Papers

In this work we construct three-dimensional Chern–Simons gravity theories for the six resonant $JPZ$ algebras generated by the Lorentz generators $J_a$, translations $P_a$, and an additional Lorentz-like generator $Z_a$. The resonance condition together with the Jacobi identities leaves precisely six configurations arising from the semigroup expansions. Our main result is that three of them, $B_4$, $\widetilde C_4$, and $C_4$, are isomorphic to $iso(2,1)\oplus so(2,1)$, although they yield different gravitational realizations when we keep the original $JPZ$ field identification fixed. For each case $JPZ$, we determine the invariant tensors, gauge curvatures, Chern–Simons action, field equations, and the corresponding maximal-rank coupling sectors. The field equations can be written in the compact form $\Omega_\sigma\mathbf F=0$, which makes explicit how the additional field $h^a$ contributes to the curvature, torsion, and the remaining gauge-curvature components. We use the direct-sum isomorphisms to classify the local metric sectors and to relate them to known global and asymptotic solutions, while keeping the gravitational interpretation tied to the original $(\omega,e,h)$ fields.

We study the optimal score $T_{n,m}$ in a complete feedback card guessing game. The deck has $n$ types and $m$ cards of each type. Its predictable compensator $S_{n,m}$ is the sum of the conditional success probabilities. We prove that Var$(S_{n,m})\leq C((\log\log n)^2+m/\log n)$, uniformly in $m$ for large $n$. This bound yields a central limit theorem for every sequence $m=m_n\geq1$ as $n\to\infty$. The score variance is asymptotic to its mean. We also give uniform Kolmogorov bounds using the conditional Bernoulli moments. For $m,n\to\infty$, the excess mean is asymptotic to $(\log n)\log\min\{m,\log n\}+(\pi/\sqrt2)\sqrt{m\log n}$. The two contributions balance at $m\asymp(\log n)(\log\log n)^2$. The variance proof uses reversed occupancy hitting times. Discrete hypergeometric tail estimates control their fluctuations in the large-deviation, Gaussian, and saturation regimes. For fixed $n$, we also show that the compensator has a Brownian-bridge functional limit as $m\to\infty$.

With the incessant demand for green and sustainable communications, energy efficiency (EE) has become a cornerstone of sixth-generation (6G) network design, especially for cell-free millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, which can achieve significant throughput gains by leveraging large-scale antenna arrays. Adaptive radio frequency (RF) chain activation (ARFA) is a key technique for reducing power consumption without severely degrading the achievable rate, thereby enhancing the total EE of 6G MIMO systems. In this paper, we propose a minimum-cost maximum-flow (MCMF)-based ARFA scheme to reduce unnecessary power consumption and maximize the total EE of uplink mmWave cell-free massive MIMO systems. Simulation results indicate that the proposed approach can significantly improve the total EE while maintaining a relatively high achievable rate and acceptable computational complexity.

In a smart grid, consumers can also play the role of producers and sellers of energy. Therefore, the control of a smart grid over time becomes a dynamic game with a large number of small players and one or several large players. This is much more complicated than the control of an energy system with a single producer. The framework of mean-field games with common noise allows the transformation of such a complicated model into a control problem for a typical prosumer (producer and consumer in one) optimizing his behavior against a flow of other such prosumers. In our model, we introduce 2 decision variables for such a controller: one describing the amount of electric energy bought from the grid (or sold to it), and the second one describing the charging rate for our battery. The cost function is designed to satisfy two goals: satisfying the demand of the consumer (a single home) and minimizing the payment for energy. Players are allowed to sell/buy energy from the grid. Common noise is hidden in price volatility and sun irradiance, which influence all the players. We compute the optimal controls for our model and simulate solutions on real data. The novelty of our construction, compared to other works on smart grid control, lies in combining the minimization of the cost of energy and sustaining some level of demand satisfaction. We analyze the impact of battery usage on achieving a balance between these two criteria. We also take into account that the smart grid is only part of the energy market, which makes consumer strategies dependent on energy consumption outside the grid.

