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On a Geometry of Interbrain Networks

Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their explanatory capacity to descriptive observations. Inspired by the successful integration of geometric insights in network science, we propose leveraging discrete geometry to examine the dynamic reconfigurations in neural interactions during social exchanges. Unlike conventional synchrony approaches, our method interprets inter-brain connectivity changes through the evolving geometric structures of neural networks. This geometric framework is realized through a pipeline that identifies critical transitions in network connectivity using entropy metrics derived from curvature distributions. By doing so, we significantly enhance the capacity of hyperscanning methodologies to uncover underlying neural mechanisms in interactive social behavior.

q-bio.NC

Less Data, Faster Training: repeating smaller datasets speeds up learning via sampling biases

This work investigates the ``small-vs-large gap'', where repeating on fewer samples can lead to compute saving during training compared to using a larger dataset. This is observed across algorithmic tasks, architectures and optimizers and cannot be explained using prior theory. We argue that the speedup comes from appropriate layer-wise growth enabled by sampling biases, which is more pronounced when the dataset size is smaller. We provide both theoretical analysis and empirical evidence from various interventions. Our results suggest that using a smaller dataset with more repetitions is not just a fallback strategy under data scarcity, but can be proactively leveraged as a favorable inductive biases for optimization, particularly in reasoning tasks.

cs.LG

Controlling Refusal Behavior of LLMs via Stiefel-Constrained Rotation Steering

Activation steering has emerged as a lightweight approach for controlling model refusal at inference time. A growing line of research explores trainable rotations of activations to develop geometrically principled intervention mechanisms. However, existing techniques rely on auxiliary constructs, such as refusal vectors, to define these rotations. In our work, we develop a self-contained methodology for learning parameter-efficient rotational transformations based on Riemannian optimization. We empirically validate the proposed scheme, demonstrating its superiority in intervention efficiency. An extensive ablation study highlights the importance of key design choices in our method. Our results identify the proposed rotation-based steering scheme as a promising direction for more reliable control over the behavior of LLMs.

cs.LG

Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

Reliable attractor recall conventionally requires broad basins of attraction. However, in reservoir-computing based associative memory, temporal cues reliably recover dynamical memories despite basins dominated by unpredictable, riddled-like regions. We reveal that memory basins exhibit an ``octopus-like'' structure: a robust ``head'' near the attractor and thin, intertwined ``tentacles'' spanning state space. Initial states in tentacular regions yield near-zero uncertainty exponents, making the recalled memory effectively unpredictable at finite precision. Yet, cue-driven generalized synchronization bypasses this unpredictability, driving the system into the robust basin head. This mechanism yields a quantitative relation linking minimum cue duration, synchronization rate, and basin-head radius. Trained recurrent neural networks exhibit similar geometry, suggesting this phenomenon extends beyond reservoir computing.

nlin.CD

It's a matter of timescale: non-linear utility in successor features and multi-objective planning and learning

Time is of the essence when dealing with multiple reward signals and non-linear utility. In this paper we argue that the current main approaches in multi-objective RL (SER and ESR), and successor features, are insufficient. While each approach deals with non-linear effects on user utility on different timescales, none of them take into account that different effects happening on different timescales can happen within the same decision problem. We motivate that this can indeed be the case by an example, both intuitively and numerically, leading to a new perspective, and a significant and non-trivial gap in the literature.

cs.LG

A Stable Aggregation Method for Quantum Federated Learning

Quantum federated learning (QFL) enables clients to train quantum neural network (QNN) models without sharing private data. We find that aggregation in QFL is unstable under heterogeneous data, unreliable communication, variable fidelity, latency, and quantum hardware noise. Moreover, QFL is non-trivially challenging because several QNN parameters are periodic angles, where Euclidean averaging often fails to capture the inherent dynamics. We develop a novel self-consistent midpoint aggregation method for stable QFL design and implementation. We combine QoS-aware client weighting, circular parameter aggregation, and bounded midpoint-based update control. We perform several angular tests and IBM real Quantum machines experiments for validation confirming our approach. Extensive evaluations and experiments on medical and financial datasets show improved stability, lower volatility, and competitive accuracy.

cs.AI

Deep learning based numerical approximation algorithms for stochastic partial differential equations

In this article, we introduce a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied to a set of simulated noise trajectories, it yields empirical distributions of SPDE solutions, from which functionals like the mean and variance can be estimated. We test the performance of the method on stochastic heat equations with additive and multiplicative noise as well as stochastic Black-Scholes equations with multiplicative noise and Zakai equations from nonlinear filtering theory. In all cases, the proposed algorithm yields accurate results with short runtimes in up to 100 space dimensions.

math.NA

Off the Normal Path: Learning Spatial Density Models of Node Mobility

We consider the problem of learning models of spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain. Deriving such models can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability of off-the-shelf mixture density network models and of, two varieties of, normalizing flows for the description of mobile node density over a disk. We introduce the use of Möbius distributions to retain symmetric spatial relations. Our results indicate that mixtures of Möbius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.

cs.NI

Constant Individual Regret in General Games

Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite $N$-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If $m_{\max}$ denotes the largest action-set size, then, simultaneously for every horizon $T\geq1$, it guarantees that each of the $N$ players in the game incurs regret upper bounded by $O(\textrm{poly}(N, \log m_{\max}))$. Our algorithm leverages a new form of optimism inspired by modern filter design.

