Ravi Prasad

Ravi Prasad

Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of Monte Carlo algorithms, focusing on the persistent tension between statistical efficiency and computational cost. We describe the historical development from the foundational Metropolis Hastings algorithm to contemporary methods like Hamiltonian Monte Carlo. A central emphasis of this survey is the rigorous discussion of time and space complexity, including upper, lower, and asymptotic tight bounds for each major algorithm class. We examine the specific motivations for developing these methods and the key theoretical and practical observations such as the introduction of gradient information and adaptive tuning in HMC that led to successively better solutions. Furthermore, we provide a justification framework that discusses explicit situations in which using one algorithm is demonstrably superior to another for the same problem. The paper concludes by assessing the profound significance and impact of these algorithms and detailing major current research challenges.

Elias Hossain, Swayamjit Saha, Somshubhra Roy et al.

Even when prompts and parameters are secured, transformer language models remain vulnerable because their key-value (KV) cache during inference constitutes an overlooked attack surface. This paper introduces Malicious Token Injection (MTI), a modular framework that systematically perturbs cached key vectors at selected layers and timesteps through controlled magnitude and frequency, using additive Gaussian noise, zeroing, and orthogonal rotations. A theoretical analysis quantifies how these perturbations propagate through attention, linking logit deviations to the Frobenius norm of corruption and softmax Lipschitz dynamics. Empirical results show that MTI significantly alters next-token distributions and downstream task performance across GPT-2 and LLaMA-2/7B, as well as destabilizes retrieval-augmented and agentic reasoning pipelines. These findings identify cache integrity as a critical yet underexplored vulnerability in current LLM deployments, positioning cache corruption as a reproducible and theoretically grounded threat model for future robustness and security research.