Ask or search anything...

The observation that every two-person adversarial game is an affine transformation of a zero-sum game is traceable to Luce & Raiffa (1957) and made explicit in Aumann (1987). Recent work of (ADP) Adler et al. (2009), and of Raimondo (2023) in increasing generality, proves what has so far remained a conjecture. We present two proofs of an even more general formulation: the first draws on multilinear utility theory developed by Fishburn & Roberts (1978); the second is a consequence of the ADP proof itself for a special case of a two-player game with a set of three actions.

State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these models can grade proofs: detecting errors, judging their severity, and assigning fair scores beyond binary correctness. We study proof-analysis capabilities using a corpus of 90 Gemini 2.5 Pro-generated solutions that we grade on a 1-4 scale with detailed error annotations, and on MathArena solution sets for IMO/USAMO 2025 scored on a 0-7 scale. Our analysis shows that models can reliably flag incorrect (including subtly incorrect) solutions but exhibit calibration gaps in how partial credit is assigned. To address this, we introduce agentic workflows that extract and analyze reference solutions and automatically derive problem-specific rubrics for a multi-step grading process. We instantiate and compare different design choices for the grading workflows, and evaluate their trade-offs. Across our annotated corpus and MathArena, our proposed workflows achieve higher agreement with human grades and more consistent handling of partial credit across metrics. We release all code, data, and prompts/logs to facilitate future research.

In higher dimensional theories, we often assume that the extra dimensions form an orientable space, perhaps with singularities. However, many physical theories are well-defined on non-orientable spaces, and many spaces are not orientable, so it is reasonable to explore what happens if the assumption of orientability is relaxed. Here we consider the simplest example of free 6D theories compactified on a flat Klein bottle. We focus on a Dirac fermion in 6D, with boundary conditions that define ${\rm pin}^+$ and ${\rm pin}^-$ structures. Translation invariance is broken by the boundary conditions, which leads to sharp features localized near the parity walls (fixed points of the reflection used to construct the Klein bottle). For a scalar field, there is a position-dependent energy density, peaked near the parity walls. A Dirac fermion can lead to breaking of parity, charge conjugation and CP in 3+1 dimensions. Order parameters for this breaking are provided by the vevs of certain fermion bilinears, again peaked near the parity walls. As one potential application, these results suggest mechanisms for CP violation and baryogenesis, enabled by compactification on a Klein bottle.

Skin cancer poses a significant public health challenge, necessitating efficient diagnostic tools. We introduce UCM-Net, a novel skin lesion segmentation model combining Multi-Layer Perceptrons (MLP) and Convolutional Neural Networks (CNN). This lightweight, efficient architecture, deviating from traditional UNet designs, dramatically reduces computational demands, making it ideal for mobile health applications. Evaluated on PH2, ISIC 2017, and ISIC 2018 datasets, UCM-Net demonstrates robust performance with fewer than 50KB parameters and requires less than 0.05 Giga Operations Per Second (GLOPs). Moreover, its minimal memory requirement is just 1.19MB in CPU environment positions. It is a potential benchmark for efficiency in skin lesion segmentation, suitable for deployment in resource-constrained settings. In order to facilitate accessibility and further research in the field, the UCM-Net source code is this https URL.

Deep learning (DL) has recently changed the development of intelligent systems and is widely adopted in many real-life applications. Despite their various benefits and potentials, there is a high demand for DL processing in different computationally limited and energy-constrained devices. It is natural to study game-changing technologies such as Binary Neural Networks (BNN) to increase deep learning capabilities. Recently remarkable progress has been made in BNN since they can be implemented and embedded on tiny restricted devices and save a significant amount of storage, computation cost, and energy consumption. However, nearly all BNN acts trade with extra memory, computation cost, and higher performance. This article provides a complete overview of recent developments in BNN. This article focuses exclusively on 1-bit activations and weights 1-bit convolution networks, contrary to previous surveys in which low-bit works are mixed in. It conducted a complete investigation of BNN's development -from their predecessors to the latest BNN algorithms/techniques, presenting a broad design pipeline and discussing each module's variants. Along the way, it examines BNN (a) purpose: their early successes and challenges; (b) BNN optimization: selected representative works that contain essential optimization techniques; (c) deployment: open-source frameworks for BNN modeling and development; (d) terminal: efficient computing architectures and devices for BNN and (e) applications: diverse applications with BNN. Moreover, this paper discusses potential directions and future research opportunities in each section.