Let $p$ be an odd prime and let $C_R$ be the van der Geer-van der Vlugt curve $y^p-y=xR(x)$ over an algebraically closed field of characteristic $p$, where $R(x)=\sum_{i=0}^{h}a_ix^{p^i}$ is an additive polynomial of degree $p^h$. We determine the image and the rank of every power of the Cartier operator $\Cart$ on $H^0(C_R,\Omg)$. For $1\le r\le h-1$ the image of $\Cart^r$ is spanned by an explicit set of monomial differentials that does not depend on $R$, and $\rank(\Cart^r)=p^{h-r-1}\binom{p+r}{r+2}$. The last iterate detects the linear coefficient: $\rank(\Cart^h)=0$ if $a_0=0$ and $\rank(\Cart^h)=\binom{(p-1)/2+h}{h+1}$ if $a_0\neq0$, so the nilpotency index of $\Cart$ is $h$ or $h+1$. Hence, for $h\ge2$, the loci $a_0=0$ and $a_0\ne0$ have the same $a$-number, which is the largest $a$-number of a one-point Artin-Schreier curve with pole order $p^h+1$, but they share no Ekedahl-Oort type. Over finite fields we deduce that a curve over $\F_{p^{2n}}$ that is geometrically isomorphic to $C_R$ can be $\F_{p^{2n}}$-maximal or $\F_{p^{2n}}$-minimal only if $n\ge h$, and only if $n\ge h+1$ when $a_0\neq0$. Explicit examples show that the second bound is attained for $(p,h)=(3,1)$, $(3,2)$ and $(5,2)$.

Cavity optomechanical models typically treat a sensor either as a perturbative polarizable object in a pre-existing optical field, or solve the field at a fixed equilibrium and linearize in a fixed optical-mode basis. Neither self-consistently determines the spatially resolved cavity field, the optical force, the mechanical equilibrium, and the back-action when a finite-thickness dielectric plate intercepts the entire optical mode and restructures the intracavity field. In this companion paper to [1], we develop that treatment by extending the vacuum two-photon formalism to finite-thickness planar dielectrics, incorporating their Fresnel reflection, internal propagation, optical forces, and mechanical back-action directly into the field equations. We derive the carrier and sideband transfer functions needed to describe the coupled optical-mechanical system, including optomechanical cooling and the response to external perturbations. The result is a systematic starting point for calculating detector response and noise budgets for cavity experiments with intracavity dielectrics, including gravitational wave detectors deploying levitated sensors.

Holographic devices must reconstruct an entire light field given a finite number of spatial light modulator (SLM) pixels, and must do so using scalar-wave diffraction from coherent illumination alone. As a result, computer-generated holography (CGH) often has speckling artifacts. We propose HoOPOE (Holography-Optimized Perceptual ObjectivE function), a CGH-specific, perceptually-aware loss function that hides speckles from human vision. HoOPOE is effective for CGH optimizations because it accounts for the human visual system's sensitivity to spatio-temporal frequencies and color, and its parameters are tuned to maximize its performance as a loss function for CGH. We use HoOPOE to generate holograms for mesh-derived focal stacks. We then conduct a user study to benchmark HoOPOE-generated holograms against existing loss functions. HoOPOE yields the most visually pleasing results; users prefer HoOPOE 68% of the time over the next best objective function on average.

Generative safety guards must classify requests correctly and return outputs that applications can parse. Reasoning guards can improve classification accuracy while producing outputs that applications cannot parse. When applications cannot extract a correct prediction, fallback handling can allow harmful requests or block safe ones. We introduce Resolve–Express–Act (REA), a framework that traces judgments through parsing and fallback to application actions. Experiments on classifiers and safety guards show that correct predictions can appear in incorrectly formatted outputs. Parsing the safety verdict preserves the reasoning guard's accuracy advantage, while stricter explanation requirements reject additional correct predictions. Accepting formatting variations recovers most rejected correct predictions. Held-out tests confirm that output requirements and generation limits affect whether correct predictions can be parsed. In our fail-open replay, matching the parser to the output and fixing formatting reduced the fraction of harmful requests allowed despite correct guard judgments from 95.5% to 0%. A fixed-output comparison shows that model-based extraction can preserve guard verdicts, but is not automatically reliable; deterministic normalization already repairs the observed native-format failures. Fallback replay shows that the same correct prediction can lead to different safety actions depending on the parser and fallback policy, including allowing requests the guard correctly identifies as harmful.

