Papers

Transformer language models (LMs) are feed-forward: deep-layer representations are never fed back to shallower layers, and the only pathway for information to flow downward across generation steps is the decoded token. This narrow channel forces models to recompute intermediate results and to discard alternative continuations. In this work, we remove this bottleneck during pretraining, introducing the LIFT (Latent Information Feedback Transformer) architecture and training method which enable LMs to propagate state across generation. We achieve this by turning recurrent-state learning into a teacher-forced prediction problem: each input token is paired with an information-dense state, derived from the next-token distribution of an off-the-shelf pretrained LM. The model, extended with a small number of additional parameters, is then trained to predict both the next token and the next state. As the input states are precomputed, pretraining remains fully parallel across positions. At inference, the model's own predicted states are fed back, with a minor computational overhead that decreases with model size. Experiments with pretrained models ranging from 135M to 1B parameters show that LIFT consistently outperforms standard Transformers and baselines on language modeling, downstream reasoning tasks, and procedural tasks under token-matched budget, while being on par with or ahead of compute-matched Transformers. Moreover, a controlled study on a state-tracking task shows that a tiny LIFT outperforms same-size Transformers trained on 8x more data, even when trained with the states of a Transformer that fails the task. Overall, we show that LMs can learn to exploit deep-to-shallow feedback during pretraining via scalable teacher supervision.

Interface-confined superconductivity emerges from the interaction of electronic states across chemically distinct boundaries, providing a route to engineer superconducting phases where magnetism and topology coexist. Determining the intrinsic nature of such superconductivity, however, is challenging because the superconducting layer is only a few nanometers thick and buried beneath several normal layers. Here, we measure the whole-sample Meissner response of six $\mathrm{FeTe}$-based heterostructures in a uniform magnetic field using a frequency-domain tunnel-diode resonator. In the ultrathin limit, the conventional normalization of the measured susceptibility, $\chi(T\to0)=-1$, fails by tens of percent. We establish the appropriate calibration and invert $\chi(T)$ to determine the London penetration depth $\lambda(T)$. Two key results emerge. First, the broad transitions observed in $\chi(T)$ arise naturally from the extreme geometry and large $\lambda$, without requiring chemical or structural inhomogeneity; the extracted $\lambda(T)$ closely tracks the resistive transition. Second, $\lambda(T)$ and the corresponding superfluid density are inconsistent with a fully gapped isotropic $s$-wave state and instead indicate a strongly anisotropic order parameter possibly with line nodes or deep gap minima. The inferred $\lambda(0)$ is of order $1\,\mu$m, consistent with an independent analysis of the 2D phase stiffness. Despite the distinct chemical, magnetic, and topological character of the three overlayers, all six FeTe heterostructures exhibit similar low-temperature power-law behavior, with no systematic dependence of the superconducting response on overlayer identity. These results point to the interfacial $\mathrm{FeTe}$ layer as the common origin of superconductivity.

As agents take on longer and more complex problems, controlling the execution becomes a task in its own right. Each step in the run brings new control choices, like which partial work to build on, whether to start fresh, or when to stop. We introduce agentic meta-reasoning, an inference-time harness that makes these choices an explicit and structured reasoning process. Workers carry out the task-level computation, while a controller consolidates what the run has established, explores next options, assesses what each option is worth under the remaining budget, and dispatches the chosen work with context drawn from persistent memory. Between decisions the controller carries only a compact account of the run rather than replaying its full history. Our baselines span production coding agents and research harnesses, together with a Direct Control Agent using the same workers and compute budget allowance. On ProgramBench, which tests long-horizon agentic capability through program reconstruction, meta-reasoning achieves 71.5% with GPT-5.5 against 58.0% for Codex; with Opus 4.8 it achieves 67.2% against 65.5% for Claude Code. On the other benchmarks, spanning abstract reasoning, multi-domain long-horizon reasoning, and proof generation, it gains between 3.6 and 4.2 points over direct control, averaged across three frontier models. It keeps improving over the tested budget ranges where direct control plateaus, though its overhead can hurt at small budgets. Artifact-graph analysis reveals more reuse of earlier work, higher coverage of correct solutions in most settings, and nonuniform gains in final selection. These results indicate that spending computation on structured control becomes more important as agents scale to longer runs.

