ARIADNE: A Perception-Reasoning Synergy Framework for Trustworthy Coronary Angiography Analysis

Conventional pixel-wise loss functions fail to enforce topological constraints in coronary vessel segmentation, producing fragmented vascular trees despite high pixel-level accuracy. We present ARIADNE, a two-stage framework coupling preference-aligned perception with RL-based diagnostic reasoning for topologically coherent stenosis detection. The perception module employs DPO to fine-tune the Sa2VA vision-language foundation model using Betti number constraints as preference signals, aligning the policy toward geometrically complete vessel structures rather than pixel-wise overlap metrics. The reasoning module formulates stenosis localization as a Markov Decision Process with an explicit rejection mechanism that autonomously defers ambiguous anatomical candidates such as bifurcations and vessel crossings, shifting from coverage maximization to reliability optimization. On 1,400 clinical angiograms, ARIADNE achieves state-of-the-art centerline Dice of 0.838, reduces false positives by 41% compared to geometric baselines. External validation on multi-center benchmarks ARCADE and XCAD confirms generalization across acquisition protocols. This represents the first application of DPO for topological alignment in medical imaging, demonstrating that preference-based learning over structural constraints mitigates topological violations while maintaining diagnostic sensitivity in interventional cardiology workflows.

Training Generalizable Collaborative Agents via Strategic Risk Aversion

Many emerging agentic paradigms require agents to collaborate with one another (or people) to achieve shared goals. Unfortunately, existing approaches to learning policies for such collaborative problems produce brittle solutions that fail when paired with new partners. We attribute these failures to a combination of free-riding during training and a lack of strategic robustness. To address these problems, we study the concept of strategic risk aversion and interpret it as a principled inductive bias for generalizable cooperation with unseen partners. While strategically risk-averse players are robust to deviations in their partner's behavior by design, we show that, in collaborative games, they also (1) can have better equilibrium outcomes than those at classical game-theoretic concepts like Nash, and (2) exhibit less or no free-riding. Inspired by these insights, we develop a multi-agent reinforcement learning (MARL) algorithm that integrates strategic risk aversion into standard policy optimization methods. Our empirical results across collaborative benchmarks (including an LLM collaboration task) validate our theory and demonstrate that our approach consistently achieves reliable collaboration with heterogeneous and previously unseen partners across collaborative tasks.

Provably Convergent Actor-Critic in Risk-averse MARL

Learning stationary policies in infinite-horizon general-sum Markov games (MGs) remains a fundamental open problem in Multi-Agent Reinforcement Learning (MARL). While stationary strategies are preferred for their practicality, computing stationary forms of classic game-theoretic equilibria is computationally intractable -- a stark contrast to the comparative ease of solving single-agent RL or zero-sum games. To bridge this gap, we study Risk-averse Quantal response Equilibria (RQE), a solution concept rooted in behavioral game theory that incorporates risk aversion and bounded rationality. We demonstrate that RQE possesses strong regularity conditions that make it uniquely amenable to learning in MGs. We propose a novel two-timescale Actor-Critic algorithm characterized by a fast-timescale actor and a slow-timescale critic. Leveraging the regularity of RQE, we prove that this approach achieves global convergence with finite-sample guarantees. We empirically validate our algorithm in several environments to demonstrate superior convergence properties compared to risk-neutral baselines.

Renormalizable Spectral-Shell Dynamics as the Origin of Neural Scaling Laws

Neural scaling laws and double-descent phenomena suggest that deep-network training obeys a simple macroscopic structure despite highly nonlinear optimization dynamics. We derive such structure directly from gradient descent in function space. For mean-squared error loss, the training error evolves as $\dot e_t=-M(t)e_t$ with $M(t)=J_{θ(t)}J_{θ(t)}^{\!*}$, a time-dependent self-adjoint operator induced by the network Jacobian. Using Kato perturbation theory, we obtain an exact system of coupled modewise ODEs in the instantaneous eigenbasis of $M(t)$. To extract macroscopic behavior, we introduce a logarithmic spectral-shell coarse-graining and track quadratic error energy across shells. Microscopic interactions within each shell cancel identically at the energy level, so shell energies evolve only through dissipation and external inter-shell interactions. We formalize this via a \emph{renormalizable shell-dynamics} assumption, under which cumulative microscopic effects reduce to a controlled net flux across shell boundaries. Assuming an effective power-law spectral transport in a relevant resolution range, the shell dynamics admits a self-similar solution with a moving resolution frontier and explicit scaling exponents. This framework explains neural scaling laws and double descent, and unifies lazy (NTK-like) training and feature learning as two limits of the same spectral-shell dynamics.