We consider the cone Yang-Mills functional recently introduced by Tseng and Zhou. This functional generalizes the Yang-Mills functional by coupling it to a closed 2-form which can represent a geometric structure of interest, e.g. a symplectic form or Ricci form. While the perspective of dimensional reduction is not always possible, we show that a cone Yang-Mills field is always locally the dimensional reduction of a pure Yang-Mills field. We then prove a monotonicity formula and use the dimensional reduction framework to prove an $\epsilon$-regularity theorem in two ways. Finally, we prove a compactness theorem for sequences of cone Yang-Mills connections with bounded action and $L^p$-bounded Higgs fields. Away from a singular set of codimension at least 4 and after suitable bundle identifications, the sequence subconverges in the $C^\infty_{\operatorname{loc}}$-topology.

Multi-agent systems promise a new axis for scaling inference: rather than having one agent think longer or sample more attempts, a task is split across many agents that work in parallel and coordinate. However, in practice, more agents can easily produce duplicate work, coordination failures, and higher costs. We therefore formulate team design as a compute allocation problem: starting from a solo agent, where should additional inference compute go to reach the reward-cost Pareto frontier? We build a minimal multi-agent harness from the ground up and trace this frontier by varying, one at a time, the workflow stage at which a lead delegates to its workers (planning, implementation, or verification), the models that form the team, and the number of workers. On ProgramBench, teams outperform solo agents but cost three to seven times as much. With the right compute allocation, however, a heterogeneous 17-agent team comes within 1.4 points of a strong homogeneous 5-agent team at 70% lower cost. This efficiency stems from three findings. First, planning is the most valuable use of workers: in a homogeneous team whose lead decides how many workers to spawn, a lead that delegates only planning to its workers, and then implements and verifies the code itself, matches the reward of a lead that delegates to workers throughout planning, implementation, and verification, at half the cost. Second, cheap models pay off as planners but not as implementers: a strong lead with cheap planners recovers 47.5% of the reward gain of an all-strong team for only 13.9% of its additional cost, whereas cheap implementers lower reward. Third, planners keep improving reward as the team grows, whereas implementers and verifiers plateau beyond four workers. Together, our results offer a guide to spending an agent budget where it counts, given the task, cost, and latency constraints a user has.

Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure $SU(3)$ lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model $\texttt{H2-2}$, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires $\sim 25n$ entangling gates for $n$ Trotter steps.

Social media platforms generate vast volumes of user-generated content that often obscure meaningful discourse, a phenomenon conceptualized as social noise. While existing misinformation detection methods primarily focus on factual verification, they largely overlook the role of social noise in amplifying misinformation. This study assesses the performance of six text-based models and a graph neural network (GNN) in mitigating the effects of misinformation using predefined social noise constructs. The dataset consists of 500,000 tweets collected from the X platform using the Ukraine hashtag during the Russia-Ukraine conflict from March 2024 to March 2025. Advanced machine learning models achieve strong performance, with accuracies ranging from 79.94% to 97.17%. RoBERTa demonstrates the highest performance, with an accuracy of 97.17%, Cohen's kappa of 0.9660, MCC of 0.9660, and AUC of 0.9977. The GNN achieves an accuracy of 64.52% and an AUC of 0.899, demonstrating performance above random-chance classification by exploiting the relational structure between tweets. All text-based models achieve kappa values greater than 0.75, indicating substantial overall agreement. Explainable AI analysis using LIME reveals that 89.6% of predictive weight is attributed to contextual features rather than isolated keywords. The findings highlight that integrating social noise into AI pipelines enhances misinformation detection and supports more effective mitigation strategies in large-scale social media environments.

As the complexity of space missions increases, autonomous spacecraft guidance must accommodate transitions between mission phases with distinct dynamics, objectives, and constraints. Rendezvous and proximity operations (RPO) are particularly challenging because they span multiple operating regimes, from orbital-scale matching and far-range approach to close-range maneuvering and terminal docking. Existing reinforcement-learning approaches generally address only a subset of this sequence or rely on manually defined switching conditions between controllers. This study presents a hierarchical reinforcement-learning framework for autonomous, three-degree-of-freedom RPO that spans the complete trajectory from orbit matching to docking. Five specialized policies are trained for orbit matching, far-range approach, mid-range approach, close-range approach, and docking. A learned high-level manager policy then selects among these phase-specific controllers based on the evolving spacecraft state. The hierarchical approach is evaluated over the full end-to-end rendezvous sequence and compared with a fixed sequential-invocation heuristic to assess trajectory performance and transition behavior. Training and inference metrics are also analyzed for the individual phase policies and the complete hierarchical system.