We introduce LIFT, a unified image-to-video generation framework that complements camera control with Layout-In-FuTure control, enabling users to specify what should appear in a future view and where it should appear. This addresses a practical need in controllable video generation: given an initial image, users often care not only about how the camera moves, but also about what the scene should look like at key future moments, especially the final frame. Existing camera controls specify viewpoint trajectories, while text prompts provide only coarse semantic guidance; neither precisely determines the content and spatial layout of future views. This limitation becomes particularly pronounced under large viewpoint changes, where the camera reveals regions that are not visible in the first frame. LIFT therefore uses the last-frame layout as an explicit control signal for the desired future scene. Since learning from such sparse layout guidance is substantially more challenging than conditioning on dense per-frame layouts, we introduce on-policy self-distillation (OPSD) to transfer the control capability of a dense-layout teacher to a last-frame-layout student. We further curate LIFT-Vista, a dataset featuring large viewpoint changes with camera and temporally consistent layout annotations. Experiments show that LIFT improves video quality, future-layout controllability, and camera controllability over other methods.

In the study of quantum process tomography, it has remained open how to learn a unitary channel in diamond distance with strictly parallel queries as efficiently as with sequential queries. Sequential queries allow one to exploit adaptivity to refine the estimate and adjust the learning strategy accordingly, whereas such adjustments are impossible for parallel queries. From the perspective of higher-order quantum operations, any parallel learning strategy can be simulated by a sequential one, whereas the converse does not hold in general, suggesting that sequential learning strategies are potentially more powerful. Contrary to this intuition, we present a new protocol for learning an unknown $d$-dimensional unitary channel to within $\varepsilon$ in diamond distance using $\mathcal{O}(d^2/\varepsilon)$ parallel queries, matching the lower bound presented in [Haah, Kothari, O'Donnell, and Tang, FOCS '23]. Our protocol thus closes the gap between parallel and sequential strategies for unitary channel tomography. As applications, it achieves optimal query complexity for boundary-regime quantum channel tomography and improves the query efficiency of the best-known protocol for tomography of fermionic linear optics.

We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.

Agent performance depends on both reasoning ability and the environment in which it acts. We study test-time AI-for-AI, asking how a Builder can learn to construct better execution environments for a Target while both models' weights remain fixed. To make the Builder's experience reusable, we introduce Meta-Skill: principles specifying when support is needed and what resources to provide. The Builder learns these principles from Target's execution feedback on the development set, then uses the frozen skill bank to construct harnesses for unseen tasks. Across Harness-Bench and NewtonBench, full-bank meta-skills improve macro-average performance by 8.95 percentage points over no-skill construction, and 12.02 points over direct delivery of the same bank to the Target. These results highlight the value of translating experience into executable support. Gains when the same model serves both roles further suggest a path to system level self-improvement through learning to build better environments.

A small trainable advisor can steer a frozen language-model executor using natural-language advice. In addition to learning from task rewards, the advisor can use feedback from completed interactions to improve its advice. However, a plausible correction need not change execution, yet learning from such corrections can still affect the advisor's future decisions in other contexts. In a shared-parameter model, we prove that such corrections can limit learning if their targets favor useful advice less strongly than those of other corrections. Keeping them less often than the rest improves the model's eventual performance compared to learning from every correction. Motivated by this, our method, Advisor Self-Distillation (AdviSD), pairs outcome-based reinforcement learning with self-distillation from a feedback-conditioned copy of the advisor selectively. Reflection proposes corrections, and the advisor scores the same recorded executor response with and without its issued advice, using the magnitude of the difference to select decisions for supervision. This approach does not require executor likelihoods or additional executor rollouts. Experiments with Qwen3-8B advisors for Gemini and Claude show that AdviSD outperforms advisor-GRPO by 4.2-6.4 percentage points on BFCL-v3 and by 3.9-5.1 score points on EnvScaler. The trained advisors generalize to out-of-domain tasks and transfer across different executor versions and model families. AdviSD also beats matched-count random selection, supporting the value of its selection rule.

