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Recent 3D Gaussian splatting methods built atop SMPL achieve remarkable visual fidelity while continually increasing the complexity of the overall training architecture. We demonstrate that much of this complexity is unnecessary: by replacing SMPL with the Momentum Human Rig (MHR), estimated via SAM-3D-Body, a minimal pipeline with no learned deformations or pose-dependent corrections achieves the highest reported PSNR and competitive or superior LPIPS and SSIM on PeopleSnapshot and ZJU-MoCap. To disentangle pose estimation quality from body model representational capacity, we perform two controlled ablations: translating SAM-3D-Body meshes to SMPL-X, and translating the original dataset's SMPL poses into MHR both retrained under identical conditions. These ablations confirm that body model expressiveness has been a primary bottleneck in avatar reconstruction, with both mesh representational capacity and pose estimation quality contributing meaningfully to the full pipeline's gains.

EEG recordings contain rich information about neural activity but are subject to artifacts, noise, and superficial differences due to sensors, amplifiers, and filtering. Independent component analysis and automatic labeling of independent components (ICs) enable artifact removal in EEG pipelines. Convolutional Monge Mapping Normalization (CMMN) is a recent tool used to achieve spectral conformity of EEG signals, which was shown to improve deep neural network approaches for sleep staging. Here we propose a novel extension of the CMMN method with two alternative approaches to computing the source reference spectrum the target signals are mapped to: (1) channel-averaged and $l_1$-normalized barycenter, and (2) a subject-to-subject mapping that finds the source subject with the closest spectrum to the target subject. Notably, our extension yields space-time separable filters that can be used to map between datasets with different numbers of EEG channels. We apply these filters in an IC classification task, and show significant improvement in recognizing brain versus non-brain ICs. Clinical relevance - EEG recordings are used in the diagnosis and monitoring of multiple neuropathologies,

This work studies certain notions of entropy that can be associated to (i) a representation of a separable, unital C*-algebra $\mathfrak{A}$ and (ii) an auxiliary random sequence $(π_n)_{n\ge 1}$ of finite-dimensional representations of $\mathfrak{A}$. This continues a previous research program into the properties of these entropy notions when each $π_n$ is deterministic, which uncovered a range of analogies with entropy in ergodic theory and also with non-commutative generalizations of Szegő's limit theorems. We associate two new notions of entropy to data as in (i) and (ii) above: `annealed' AP entropy, which is roughly a kind of first-moment average of deterministic AP entropies; and `zeroth-order' AP entropy, which controls the large deviations probabilities that certain positive definite functions appear in the representations $π_n$ at all. After developing some of this general theory, we then focus on the special case in which $\mathfrak{A}$ is the group C*-algebra of a finitely-generated free group and each $π_n$ is generated by choosing a tuple of $n$-by-$n$ unitary matrices independently at random from Haar measure. In that case, explicit formulas can be derived for some o

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on Følner sequences for amenable groups, entropy defined using a random ordering of the group, and Bowen's sofic entropy for sofic groups. In this work we pursue these notions across an analogy between ergodic theory and representation theory. We arrive at new quantities associated to unitary representations of groups and representations of other C*-algebras. Our main results show that these new quantities can often be evaluated as Fuglede--Kadison determinants. The resulting determinantal formulas offer various non-commutative generalizations of Szegő's limit theorem for Toeplitz determinants. They make contact with Arveson's theory of subdiagonal subalgebras, and also with some entropy formulas in the ergodic theory of actions by automorphisms of compact Abelian groups.

Prompt engineering for large language models (LLMs) is often a manual time-intensive process that involves generating, evaluating, and refining prompts iteratively to ensure high-quality outputs. While there has been work on automating prompt engineering, the solutions generally are either tuned to specific tasks with given answers or are quite costly. We introduce GRAD-SUM, a scalable and flexible method for automatic prompt engineering that builds on gradient-based optimization techniques. Our approach incorporates user-defined task descriptions and evaluation criteria, and features a novel gradient summarization module to generalize feedback effectively. Our results demonstrate that GRAD-SUM consistently outperforms existing methods across various benchmarks, highlighting its versatility and effectiveness in automatic prompt optimization.

Let $S$ and $T$ be measure-preserving transformations of a probability space $(X,{\mathcal B},μ)$. Let $f$ be a bounded measurable functions, and consider the integrals of the corresponding `double' ergodic averages: \[\frac{1}{n}\sum_{i=0}^{n-1} \int f(S^ix)f(T^ix)\ dμ(x) \qquad (n\ge 1).\] We construct examples for which these integrals do not converge as $n\to\infty$. These include examples in which $S$ and $T$ are rigid, and hence have entropy zero, answering a question of Frantzikinakis and Host. Our proof begins with a corresponding construction for orthogonal operators on a Hilbert space, and then obtains transformations of a Gaussian measure space from them.

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Space solar power (SSP), envisioned for decades as a solution for continuous, stable, and dynamically dispatchable clean energy, has seen tremendous interest and a number of experimental demonstrations in the last few years. A practical implementation has been elusive to date, owing to the high launch costs associated with heavy, rigid photovoltaic (PV) and wireless power transfer (WPT) arrays. Lightweight and flexible solutions for WPT have been demonstrated terrestrially but, to date, have not been deployed and tested in space. In this paper, we present an experimental space demonstration of a lightweight, flexible WPT array powered by custom radio frequency integrated circuits (RFICs). The transmit arrays, receive arrays, and the rest of the system were operated and tested for eight months in Low Earth Orbit (LEO). Results from these experiments, including pointing of the array's beam to Earth and its detection by a ground station, are presented and discussed in detail. Observations and results from this mission uncover existing strengths and weaknesses that inform future steps toward realizing SSP.

Chain-of-thought (CoT) outputs let us read a model's step-by-step reasoning. Since any long, serial reasoning process must pass through this textual trace, the quality of the CoT is a direct window into what the model is thinking. This visibility could help us spot unsafe or misaligned behavior (monitorability), but only if the CoT is transparent about its internal reasoning (faithfulness). Fully measuring faithfulness is difficult, so researchers often focus on examining the CoT in cases where the model changes its answer after adding a cue to the input. This proxy finds some instances of unfaithfulness but loses information when the model maintains its answer, and does not investigate aspects of reasoning not tied to the cue. We extend these results to a more holistic sense of monitorability by introducing verbosity: whether the CoT lists every factor needed to solve the task. We combine faithfulness and verbosity into a single monitorability score that shows how well the CoT serves as the model's external `working memory', a property that many safety schemes based on CoT monitoring depend on. We evaluate instruction-tuned and reasoning models on BBH, GPQA, and MMLU. Our results