Generative retrieval is known for its efficient end-to-end indexing and retrieval. In particular, numeric Document Identifiers (DocIDs) are generally more efficient because they are shorter and generally fixed-length sequences over a small vocabulary, requiring fewer decoding steps during beam search. However, they tend to generalize poorly to unseen documents and must be learned during indexing-stage training. In this paper, we propose a numeric DocID design for generative retrieval that enables better adaptation to unseen documents without retraining. Our DocID design inherits the language model's knowledge: each DocID is a sequence of tokens factorized into bits, and each token is scored as the sum of its bits. Unlike existing numeric DocIDs, whose tokens carry meaning only through embeddings memorized during indexing training, each bit here derives its meaning from the model's representation. Therefore, the DocIDs of unseen documents remain scorable without retraining. Experiments on three benchmarks show that our DocID design substantially improves unseen-document retrieval while maintaining comparable performance on seen documents. It achieves over 20 percentage points higher Hit@10 on unseen documents and up to 7 times lower inference latency than existing numeric DocID designs on NQ320K and TriviaQA, while performing only 3 percentage points below weight-update methods on MS MARCO without additional training. These results show that an appropriate DocID design can heavily reduce retraining costs when adapting generative retrievers to new documents.

Fréchet Distributional (FD) objectives provide an effective distribution-level signal for post-training generative models. For latent generative models, however, existing FD-based post-training methods optimize only the latent generator while keeping the decoder frozen: the decoder is trained on reconstruction latents obtained from real images but deployed on generator-produced latents at generation time. When these latent distributions differ, this decoder train-generation mismatch means that the decoder is deployed on inputs drawn from a distribution it was not directly trained on. We introduce Fréchet Distributional Decoder Alignment (FDDA), an efficient post-training method that freezes the latent generator and directly optimizes the decoder on generation-time latents using an FD objective. A single epoch of FDDA consistently improves gFID and gFDr$^6$ across diverse flow-based and autoregressive latent generative models. Across all 11 evaluated models, FDDA reduces gFDr$^6$ by 34.0-59.6% from the original pretrained models and provides a further 10.2-57.2% reduction after generator-side FD post-training. FDDA also reduces total wall-clock time by factors of $3.6\times$-$328.7\times$ relative to generator-side FD post-training across these models. These results show that generator-side post-training alone does not exhaust the benefits of FD optimization, and that further gains can be obtained by adapting the decoder at substantially lower cost.

We investigate a newsvendor problem where a decision-maker observes a $z$-dimensional vector of covariates, and wants to learn how much stock to order given a sample of size $n$ of censored demand data to minimize costs. Demand is censored when insufficient stock is available to meet it, and past stocking quantities are known. We propose a new model-agnostic loss function approach to estimate optimal order quantities using observational data, and characterize the optimal newsvendor policy as the policy that minimizes our proposed loss function. Our method requires only a single estimation step, can be scaled to datasets with hundreds of thousands of data points, and does not suffer from the same instabilities as inverse censoring probability weighting methods. We describe how this loss function can be implemented in linear empirical risk minimization, kernel weights optimization and deep neural network algorithms, and provide excess risk generalization bounds for their out-of-sample performance. Moreover, we show through numerical experiments that our method quickly converges to the optimal policy on synthetic data, and leads to improved performance on real world retail data.

A Dirac mass is characterized not only by its magnitude but also by its sign, which influences the Berry curvature, Hall response, and the propagation direction of chiral boundary modes. However, local spectroscopy of magnetic topological surfaces has so far accessed only the gap magnitude $|M|$. Here we show how the topological sign of $M$ can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin–orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a $C_3$ axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.

Spiking Neural Networks (SNNs) are promising for energy-efficient spatiotemporal pattern recognition at the edge, but efficient deployment and on-device adaptation require specialized hardware. In this work, we present an FPGA implementation of multilayer SNNs for spatiotemporal pattern classification, in which both inference and training take place on the same hardware. Our design adopts a temporal-forward-only training algorithm that avoids the memory and latency overhead associated with traditional Backpropagation Through Time (BPTT). A mixed-precision scheme balances training stability with resource efficiency, and architectural optimization maximizes hardware and memory utilization. We further identify and resolve hazards that arise when inference and learning share the same memory, including port conflicts between the forward and backward access patterns and read-after-write dependencies in floating-point potential accumulation. Experimental evaluations on MNIST and five multivariate time-series classification datasets demonstrate that, with fully on-chip training, our SNN model achieves accuracy comparable to SNN or LSTM trained with BPTT. Compared to CPU and GPU based implementations, our FPGA design delivers 2.5 to 6 times higher throughput while consuming an order of magnitude less energy per sample.

