV camera feeds, ensuring data security. To mitigate FHE's latency, Knowledge Distillation is employed to compress the network, resulting in an impressive 18x speedup without compromising performance, as evidenced by an R-squared score of 0.9499 compared to the original model's score of 0.9631. Our methodology underscores the feasibility of processing encrypted data for UAV navigation tasks, emphasizing security alongside performance efficiency and timely processing. These findings pave the way for deploying autonomous UAVs in sensitive environments, bolstering their resilience against potential security threats.