cs.LG

On-board ML for Trace Gas detection in Imaging Spectroscopy data

Data collected during aerial and spaceborne imaging spectroscopy campaigns enables the detection of transient events such as trace gas emissions. However, current processing pipelines depend on slow, on-the-ground processing, which delays the time to information of each detected event and prohibits immediate follow-up actions. During the Tokyo Field Campaign of March 2026, we explored on-board processing of Imaging Spectroscopy data from the equipped AVIRIS-5 sensor. Due to communication bottlenecks, full datacubes cannot be downlinked immediately during the flight. Instead we downlink the potential events predicted by our efficient and small machine learning model. We show the first on-board detection of methane point source emission with Imaging Spectroscopy data using Edge ML.

cs.LG

Shortcomings and capacities of real-constrained neural networks in complex spaces

We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class. We use weights drawn from the complex Gaussian, which converge asymptotically in norm to the square root of dimension almost surely. Our methods depend on Gardner volume-type comparisons at critical capacity. Our proof relies on an application of the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, nonstandard in literature. With the HCIZ formula, we may obtain a more robust approximation for the final asymptotic ratio. This strategy is applicable to our work specifically since we integrate over the unitary and orthogonal compact manifolds, facilitated via the Weyl integration formula and the Haar measure.

cs.LG

Can machines think efficiently?

The Turing Test is no longer adequate for distinguishing human and machine intelligence. With advanced artificial intelligence systems already passing the original Turing Test and contributing to serious ethical and environmental concerns, we urgently need to update the test. This work expands upon the original imitation game by accounting for an additional factor: the energy spent answering the questions. By adding the constraint of energy, the new test forces us to evaluate intelligence through the lens of efficiency, connecting the abstract problem of thinking to the concrete reality of finite resources. Further, this proposed new test ensures the evaluation of intelligence has a measurable, practical finish line that the original test lacks. This additional constraint compels society to weigh the time savings of using artificial intelligence against its total resource cost.

cs.LG

Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control

We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under known distributions, and show that it reduces to a prediction set-based solution for the CVaR. This provides an operational interpretation of conformal prediction-type prediction sets. For unknown distributions, we develop a data-driven calibration strategy, based on a synthetic model for the likelihood and held-out calibration data, yielding high-probability control of the OCE risk. The approach is evaluated on two wireless beamforming settings.

stat.ML

Accelerate Vector Diffusion Maps by Landmarks

We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.

stat.ML

A Target-Centric Survey of Quantization-Aware Training

The rapid development of LLMs incurs prohibitive memory footprints and intensive computational demands. Quantization-Aware Training (QAT) techniques have emerged as a promising solution to address these challenges by explicitly simulating quantization effects during model training, yielding low-bit models that achieve accuracy comparable to their full-precision counterparts. In this work, we provide a target-centric survey of QAT, aimed at clarifying both its theoretical foundations and its evolving implementation landscape. We systematically review existing QAT methods through a target-centric taxonomy and synthesize cross-target differences in error characteristics, numerical formats, and strategy transferability. We further summarize QAT evaluation paradigms and discuss challenges in optimization and deployment, outlining potential directions for future research.

cs.LG

Online Learning with LLM Experts from Limited Feedback

We study adaptive routing of prompts to large language model (LLM) experts to maximize response quality in an online setting with limited feedback. We formulate it as a bandit problem with $K$ actions that represent experts and $d$ features that encode prompts, over a horizon of $T$ rounds. We propose algorithms that strategically select and observe rewards to minimize regret. In the full-information setting, we achieve a regret of $\tilde{O}(d T / \sqrt{m})$, while in the bandit setting we achieve $\tilde{O}(d T \sqrt{K / m})$, where $m \ll T$ is a budget on feedback. Our experiments show that we efficiently learn high-quality routing strategies across diverse LLMs from limited feedback.

cs.LG

Frontier LLMs are effective batch optimizers: Assessing reasoning models in continuous and discrete settings

Frontier large language models (LLMs) have become attractive priors for optimization due to their large-scale pretraining that enables them to navigate a variety of optimization settings. However, the effectiveness of modern reasoning LLMs in batch optimization settings remains underexplored. Here we investigate the performance of the current generation of frontier LLMs as batch optimizers in both continuous and discrete settings. We find that while LLMs are competitive zero-shot batch optimizers for numerical test functions, their performance is brittle compared to classical non-LLM optimization approaches. However, LLM priors are significantly better in semantically rich settings, indicating that their batch optimization behavior is highly effective when navigating and reasoning over the discrete spaces most similar in structure to their pretraining data.

cs.LG

Secure AI-Driven Super-Resolution for Real-Time Mixed Reality Applications

Immersive formats such as 360° and 6DoF point cloud videos require high bandwidth and low latency, posing challenges for real-time AR/VR streaming. This work focuses on reducing bandwidth consumption and encryption/decryption delay, two key contributors to overall latency. We design a system that downsamples point cloud content at the origin server and applies partial encryption. At the client, the content is decrypted and upscaled using an ML-based super-resolution model. Our evaluation demonstrates a nearly linear reduction in bandwidth/latency, and encryption/decryption overhead with lower downsampling resolutions, while the super-resolution model effectively reconstructs the original full-resolution point clouds with minimal error and modest inference time.

cs.CR