Precise control of movement across various robotic embodiments is a longstanding challenge. Modeling complex robotic structures requires significant time, dedicated sensors, and manual labeling. Recent advancements in 4D representation learning offer an interesting alternative: can we leverage 4D features lifted from 2D observations to densely map a robot's spatial movement based on the action signal? To this end, we propose Act4R, a framework that builds on 3D foundation model to predict a robot's 3D scene flow with any given action. Act4R introduces a Spatial-Action Encoder, which encodes the current 2D robot state and its action signals into embeddings that represent future robot state in 3D. Then, both the current and future spatial embeddings are decoded into point maps to estimate action-conditioned scene flow. To effectively learn the mapping between action and future state, Act4R introduces spatial-action fusion in its transformer-based encoder, and a spatial alignment loss that guides the encoder for future flow prediction. After training on some samples of a given embodiment, Act4R can perform inverse control by optimizing the signal to achieve the desired scene flow. We evaluate Act4R on a public real-world dataset and synthetic data collected in simulator. Experiments on various robotic platforms show that Act4R outperforms the previous SoTA in scene flow prediction. Our method also performs better in inverse control, both on the action accuracy metric and in closed-loop control in simulation.

Text language models (LMs) acquire broad linguistic and factual capabilities through large-scale pretraining, while comparable capabilities remain difficult to learn from speech alone. Recent work has shown that knowledge distillation from pretrained text LMs offers a promising way to transfer their linguistic and factual capabilities to speech models. However, existing distillation approaches have largely focused on speech-input, text-output models. This idea has yet to be explored for speech-to-speech models, which operate on both speech input and speech output. In this work we introduce a speech-to-speech pretraining method that creates an internal text interface for knowledge transfer while preserving the speech-only input and output. The model first consumes speech context without its transcription, switches to text prediction, and then uses the predicted text to lead future speech generation word by word. It also provides an interface for knowledge distillation: the internal text predictions can be directly distilled from the base text LM. To the best of our knowledge, this is the first application of text LM distillation to a speech-to-speech LM. Under matched training conditions, the proposed sequence construction substantially improves the generative perplexity of spoken continuations over speech-only and interleaved speech-text models, approaching the performance of a text-leading inner-monologue model with external ASR prompt transcription. More importantly, distillation improves factual performance under both text and speech evaluation, indicating better retention of knowledge from the base text language model.

We study a continuum version of the stable marriage problem, in which each agent has a variable mass to be paired to the opposite side. An agent's mass is interpretable as the divisible time of a single atomistic agent, or as a mass of infinitesimal agents of a particular type. Our object of interest is the mapping between the vector of masses to the set of stable matches. As in the canonical stable marriage model, the set of stable matches can be multi-valued, so this mapping is a correspondence. This correspondence is continuous if and only if the stable match is unique, implying that small changes in the masses may cause discontinuous jumps in the set of stable matches.

We present a perceptual audio coder in which the entropy-coding model and the bit allocation co-adapt across blocks without model side information. Mantissas are coded by a hybrid of bit packing and arithmetic coding with per-band probability models learned online. Encoder and decoder accumulate identical histograms from decoded blocks and advance the same model state. The model enters bit allocation directly: per-band rate–distortion frontiers combine measured perceptual distortion with entropy-coded rate estimates under the current model, and a dynamic program attains the exact minimum of total objective perceptual distortion for each block's budget under the model's rate estimates, with reservoir carry-over. Under a strict per-block rate, entropy-coding-aware bit allocation lowers this distortion (band noise-to-mask ratio in linear scale) by 15-24% relative to the same solver without it, and co-adaptation removes a further 3-4% (up to 15% on oboe) that a backward-adaptive coder alone cannot realize in one pass; a MUSHRA test at 80 kbps per channel confirms the ranking.

Unsupervised clustering is widely used to discover underlying group structure, after which researchers often seek to validate these groups via post-hoc hypothesis testing on the population means. However, using the same data both to form clusters and to test for a difference in means inflates the Type I error rate. Recent work in selective inference has proposed solutions when the underlying data are drawn from a multivariate Gaussian distribution with a known covariance matrix or an unknown isotropic covariance matrix. We propose a new selective test for the difference in means between two clusters that provably controls the Type I error rate under an arbitrary unknown covariance matrix. Our test statistic does not require estimating the feature covariance matrix; instead, it leverages a Monte Carlo sampling procedure over the set of orthogonal matrices. We show that this new selective test can be computed efficiently, and we derive closed-form solutions when clusters are formed using k-means or hierarchical clustering. In simulations, we demonstrate that our proposed p-value controls the selective Type I error rate and achieves substantial power, and we illustrate its application on gene expression and drug review data sets.