Multi-source data integration problems over datasets from different sources covering different but possibly overlapping sets of entities have become increasingly important in many applications, including genomics, single-cell analysis, and healthcare research. We study a model of multi-source data integration where we observe overlapping submatrices of a low-rank matrix, each corrupted by additive noise. In such problems, one often first learns a low-dimensional representation of the entities within each source and then integrates these representations across sources. As the representations are only identifiable up to some transformation, aligning them using the sources' overlapping entities becomes a key challenge. Existing methods align these estimates in a sequential or tree-structured manner, and are therefore sensitive to the chosen order and exploit only part of the overlapping information. We propose Global Synchronized Multiple Matrix Integration (GSMMI), which formulates this alignment problem as a global synchronization problem and jointly aligns all sources using all pairwise overlaps at once. We develop an efficient, scalable iterative algorithm for GSMMI, and show both theoretically and empirically that it improves alignment accuracy, with clear gains over prior approaches even under moderate overlap. We additionally establish information-theoretic and computational lower bounds for detection in data integration, and find GSMMI to be empirically near-optimal. GSMMI applies broadly across symmetric positive semidefinite, symmetric indefinite, and asymmetric or rectangular matrices, as well as settings where sources overlap only in rows or only in columns.

Mixture-of-Experts (MoE), popularized by large language models, is a promising paradigm for scaling visual generative models. However, conventional token-wise MoE routes tokens independently within a homogeneous expert pool and regularizes expert usage toward uniformity, making it poorly matched to video data that is spatiotemporally redundant and semantically long-tailed. We show that existing visual MoEs fall into a uniformity trap: semantically under-organized routing, compounded by uniform expert-usage regularization, scatters coherent patches across disparate experts, causing routing fragmentation and structural distortion. To address this, we propose SplitMoE, a split-role sparse architecture that breaks the shackles of uniformity. To accommodate the inherent semantic imbalance, we explicitly bifurcate the expert pool into semantic experts and generic experts, with semantic experts capturing high-level semantic abstraction and generic experts preserving residual visual information and flexible generative capacity. Leveraging prototype-guided routing and pull-push regularization, SplitMoE enables tokens to cluster naturally by semantic attributes rather than arbitrary balancing constraints. Extensive results show that under an equivalent activated-parameter budget, SplitMoE outperforms traditional load-balanced MoEs in convergence speed, routing coherence, and video generation quality across standard benchmarks. By revealing an emergent coarse-to-fine denoising logic, SplitMoE provides the community with a modality-aware scaling path, serving as a critical reference for building large-scale video world models.

We introduce a local and distributed framework for decoding quantum LDPC codes. Built atop belief propagation (BP), the architecture combines strictly local processing of syndrome information, local feedback, autonomous operation, and highly parallelized decoding. We establish the framework at two complementary levels. First, we show that any code exhibiting a threshold under iterative BP decoding can be promoted to an autonomous local measurement-and-feedback dynamics while preserving that threshold. We then turn to codes for which naive BP does not itself exhibit threshold behavior. Our key observation is that BP can nevertheless provide sufficiently accurate local marginal information: active syndrome defects use these local beliefs to move, pair, and annihilate through asynchronous feedback. We demonstrate numerically that this construction exhibits threshold behavior in the point-like sectors of the two- and three-dimensional toric codes, where conventional BP decoding fails. Exploiting the graph-generality of BP, we then study the inference dynamics on the membrane-like sector of the three-dimensional toric code and in a family of bivariate-bicycle quantum LDPC codes.

The Maker Breaker Triangle Game involves two players, Maker and Breaker, who alternately claim 1 and $q$ edges of $K_n$, respectively. Maker's goal is to claim all three edges of any triangle, whereas Breaker's goal is to prevent this. The threshold bias, i.e. the minimum $q$ such that Breaker wins, is known to lie between $\big\lceil\sqrt{2n-2}-\frac{3}{2}\big\rceil$ and $\big(\sqrt{8/3}+o(1)\big)\sqrt{n}$. Determining its exact value is a longstanding open problem. In this paper, we introduce a novel version of the game in which Breaker may claim fewer than $q$ edges per round to build up a budget that he can spend in later rounds. With this additional power for Breaker, we determine the threshold bias to be precisely $\big\lceil\sqrt{2n-2}-\frac{3}{2}\big\rceil$ for all $n$, matching the known lower bound. This is the first version of the Maker Breaker Triangle Game for which the exact threshold bias is known. Even if Breaker is not allowed to use the budget for threats, we prove that the threshold bias is still $\big(\sqrt{2}+o(1)\big)\sqrt{n}$. Furthermore, we study the budget version of other Maker Breaker Games. Specifically, for the $K_4$-Game, we prove the first explicit lower and upper bounds on the threshold bias in both the original and the budget version of the game.

