arXiv subjects

Xavier Cadet

Publications and source records attributed to Xavier Cadet.

15 recordsLinked to original sources

arXiv2026

BlueSTAR: Tiered Agentic Architecture for Autonomous Cyber Defense

Cyber attacks are increasingly automated, narrowing the time available for human analysts to detect, reason about, and respond to intrusions. Large language models (LLMs) offer a promising foundation for autonomous cyber defense because they can correlate heterogeneous evidence and reason about previously unseen threats. However, directly applying LLMs to operational security telemetry is impractical: raw logs arrive faster than current models can process them, individual events are often ambiguous, and unconstrained LLM actions can introduce significant operational risk. We present BlueSTAR, a tiered agentic architecture for autonomous cyber defense in enterprise IT/OT networks. BlueSTAR first transforms high-volume security telemetry into compact indicators of compromise. We further introduce a resilience metric that jointly captures attacker reach, impact on mission-critical assets, and disruption caused by defensive actions. We evaluate BlueSTAR on two live enterprise IT/OT cyber ranges using seven attack chains based on real-world intrusion techniques. Across attack chains, BlueSTAR retains the fast containment of deterministic response for known threats while successfully defending against attacks requiring contextual and cross-cycle reasoning, including credential theft, repeated compromise, concurrent attackers, and attacks against physical processes.

cs.CR↗

arXiv2026

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations

Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately. What happens at the extreme of this spectrum, when the architecture's expressible function class collapses to a finite-dimensional algebraic variety? We study two-layer networks with a holomorphic monomial activation sigma(z)=z^k, trained on modular tasks encoded via roots of unity. Here the network output, regardless of hidden width, is confined to a (k+1)-dimensional subspace of characters of (Z_p)^2, an O(k/p^2) slice of the full function space. We give a complete algebraic characterisation of this subspace: a task is representable if and only if its discrete Fourier support lies on the diagonal u+v = k (mod p), which for linear-phase targets reduces to the arithmetic criterion m+n=k. This is not merely a constraint on eventual generalisation but on memorisation itself: because the outputs are algebraically confined, a non-representable target cannot be fit even on the training set, and we prove a positive lower bound on the training loss, independent of width. Across 585 runs the algebraic prediction matches the observed outcome with 99.8% accuracy, with no memorisation regime and no grokking; outcomes split cleanly into instant success and outright failure. This binary behaviour is the limiting case of the capacity-grokking relationship: when the expressible class shrinks to a fixed algebraic object, the question of when a network will grok dissolves into whether it can represent the target at all. A bottleneck ablation connects this extreme to standard networks, tracing a continuous path from representational failure, through memorisation without generalisation, to grokking with a shrinking gap as capacity grows.

cs.LG↗

arXiv2026

DNQ: Deep Nash Q-Network for Partially Observable n-Player Games

Many real-world competitive systems require multiple decision-makers to act simultaneously under shared constraints, limited information, and repeated interaction, as in auctions, resource allocation, and security competition. We study multi-turn simultaneous bidding as a controlled testbed for such problems and propose DNQ, a solver-in-the-loop equilibrium supervision framework for training bidding agents. DNQ alternates between trajectory collection, critic-based payoff estimation, equilibrium computation, and policy imitation. At each visited state, a shared critic predicts either pairwise payoff matrices or an exact N-player payoff tensor, an external solver computes equilibrium strategies, and the agents are trained by minimizing the KL divergence between their masked policies and the solver-derived equilibrium targets. We focus on a scalable pairwise formulation that greatly reduces equilibrium-solving cost and training time compared with the exact formulation, while the shared critic amortizes payoff learning across agents and states. Experiments compare the pairwise and exact variants using critic loss, policy entropy, bidding resource usage, and training cost, showing that the pairwise method scales to larger numbers of agents, whereas the exact method becomes computationally impractical as the joint game grows. These results illustrate the trade-off between strategic fidelity and scalability in repeated competitive environments.

cs.GT↗

arXiv2026

RADAR: Relative Angular Divergence Across Representations

Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited data, yet this practice does not always improve downstream performance and can sometimes lead to a loss of performance, known as negative transfer. We propose RADAR, a simple, geometrically grounded metric for estimating cross-domain transferability in foundation models. RADAR analyzes the layer-wise evolution of representations by measuring angular alignments and relative changes in distance along layer-to-layer displacement trajectories, and by comparing empirical distributions of within-domain and cross-domain dynamics. We hypothesize that domain transferability is related to the divergence between these trajectory distributions. We evaluate the metric across multiple modalities, including cross-lingual sentiment classification with text embedding models and cross-domain image classification with foundation vision models. Across several settings, RADAR provides competitive predictive performance relative to existing transferability metrics on several vision and text benchmarks, with particularly strong results when domain transitions are smooth or cleanly separated. Our ablations further suggest that the effectiveness of transferability estimation depends on the geometry of the model's internal representation space, with different modalities favoring different topological formulations.