Browser agents need to make decisions and execute actions on behalf of users while consuming untrusted webpages, creating opportunities for malicious instructions embedded in webpages to redirect legitimate tasks. We introduce BrowseSafe++, which extends BrowseSafe from 14,719 pages to 38,675 pairs of pages. Most of its prompt injections were observed in the wild on production websites. We keep each injection unchanged and rewrite the sensitive parts of the page around it to protect privacy. Each attacked page has a clean copy of the same page as its control. Both are provided as HTML, Markdown, an accessibility tree, and a screenshot. Every pair includes a user task and its expected answer. The benchmark includes twelve types of websites, from news articles to shared documents and forums, with 24 attack types appearing in 18 different locations on a page. We use these paired pages to train BrowseSafe-Guard, two 0.8B-parameter detectors for text and screenshots. Both achieve higher F1 scores than the detector based on frontier models, while keeping false-positive rates on benign pages and inference cost low. BrowseSafe-Adapt revises benchmark injections from browser-agent feedback, and attacks that succeed on only a few percent of tasks when replayed directly reach up to 95.41% success once adapted.

Language models are often evaluated alone but increasingly deployed together, routed between, made to debate, ensembled, or collaboratively trained. For a model inside a system, what matters most is not how well it performs on its own, but how much the system gains from its presence. We call this a model's compositional strength and formalize it using the Shapley value of a cooperative game over coalitions of a model pool, and use a model's leave-one-out contribution to the full coalition as a tractable proxy, requiring n+1 rather than 2^n system evaluations. Evaluating individual vs. compositional strengths across five model pools, twelve collaboration methods, and twelve datasets, we find them largely uncorrelated: in 12 of 15 (pool, method-family) settings, individual strength does not translate into compositional advantages, and the coupling is weakest among general-purpose models that practitioners are most likely to deploy. Standalone benchmarks are therefore often poor proxies for models' value in collaborative systems. We then propose compositional reinforcement learning (C-RL), which trains a policy inside a live multi-model system and rewards the outcome produced by the system as a whole, rather than the policy's correctness in isolation. The leave-one-out baseline in Shapley values cancels under a group policy gradient, so this needs no additional rollout cost beyond RL on the collaborative system's outcome and never requires running a coalition without the policy. Across three collaboration protocols and eight tasks spanning reasoning, coding, and scientific discovery, C-RL produces the strongest collaborator in 21 of 24 settings, lifting collaborative performance by +4.0 to +5.4 pts on average (~3x the gain of baselines), up to +13.1 pts.

Törnquist (arXiv:1310.3250) proved that if there exists a $\boldsymbol{\Sigma}^1_2$ maximal almost disjoint (MAD) family, then there exists a $\boldsymbol{\Pi}^1_1$ MAD family. Since then, several other "complexity reduction" proofs have been found for other combinatorial objects, such as maximal independent families or ultrafilters. All of these proofs have relied on $\boldsymbol{\Pi}^1_1$-uniformization, so they did not easily lift to higher projective levels. In this paper, we introduce a principle weaker than Uniformization which we call "Functional Projection", and show that this principle is sufficient for most complexity reduction proofs. On the other hand, we prove that in $L[U]$, the canonical inner model for a measurable cardinal, Functional Projection holds for $\boldsymbol{\Pi}^1_2$ relations. As an immediate corollary, we obtain that in $L[U]$ there are $\boldsymbol{\Pi}^1_2$ witnesses for many combinatorial families.

We prove that for $k=4$ the quantum uniformity measures are norms, whereas for every $k\geq5$ the triangle inequality fails. This gives a complete answer to an open question of Bu, Gu, and Jaffe. The $k=4$ case is proved using the Cauchy–Schwarz inequality for the quantum uniformity pairing $\langle\cdot,\cdot\rangle_{Q^4}$ introduced here, together with the triangle inequality in a suitable finite-dimensional Bochner $L^8$ space. For $k\geq5$, we construct systems of linear equations over a finite field and derive a contradiction from the structure theory of norming linear systems.