Reliable, informative, and individual uncertainty quantification (UQ) remains missing in current ML community. This hinders the effective application of AI/ML to risk-sensitive domains. Most methods either fail to provide coverage on new data, inflate intervals so broadly that they are not actionable, or assign uncertainties that do not track actual error, especially under a distribution shift. In high-stakes drug discovery, protein-ligand affinity (PLI) prediction is especially challenging as assay noise is heterogeneous, chemical space is imbalanced and large, and practical evaluations routinely involve distribution shift. In this work, we introduce a novel uncertainty quantification method, Trustworthy Expert Split-conformal with Scaled Estimation for Efficient Reliable Adaptive intervals (TESSERA), that provides per-sample uncertainty with reliable coverage guarantee, informative and adaptive prediction interval widths that track the absolute error. We evaluate on protein-ligand binding affinity prediction under both independent and identically distributed (i.i.d.) and scaffold-based out-of-distribution (OOD) splits, comparing against strong UQ baselines. TESSERA attains near-nominal coverage and the best coverage-width trade-off as measured by the Coverage-Width Criterion (CWC), while maintaining competitive adaptivity (lowest Area Under the Sparsification Error (AUSE)). Size-Stratified Coverage (SSC) further confirms that intervals are right-sized, indicating width increases when data are scarce or noisy, and remain tight when predictions are reliable. By unifying Mixture of Expert (MoE) diversity with conformal calibration, TESSERA delivers trustworthy, tight, and adaptive uncertainties that are well-suited to selective prediction and downstream decision-making in the drug-discovery pipeline and other applications.

A torus-shaped sail consists of a reflective membrane attached to an inflatable torus-shaped rim. The sail's deployment from its stowed configuration is initiated by introducing inflation pressure into the toroidal rim with an attached circular flat membrane coated by heat-sensitive materials that undergo thermal desorption (TD) from a solid to a gas phase. Our study of the deployment and acceleration of the sail is split into three steps: at a particular heliocentric distance a torus-shaped sail is deployed by a gas inflated into the toroidal rim and the membrane is kept flat by the pressure of the gas; under heating by solar radiation, the membrane coat undergoes TD and the sail is accelerated via TD of coating and solar radiation pressure (SRP); when TD ends, the sail utilizes thrust only from SRP. We study the stability of the torus-shaped sail and deflection and vibration of the flat membrane due to the acceleration by TD and SRP. The stability of the toroidal rim is addressed.

Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can dramatically affect performance. Yet, theoretical understanding of optimal learning strategies remains sparse, especially due to the intricate interplay between evolving meta-parameters and nonlinear learning dynamics. The search for optimal protocols is further hindered by the high dimensionality of the learning space, often resulting in predominantly heuristic, difficult to interpret, and computationally demanding solutions. Here, we combine statistical physics with control theory in a unified theoretical framework to identify optimal protocols in prototypical neural network models. In the high-dimensional limit, we derive closed-form ordinary differential equations that track online stochastic gradient descent through low-dimensional order parameters. We formulate the design of learning protocols as an optimal control problem directly on the dynamics of the order parameters with the goal of minimizing the generalization error at the end of training. This framework encompasses a variety of learning scenarios, optimization constraints, and control budgets. We apply it to representative cases, including optimal curricula, adaptive dropout regularization and noise schedules in denoising autoencoders. We find nontrivial yet interpretable strategies highlighting how optimal protocols mediate crucial learning tradeoffs, such as maximizing alignment with informative input directions while minimizing noise fitting. Finally, we show how to apply our framework to real datasets. Our results establish a principled foundation for understanding and designing optimal learning protocols and suggest a path toward a theory of meta-learning grounded in statistical physics.

Accurate and robust prediction of patient's response to drug treatments is critical for developing precision medicine. However, it is often difficult to obtain a sufficient amount of coherent drug response data from patients directly for training a generalized machine learning model. Although the utilization of rich cell line data provides an alternative solution, it is challenging to transfer the knowledge obtained from cell lines to patients due to various confounding factors. Few existing transfer learning methods can reliably disentangle common intrinsic biological signals from confounding factors in the cell line and patient data. In this paper, we develop a Coherent Deconfounding Autoencoder (CODE-AE) that can extract both common biological signals shared by incoherent samples and private representations unique to each data set, transfer knowledge learned from cell line data to tissue data, and separate confounding factors from them. Extensive studies on multiple data sets demonstrate that CODE-AE significantly improves the accuracy and robustness over state-of-the-art methods in both predicting patient drug response and de-confounding biological signals. Thus, CODE-AE provides a useful framework to take advantage of in vitro omics data for developing generalized patient predictive models. The source code is available at this https URL.