When Does Learning Renormalize? Sufficient Conditions for Power Law Spectral Dynamics

Empirical power--law scaling has been widely observed across modern deep learning systems, yet its theoretical origins and scope of validity remain incompletely understood. The Generalized Resolution--Shell Dynamics (GRSD) framework models learning as spectral energy transport across logarithmic resolution shells, providing a coarse--grained dynamical description of training. Within GRSD, power--law scaling corresponds to a particularly simple renormalized shell dynamics; however, such behavior is not automatic and requires additional structural properties of the learning process. In this work, we identify a set of sufficient conditions under which the GRSD shell dynamics admits a renormalizable coarse--grained description. These conditions constrain the learning configuration at multiple levels, including boundedness of gradient propagation in the computation graph, weak functional incoherence at initialization, controlled Jacobian evolution along training, and log--shift invariance of renormalized shell couplings. We further show that power--law scaling does not follow from renormalizability alone, but instead arises as a rigidity consequence: once log--shift invariance is combined with the intrinsic time--rescaling covariance of gradient flow, the renormalized GRSD velocity field is forced into a power--law form.

A Generalized Spectral Framework to Expain Neural Scaling and Compression Dynamics

Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported for related settings such as model compression. Motivated by recent progress in spectral analyses of neural representations, this paper develops a \emph{generalized spectral framework} that unifies learning dynamics and compression phenomena under a common functional ansatz. We generalize the spectral evolution function from the linear kernel form $g(λt)=λt$ to an asymptotically polynomial function $g(λ,t;β)$, characterized by an effective spectral--temporal elasticity $ρ(β)$. This framework recovers existing lazy and feature-learning theories as special cases and yields an invariant relation between learning and compression

SONAR: Self-Distilled Continual Pre-training for Domain Adaptive Audio Representation

Self-supervised learning (SSL) on large-scale datasets like AudioSet has become the dominant paradigm for audio representation learning. While the continuous influx of new, unlabeled audio presents an opportunity to enrich these static representations, a naive approach is to retrain the model from scratch using all available data. However, this method is computationally prohibitive and discards the valuable knowledge embedded in the previously trained model weights. To address this inefficiency, we propose SONAR (Self-distilled cONtinual pre-training for domain adaptive Audio Representation), a continual pre-training framework built upon BEATs. SONAR effectively adapts to new domains while mitigating catastrophic forgetting by tackling three key challenges: implementing a joint sampling strategy for new and prior data, applying regularization to balance specificity and generality, and dynamically expanding the tokenizer codebook for novel acoustic patterns. Experiments across four distinct domains demonstrate that our method achieves both high adaptability and robust resistance to forgetting.

KL-regularization Itself is Differentially Private in Bandits and RLHF

Differential Privacy (DP) provides a rigorous framework for privacy, ensuring the outputs of data-driven algorithms remain statistically indistinguishable across datasets that differ in a single entry. While guaranteeing DP generally requires explicitly injecting noise either to the algorithm itself or to its outputs, the intrinsic randomness of existing algorithms presents an opportunity to achieve DP ``for free''. In this work, we explore the role of regularization in achieving DP across three different decision-making problems: multi-armed bandits, linear contextual bandits, and reinforcement learning from human feedback (RLHF), in offline data settings. We show that adding KL-regularization to the learning objective (a common approach in optimization algorithms) makes the action sampled from the resulting stochastic policy itself differentially private. This offers a new route to privacy guarantees without additional noise injection, while also preserving the inherent advantage of regularization in enhancing performance.

Learning to Steer Learners in Games

We consider the problem of learning to exploit learning algorithms through repeated interactions in games. Specifically, we focus on the case of repeated two player, finite-action games, in which an optimizer aims to steer a no-regret learner to a Stackelberg equilibrium without knowledge of its payoffs. We first show that this is impossible if the optimizer only knows that the learner is using an algorithm from the general class of no-regret algorithms. This suggests that the optimizer requires more information about the learner's objectives or algorithm to successfully exploit them. Building on this intuition, we reduce the problem for the optimizer to that of recovering the learner's payoff structure. We demonstrate the effectiveness of this approach if the learner's algorithm is drawn from a smaller class by analyzing two examples: one where the learner uses an ascent algorithm, and another where the learner uses stochastic mirror ascent with known regularizer and step sizes.

Understanding Artificial Neural Network's Behavior from Neuron Activation Perspective

This paper explores the intricate behavior of deep neural networks (DNNs) through the lens of neuron activation dynamics. We propose a probabilistic framework that can analyze models' neuron activation patterns as a stochastic process, uncovering theoretical insights into neural scaling laws, such as over-parameterization and the power-law decay of loss with respect to dataset size. By deriving key mathematical relationships, we present that the number of activated neurons increases in the form of $N(1-(\frac{bN}{D+bN})^b)$, and the neuron activation should follows power-law distribution. Based on these two mathematical results, we demonstrate how DNNs maintain generalization capabilities even under over-parameterization, and we elucidate the phase transition phenomenon observed in loss curves as dataset size plotted in log-axis (i.e. the data magnitude increases linearly). Moreover, by combining the above two phenomenons and the power-law distribution of neuron activation, we derived the power-law decay of neural network's loss function as the data size scale increases. Furthermore, our analysis bridges the gap between empirical observations and theoretical underpinnings, offering experimentally testable predictions regarding parameter efficiency and model compressibility. These findings provide a foundation for understanding neural network scaling and present new directions for optimizing DNN performance.