cs.LG↗

arXiv2026

Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability

While world models learn compact representations of complex environments, they lack a physics-grounded metric to assess the structural fidelity of their latent spaces. We identify the wavelet scaling exponent $\alpha$ as a critical diagnostic, proposing optimal representations satisfy variance equipartition ($\alpha \approx 1/2$) -- mirroring Kolmogorov's inertial range. We establish $\alpha = 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels. Using tensor-network theory, we prove latents with $\alpha > 1/2$ reside in an area-law phase admitting efficient classical emulation, while $\alpha < 1/2$ triggers a volume-law phase where the Matrix Product State bond dimension $\chi$ grows exponentially with qubit count $n$. Analyzing pre-trained VideoMAE latents reveals a dichotomy: spatial tokens approach the equipartition limit ($\alpha \approx 0.423$), but permutation-invariant feature channels exhibit unstructured disorder ($\alpha \approx -0.123$). This forces real-world latents deep into the volume-law phase, providing a data-driven necessary condition for simulation hardness. Finally, we apply Weingarten calculus to derive the exact variance of the scrambled transition probability under a 2-design ensemble. We prove this variance scales strictly as $\Var[X] = \Theta(d^{-2})$. We confirm this numerically with a log-log slope of $-1.881$ ($R^2 = 0.999$), identifying a formidable shot-noise wall demanding a measurement budget of $M = \Omega(d^2)$ that constrains quantum machine learning scalability.

quant-ph↗

arXiv2026

Retrieval-Augmented LLMs for Security Incident Analysis

Investigating cybersecurity incidents requires collecting and analyzing evidence from multiple log sources, including intrusion detection alerts, network traffic records, and authentication events. This process is labor-intensive: analysts must sift through large volumes of data to identify relevant indicators and piece together what happened. We present a RAG-based system that performs security incident analysis through targeted query-based filtering and LLM semantic reasoning. The system uses a query library with associated MITRE ATT&CK techniques to extract indicators from raw logs, then retrieves relevant context to answer forensic questions and reconstruct attack sequences. We evaluate the system with eight LLM configurations on malware traffic incidents and a multi-stage Active Directory attack. We find that LLMs have different performance and tradeoffs, with Claude Sonnet 4 achieving 94% and DeepSeek V3 achieving 89% average recall across 17 malware scenarios, while DeepSeek costs 15$\times$ less than Claude per analysis, and locally-deployed Llama 3.1:70b achieves 81% recall at zero per-query cost. Attack step detection on the Active Directory scenario reaches 100% precision and up to 96% recall with an enumeration prompt. These results demonstrate that combining targeted query-based filtering with RAG-based retrieval -- confirmed essential by ablation studies -- enables accurate, cost-effective security analysis within LLM context limits.

cs.CR↗

arXiv2026

ABCD: All Biases Come Disguised

Multiple-choice question (MCQ) benchmarks have been a standard evaluation practice for measuring LLMs' ability to reason and answer knowledge-based questions. Through a synthetic NonsenseQA benchmark, we observe that different LLMs exhibit varying degrees of label-position-few-shot-prompt bias, where the model either uses the answer position, the label in front of the answer, the distributions of correct answers present in the few-shot prompt, or a combination of all to answer each MCQ question. We propose a simple bias-reduced evaluation protocol that replaces the labels of each question with uniform, unordered labels and prompts the LLM to use the whole answer presented. With a simple sentence similarity model, we demonstrate improved robustness and lower standard deviation between different permutations of answers with a minimal drop in LLM's performance, exposing the LLM's capabilities under reduced evaluation artifacts, without any help from the prompt examples or the option labels. Across multiple benchmarks and models, this protocol substantially improves the robustness to answer permutations, reducing mean accuracy variance $3\times$ with only a minimal decrease in the mean model's performance. Through ablation studies on various embedding models and similarity functions, we show that the method is more robust than the standard ones.