We propose a continuous learning formulation for $T$ non-forgetting tasks with the spherical parameter space $\mathbb{S}^{d-1}(\sqrt{d})$ in asymptotic regime $d\rightarrow \infty$. Each task $i$ has an optimum $\bm{\Theta}_i$, minimizing its corresponding loss function $R_i(\bm{w})$ on sphere. We reduce each task $i$ to an acceptable loss region modeled by a geodesic ball $B_{\bm{\Theta}_i}(r_i(d))$ on $\mathbb{S}^{d-1}(\sqrt{d})$ centered at $\bm{\Theta}_i$ with radius $r_i(d)$. To model task dependencies (similarities), task optima $\bm{\Theta}_i$ are distributed by a Neyman-Scott clustered point process $\Phi$. Cluster centers $\{\bm{Y}_j\}_{j=1}^{N_p}$ form a homogeneous Poisson point process on sphere, while intra-cluster task optima follow a von Mises-Fisher distribution with mean $\bm{Y}_j$ and concentration $\kappa$. Each task $t\in \{1, ..., T\}$ learning algorithm is considered to be a channel $Q_{t}(\mathrm{d}\bm{w}_t | \bm{w}_{t-1}, \mathcal{K}_{t-1}(\bm{\theta}_{1:t-1}), \bm{\theta}_t)$, where $\bm{W}_t$ is the learned parameter of task $t$ and $\mathcal{K}_{t-1}(\bm{\Theta}_{1:t-1})=\bigcap_{i=1}^{t-1}B_{\bm{\Theta}_i}(r_i(d))$. Since in continual learning, the learner does not need to reach $\bm{\Theta}_t$ exactly to successfully learn task $t$, to avoid forgetting as well as reliable learning, it only needs for the learned parameter vector $\bm{W}_{t}$ to enter $B_{\bm{\Theta}_t}(r_t(d)) \cap \mathcal{K}_{t-1}(\bm{\Theta}_{1:t-1})$. Using this model, we derive an upper bound on $T$ ensuring $\mathbb{P}[\mathcal{K}_{T}(\bm{\Theta}_{1:T}) \neq \emptyset] \rightarrow 1$ as $d\rightarrow \infty$ and $\kappa/d \rightarrow \alpha$, where $\alpha>0$ is a constant. Finally, for $T$ tasks sampled uniformly from $\Phi$, we derive an upper bound for total information theoretic capacity under the non-forgetting constraint for each task.

Altermagnetism is a rapidly emerging paradigm in condensed matter magnetism, yet the number of experimentally confirmed altermagnetic candidates remains remarkably limited. Cr$_{1/4}$NbS$_2$ has long been theoretically proposed as a promising altermagnet, but there are no reports on experimental investigation of single crystals. Here, we report the successful growth of high-quality single crystals of Cr$_{1/4}$NbS$_2$ and present its structural, thermal, magnetic, and transport properties. Single-crystal X-ray diffraction provides detailed crystallographic information and confirms the hexagonal crystal symmetry ($P6_3/mmc$), one of the criteria for altermagnetic behavior. Resistivity and heat capacity measurements unambiguously identify an antiferromagnetic Néel temperature of $T_N \sim 141$ K. Magnetotransport measurements reveal non-trivial features in the magnetoresistance and Hall response, indicative of quantum diffusive transport phenomena. Cr$_{1/4}$NbS$_2$, synthesized here for the first time in single-crystalline form, therefore serves as an experimental platform for probing the rich spectrum of phenomena predicted for altermagnetic materials.

Self-supervised polysomnography foundation models (PSG FMs) aim to capture clinically useful information beyond sleep staging, yet are rarely compared with sleep-staging encoders pretrained at comparable scale and modality coverage. Using a common whole-night, missingness-aware state-space downstream modeling framework, we compared frozen representations from prominent large-scale, multi-cohort sleep-stage-supervised encoders and self-supervised PSG FMs for multilabel identification of six sleep-wake and circadian disorder groups in 7,906 PSGs from an unseen registry. Although PSG FMs outperformed an EEG-only, single-cohort supervised baseline, this ordering reversed when supervised pretraining approached comparable scale and modality coverage. Transfer learning from neural sleep scorers achieved higher overall performance while exhibiting greater downstream data efficiency. These findings underscore the need for scale- and modality-matched pretrained supervised baselines when assessing PSG FMs' downstream potential.