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the vorticity of excitons. We propose that the exciton vorticity can also be experimentally measured by the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of the quantum geometry and the Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

Balancing mutually diverging performance metrics, such as end-to-end latency, accuracy, and device energy consumption, is a challenging undertaking for deep neural network (DNN) inference in Just-in-Time edge environments that are inherently resource-constrained and loosely coupled. In this paper, we design and develop the Infer-EDGE framework that seeks to strike such a balance for latency-sensitive video processing applications. First, using comprehensive benchmarking experiments, we develop intuitions about the trade-off characteristics, which are then used by the framework to develop an Advantage Actor-Critic (A2C) Reinforcement Learning (RL) approach that can choose optimal run-time DNN inference parameters aligning the performance metrics based on the application requirements. Using real-world DNNs and a hardware testbed, we evaluate the benefits of the Infer-EDGE framework in terms of device energy savings, inference accuracy improvement, and end-to-end inference latency reduction.

Dropout is a regularization technique widely used in training artificial neural networks to mitigate overfitting. It consists of dynamically deactivating subsets of the network during training to promote more robust representations. Despite its widespread adoption, dropout probabilities are often selected heuristically, and theoretical explanations of its success remain sparse. Here, we analytically study dropout in two-layer neural networks trained with online stochastic gradient descent. In the high-dimensional limit, we derive a set of ordinary differential equations that fully characterize the evolution of the network during training and capture the effects of dropout. We obtain a number of exact results describing the generalization error and the optimal dropout probability at short, intermediate, and long training times. Our analysis shows that dropout reduces detrimental correlations between hidden nodes, mitigates the impact of label noise, and that the optimal dropout probability increases with the level of noise in the data. Our results are validated by extensive numerical simulations.

Cultural phylogenies, or "trees" of culture, are typically built using methods from biology that use similarities and differences in artifacts to infer the historical relationships between the populations that produced them. While these methods have yielded important insights, particularly in linguistics, researchers continue to debate the extent to which cultural phylogenies are tree-like or reticulated due to high levels of horizontal transmission. In this study, we propose a novel method for phylogenetic reconstruction using dynamic community detection that explicitly accounts for transmission between lineages. We used data from 1,498,483 collaborative relationships between electronic music artists to construct a cultural phylogeny based on observed population structure. The results suggest that, although the phylogeny is fundamentally tree-like, horizontal transmission is common and populations never become fully isolated from one another. In addition, we found evidence that electronic music diversity has increased between 1975 and 1999. The method used in this study is available as a new R package called DynCommPhylo. Future studies should apply this method to other cultural systems such as academic publishing and film, as well as biological systems where high resolution reproductive data is available, to assess how levels of reticulation in evolution vary across domains.

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model, deriving exact equations for the network's predictor statistics under the finite-width thermodynamic limit, i.e., $N,P\rightarrow\infty$, $P/N=\mathcal{O}(1)$, where $N$ is the network width and $P$ is the number of training examples. Our theory shows that the predictor statistics are expressed as a sum of independent kernels, each one pairing different 'attention paths', defined as information pathways through different attention heads across layers. The kernels are weighted according to a 'task-relevant kernel combination' mechanism that aligns the total kernel with the task labels. As a consequence, this interplay between attention paths enhances generalization performance. Experiments confirm our findings on both synthetic and real-world sequence classification tasks. Finally, our theory explicitly relates the kernel combination mechanism to properties of the learned weights, allowing for a qualitative transfer of its insights to models trained via gradient descent. As an illustration, we demonstrate an efficient size reduction of the network, by pruning those attention heads that are deemed less relevant by our theory.

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical attributes of neural representations as population-level mechanistic descriptors of task implementation. In particular, manifold capacity has emerged as a promising framework linking population geometry to the separability of neural manifolds. However, this metric has been limited to linear readouts. To address this limitation, we introduce a theoretical framework that leverages latent directions in input space, which can be related to contextual information. We derive an exact formula for the context-dependent manifold capacity that depends on manifold geometry and context correlations, and validate it on synthetic and real data. Our framework's increased expressivity captures representation reformatting in deep networks at early stages of the layer hierarchy, previously inaccessible to analysis. As context-dependent nonlinearity is ubiquitous in neural systems, our data-driven and theoretically grounded approach promises to elucidate context-dependent computation across scales, datasets, and models.

The Forward Physics Facility (FPF) is a proposed extension of the HL-LHC program designed to exploit the unique scientific opportunities offered by the intense flux of high energy neutrinos, and possibly new particles, in the far-forward direction. Located in a well-shielded cavern 627 m downstream of one of the LHC interaction points, the facility will support a broad and ambitious physics program that significantly expands the discovery potential of the HL-LHC. Equipped with four complementary detectors -- FLArE, FASER$\nu$2, FASER2, and FORMOSA -- the FPF will enable breakthrough measurements that will advance our understanding of neutrino physics, quantum chromodynamics, and astroparticle physics, and will search for dark matter and other new particles. With this Letter of Intent, we propose the construction of the FPF cavern and the construction, integration, and installation of its experiments. We summarize the physics case, the facility design, the layout and components of the detectors, as well as the envisioned collaboration structure, cost estimate, and implementation timeline.