cs.CL↗

arXiv2025

Hermitian Matrix Function Synthesis without Block-Encoding

Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine learning kernels, and other advanced quantum algorithms. Existing state-of-the-art techniques, including Qubitization, Quantum Singular Value Transformation (QSVT), and Quantum Signal Processing (QSP), rely heavily on block-encoding the Hermitian matrix. These methods are often constrained by the complexity of preparing the block-encoded state, the overhead associated with the required ancillary qubits, or the challenging problem of angle synthesis for the polynomial's phase factors, which limits the achievable circuit depth and overall efficiency. In this work, we propose a novel and resource-efficient approach to implement arbitrary polynomials of a Hermitian matrix by leveraging the Generalized Quantum Signal Processing (GQSP) framework. Our method circumvents the need for block-encoding and avoids the compounding post-selection overheads characteristic of LCU-based constructions, achieving a stable, degree-independent success probability. We derive closed-form expressions for symmetric polynomial expansions and demonstrate how linear combinations of GQSP circuits can realize the desired transformation. This approach reduces resource overhead and opens new pathways for quantum algorithm design for functions of Hermitian matrices, particularly in settings where the Hermitian operator arises naturally from symmetric combinations of unitaries.

quant-ph↗

arXiv2025

AsymPuzl: An Asymmetric Puzzle for multi-agent cooperation

Large Language Model (LLM) agents are increasingly studied in multi-turn, multi-agent scenarios, yet most existing setups emphasize open-ended role-play rather than controlled evaluation. We introduce AsymPuzl, a minimal but expressive two-agent puzzle environment designed to isolate communication under information asymmetry. Each agent observes complementary but incomplete views of a symbolic puzzle and must exchange messages to solve it cooperatively. Using a diverse set of current-generation and open-source LLMs, we show that (i) strong models such as GPT-5 and Claude-4.0 reliably converge across puzzle sizes on the solution by sharing complete information in two turns, (ii) weaker models often ignore partner messages or over-correct their hypotheses, and (iii) feedback design is non-trivial: simple self-feedback improves success rates, while detailed joint feedback can hurt performance. These findings show that even in simple cooperative tasks, LLM communication strategies diverge and depend on the granularity of feedback signals. AsymPuzl thus provides a testbed for probing the limits of multi-turn cooperation and opens avenues for studying coordination mechanisms.

cs.MA↗

arXiv2025

WARP: Weight Teleportation for Attack-Resilient Unlearning Protocols

Approximate machine unlearning aims to efficiently remove the influence of specific data points from a trained model, offering a practical alternative to full retraining. However, it introduces privacy risks: an adversary with access to pre- and post-unlearning models can exploit their differences for membership inference or data reconstruction. We show these vulnerabilities arise from two factors: large gradient norms of forget-set samples and the close proximity of unlearned parameters to the original model. To demonstrate their severity, we propose unlearning-specific membership inference and reconstruction attacks, showing that several state-of-the-art methods (e.g., NGP, SCRUB) remain vulnerable. To mitigate this leakage, we introduce WARP, a plug-and-play teleportation defense that leverages neural network symmetries to reduce forget-set gradient energy and increase parameter dispersion while preserving predictions. This reparameterization obfuscates the signal of forgotten data, making it harder for attackers to distinguish forgotten samples from non-members or recover them via reconstruction. Across six unlearning algorithms, our approach achieves consistent privacy gains, reducing adversarial advantage (AUC) by up to 64% in black-box and 92% in white-box settings, while maintaining accuracy on retained data. These results highlight teleportation as a general tool for reducing attack success in approximate unlearning.

cs.LG↗

arXiv2025

WAN3DNS: Weak Adversarial Networks for Solving 3D Incompressible Navier-Stokes Equations

The 3D incompressible Navier-Stokes equations model essential fluid phenomena, including turbulence and aerodynamics, but are challenging to solve due to nonlinearity and limited solution regularity. Despite extensive research, the full mathematical understanding of the 3D incompressible Navier-Stokes equations continues to elude scientists, highlighting the depth and difficulty of the problem. Classical solvers are costly, and neural network-based methods typically assume strong solutions, limiting their use in underresolved regimes. We introduce WAN3DNS, a weak-form neural solver that recasts the equations as a minimax optimization problem, allowing learning directly from weak solutions. Using the weak formulation, WAN3DNS circumvents the stringent differentiability requirements of classical physics-informed neural networks (PINNs) and accommodates scenarios where weak solutions exist, but strong solutions may not. We evaluated WAN3DNS's accuracy and effectiveness in three benchmark cases: the 2D Kovasznay, 3D Beltrami, and 3D lid-driven cavity flows. Furthermore, using Galerkin's theory, we conduct a rigorous error analysis and show that the $L^{2}$ training error is controllably bounded by the architectural parameters of the network and the norm of residues. This implies that for neural networks with small loss, the corresponding $L^{2}$ error will also be small. This work bridges the gap between weak solution theory and deep learning, offering a robust alternative for complex fluid flow simulations with reduced regularity constraints. Code: https://github.com/Wenran-Li/WAN3DNS

