Nicolas Tacheny

Nicolas Tacheny

In multi-criteria graph traversal, paths are compared via Pareto dominance, an ordering that identifies which paths are non-dominated, but says nothing about which path to expand next or when the search may stop. As a result, existing approaches rely on external mechanisms-heuristics, scalarization, or population-based exploration while Pareto dominance remains confined to passive roles such as pruning or ranking. This paper shows that, under constrained cost models, finite cost grids, Markovian transitions, and a nonzero progress measure, Pareto geometry alone is sufficient to drive both scheduling and termination. We show that extracting exclusively from the first Pareto layer, the skyline, induces a deterministic descent in a discrete completion potential, ensuring monotone progress toward solution completion. In parallel, a vector lower-bound certificate provides a stopping condition that guarantees dominance coverage of all remaining traversals without requiring a predefined number of solutions. Our analysis establishes deterministic potential descent, certified termination via dominance coverage, a uniform bound on layer width induced by cost-grid geometry, and greedy cost-space dispersion within the skyline. The resulting framework operates without scalarization, heuristic guidance, or probabilistic models, and repositions Pareto dominance from a passive filter to a deterministic driver of search.

Nicolas Tacheny

While raw cosine similarity in pretrained embedding spaces exhibits strong rank correlation with human judgments, anisotropy induces systematic miscalibration of absolute values: scores concentrate in a narrow high-similarity band regardless of actual semantic relatedness, limiting interpretability as a quantitative measure. Prior work addresses this by modifying the embedding space (whitening, contrastive fine tuning), but such transformations alter geometric structure and require recomputing all embeddings. Using isotonic regression trained on human similarity judgments, we construct a monotonic transformation that achieves near-perfect calibration while preserving rank correlation and local stability(98% across seven perturbation types). Our contribution is not to replace cosine similarity, but to restore interpretability of its absolute values through monotone calibration, without altering its ranking properties. We characterize isotonic calibration as an order-preserving reparameterization and prove that all order-based constructions (angular ordering, nearest neighbors, threshold graphs and quantile-based decisions) are invariant under this transformation.

Nicolas Tacheny

Iterative LLM systems(self-refinement, chain-of-thought, autonomous agents) are increasingly deployed, yet their temporal dynamics remain uncharacterized. Prior work evaluates task performance at convergence but ignores the trajectory: how does semantic content evolve across iterations? Does it stabilize, drift, or oscillate? Without answering these questions, we cannot predict system behavior, guarantee stability, or systematically design iterative architectures. We formalize agentic loops as discrete dynamical systems in semantic space. Borrowing from dynamical systems theory, we define trajectories, attractors and dynamical regimes for recursive LLM transformations, providing rigorous geometric definitions adapted to this setting. Our framework reveals that agentic loops exhibit classifiable dynamics: contractive (convergence toward stable semantic attractors), oscillatory (cycling among attractors), or exploratory (unbounded divergence). Experiments on singular loops validate the framework. Iterative paraphrasing produces contractive dynamics with measurable attractor formation and decreasing dispersion. Iterative negation produces exploratory dynamics with no stable structure. Crucially, prompt design directly controls the dynamical regime - the same model exhibits fundamentally different geometric behaviors depending solely on the transformation applied. This work establishes that iterative LLM dynamics are predictable and controllable, opening new directions for stability analysis, trajectory forecasting, and principled design of composite loops that balance convergence and exploration.

Nicolas Tacheny

Large-scale telecom and datacenter infrastructures rely on multi-layered service and resource models, where failures propagate across physical and logical components and affect multiple customers. Traditional approaches to root cause analysis(RCA) rely on hard-coded graph traversal algorithms or rule-based correlation engines, which are costly to maintain and tightly coupled to the infrastructure model. In this work, we introduce an agentic diagnostic framework where a Large Language Model (LLM) performs step-wise investigation using a constrained tool space exposed through the Model Context Protocol (MCP). Instead of embedding causal logic or traversal algorithms into the application, the agent autonomously navigates the infrastructure model by invoking tools for service lookup, dependency retrieval, structured and unstructured data, and event analysis, and impact discovery. We define an investigation protocol that structures the agent's reasoning and ensures grounding, reproducibility, and safe handling of missing or ambiguous information. This work lays the foundation for autonomous incident resolution and change impact mitigation. Future systems will not only diagnose and remediate infrastructure failures, but also predict the impact of planned changes on services and customers, enabling operators to mitigate risks before executing maintenance operations.