Publications

This paper presents a framework where large language models perform diagnostic investigations across complex telecom and datacenter infrastructure using the Model Context Protocol (MCP). Rather than relying on hard-coded diagnostic algorithms, the agent autonomously navigates infrastructure models by invoking contextual tools for service lookup, dependency graph traversal, and event correlation.

The work defines a structured investigation protocol that grounds the agent's reasoning process and ensures safe handling of uncertain or incomplete information. This establishes foundations for autonomous incident resolution and predictive impact analysis, enabling infrastructure operators to identify downstream risks from planned maintenance operations before execution.

Cosine similarity in pretrained embedding spaces correlates well with human judgments but suffers from systematic miscalibration due to anisotropy: scores concentrate in a narrow high-similarity band regardless of actual semantic relatedness. This paper introduces isotonic calibration, a monotonic transformation trained on human similarity judgments that restores interpretability of absolute similarity values while preserving rank correlation and local stability.

Unlike prior approaches that modify the embedding space through whitening or contrastive fine-tuning, this method leaves geometric structure intact and requires no recomputation of embeddings. We prove that all order-based constructions (angular ordering, nearest neighbors, threshold graphs, quantile-based decisions) are invariant under isotonic calibration.

Iterative LLM systems such as self-refinement, chain-of-thought, and autonomous agents are increasingly deployed, yet their temporal dynamics remain uncharacterized. This paper formalizes agentic loops as discrete dynamical systems in semantic space, defining trajectories, attractors, and dynamical regimes for recursive LLM transformations using concepts from dynamical systems theory.

The framework reveals that agentic loops exhibit classifiable dynamics: contractive (convergence toward stable semantic attractors), oscillatory (cycling among attractors), or exploratory (unbounded divergence). Experiments show that prompt design directly controls the dynamical regime—the same model exhibits fundamentally different geometric behaviors depending solely on the transformation applied. This establishes that iterative LLM dynamics are predictable and controllable, opening directions for stability analysis and principled design of composite loops.

We present a novel numerical algorithm for finding saddle points of functionals, based on the mountain pass theorem from nonlinear analysis. The method introduces a projection step that significantly improves convergence properties compared to classical minimax approaches.

The algorithm is particularly suited for problems arising in mathematical physics and partial differential equations where critical points of energy functionals correspond to physically meaningful solutions. Numerical experiments demonstrate the efficiency of the projection technique on benchmark problems from nonlinear Schrodinger equations and semilinear elliptic systems.