physics.flu-dyn↗

arXiv2025

Nash Q-Network for Multi-Agent Cybersecurity Simulation

Cybersecurity defense involves interactions between adversarial parties (namely defenders and hackers), making multi-agent reinforcement learning (MARL) an ideal approach for modeling and learning strategies for these scenarios. This paper addresses one of the key challenges to MARL, the complexity of simultaneous training of agents in nontrivial environments, and presents a novel policy-based Nash Q-learning to directly converge onto a steady equilibrium. We demonstrate the successful implementation of this algorithm in a notable complex cyber defense simulation treated as a two-player zero-sum Markov game setting. We propose the Nash Q-Network, which aims to learn Nash-optimal strategies that translate to robust defenses in cybersecurity settings. Our approach incorporates aspects of proximal policy optimization (PPO), deep Q-network (DQN), and the Nash-Q algorithm, addressing common challenges like non-stationarity and instability in multi-agent learning. The training process employs distributed data collection and carefully designed neural architectures for both agents and critics.

cs.MA↗

arXiv2025

PoolFlip: A Multi-Agent Reinforcement Learning Security Environment for Cyber Defense

Cyber defense requires automating defensive decision-making under stealthy, deceptive, and continuously evolving adversarial strategies. The FlipIt game provides a foundational framework for modeling interactions between a defender and an advanced adversary that compromises a system without being immediately detected. In FlipIt, the attacker and defender compete to control a shared resource by performing a Flip action and paying a cost. However, the existing FlipIt frameworks rely on a small number of heuristics or specialized learning techniques, which can lead to brittleness and the inability to adapt to new attacks. To address these limitations, we introduce PoolFlip, a multi-agent gym environment that extends the FlipIt game to allow efficient learning for attackers and defenders. Furthermore, we propose Flip-PSRO, a multi-agent reinforcement learning (MARL) approach that leverages population-based training to train defender agents equipped to generalize against a range of unknown, potentially adaptive opponents. Our empirical results suggest that Flip-PSRO defenders are $2\times$ more effective than baselines to generalize to a heuristic attack not exposed in training. In addition, our newly designed ownership-based utility functions ensure that Flip-PSRO defenders maintain a high level of control while optimizing performance.

cs.LG↗

arXiv2025

Quantitative Resilience Modeling for Autonomous Cyber Defense

Cyber resilience is the ability of a system to recover from an attack with minimal impact on system operations. However, characterizing a network's resilience under a cyber attack is challenging, as there are no formal definitions of resilience applicable to diverse network topologies and attack patterns. In this work, we propose a quantifiable formulation of resilience that considers multiple defender operational goals, the criticality of various network resources for daily operations, and provides interpretability to security operators about their system's resilience under attack. We evaluate our approach within the CybORG environment, a reinforcement learning (RL) framework for autonomous cyber defense, analyzing trade-offs between resilience, costs, and prioritization of operational goals. Furthermore, we introduce methods to aggregate resilience metrics across time-variable attack patterns and multiple network topologies, comprehensively characterizing system resilience. Using insights gained from our resilience metrics, we design RL autonomous defensive agents and compare them against several heuristic baselines, showing that proactive network hardening techniques and prompt recovery of compromised machines are critical for effective cyber defenses.

cs.CR↗

arXiv2024

Low-Energy On-Device Personalization for MCUs

Microcontroller Units (MCUs) are ideal platforms for edge applications due to their low cost and energy consumption, and are widely used in various applications, including personalized machine learning tasks, where customized models can enhance the task adaptation. However, existing approaches for local on-device personalization mostly support simple ML architectures or require complex local pre-training/training, leading to high energy consumption and negating the low-energy advantage of MCUs. In this paper, we introduce $MicroT$, an efficient and low-energy MCU personalization approach. $MicroT$ includes a robust, general, but tiny feature extractor, developed through self-supervised knowledge distillation, which trains a task-specific head to enable independent on-device personalization with minimal energy and computational requirements. MicroT implements an MCU-optimized early-exit inference mechanism called stage-decision to further reduce energy costs. This mechanism allows for user-configurable exit criteria (stage-decision ratio) to adaptively balance energy cost with model performance. We evaluated MicroT using two models, three datasets, and two MCU boards. $MicroT$ outperforms traditional transfer learning (TTL) and two SOTA approaches by 2.12 - 11.60% across two models and three datasets. Targeting widely used energy-aware edge devices, MicroT's on-device training requires no additional complex operations, halving the energy cost compared to SOTA approaches by up to 2.28X while keeping SRAM usage below 1MB. During local inference, MicroT reduces energy cost by 14.17% compared to TTL across two boards and two datasets, highlighting its suitability for long-term use on energy-aware resource-constrained MCUs.

cs.LG↗