Language-model (LM) harnesses enable LMs to operate effectively over long contexts using additional compute. However, existing long-context evaluations are insufficient for distinguishing modern harnesses, reflected by saturated accuracy across harnesses and largely similar evaluation costs. In this paper, we introduce a benchmark for evaluating both the effectiveness and efficiency of long-context harnesses. Our tasks require diverse retrieval strategies, including lexical search and semantic matching, together with strategic and adaptive reasoning over global and local context. Much of the context is semantically relevant but only a small subset is useful at each step, creating both a challenging search problem and different accuracy–cost tradeoffs across processing strategies. For example, one task requires identifying every person satisfying several conditions using evidence scattered across documents; strategically checking the most selective condition first can narrow the search before verifying the remaining conditions. We evaluate multiple families of frontier language models with four state-of-the-art harnesses. Our benchmarks remain challenging even for strong model–harness combinations: the best reaches 68% macro-average accuracy across four evaluation suites. More importantly, we find that the same underlying model can exhibit markedly different efficiency under different harnesses. Our results establish efficiency as an important axis for long-context evaluation and provide a testbed for developing harnesses that process context strategically rather than exhaustively.

Style transfer aims to render target content in the style of a reference image, but existing methods often suffer from content leakage, where objects, layouts, or semantics from the style reference appear in the generated output. Although prior data-driven and training-free methods can reduce leakage, they often face a leakage-degradation dilemma: stronger content suppression may weaken style fidelity, while richer style preservation may reintroduce unwanted reference content. We identify this dilemma across the full style-transfer pipeline, including feature separation, feature-space grounding, and diffusion generation. To address these issues, we propose CLeaR, a training-free framework for content-leakage-resistant style transfer. CLeaR first uses Orthogonal Subspace Projection to define content-reduced style targets in each vision foundation model (VFM) feature space. It then performs Ensemble Inversion, which optimizes a shared pixel-space style anchor satisfying style constraints across multiple VFMs. Finally, Energy-Guided Calibration maintains style alignment during diffusion sampling by steering the denoising trajectory toward the ensemble-defined style manifold. We further provide a theoretical analysis showing that the style-anchor estimation error decreases with the number of VFMs. Experiments on StyleBench demonstrate that CLeaR improves style alignment, reduces content leakage, and achieves better LLM-as-Judge evaluation compared with existing methods. The code is available at \href{https://github.com/0606zt/CLeaR}{https://github.com/0606zt/CLeaR}.

The celebrated conjecture of Lovász from 1969 asks whether every connected vertex-transitive graph has a Hamiltonian path. Bucić, Christoph, Pokrovskiy and Steiner recently proved that every such graph on $n$ vertices contains a cycle of length $n^{2/3-o(1)}$. In this paper, we improve this bound to $n^{1-o(1)}$. Our proof uses a structure theorem of Tessera and Tointon to first obtain a partition of the vertex set into sets of small diameter in the original graph. When the parts are large, we repeatedly traverse a spanning tree of maximum degree at most three in the quotient graph, and use the Lovász local lemma to join random short paths along this traversal and extract a long path in the original graph. When the parts are small, we apply Babai's contraction lemma to reduce the problem to finding a long path in a connected Cayley graph of a nilpotent group with boundedly many generators and bounded nilpotency class, and then show that such a Cayley graph on $m$ vertices contains a path on $m^{1-o(1)}$ vertices.

Can a symmetry be tested optimally without using the quantum resource naturally associated with it? For parallel subgroup-versus-Haar testing, we derive a quantitative representation-theoretic converse for every protocol with zero type-I error: the excess type-II error is bounded below by the sum of two nonnegative penalties, one for weight on suboptimal subgroup types and one for deviations of within-type Schur profiles from their typewise extremal profiles. At optimality, both penalties vanish, yielding support and weight locking for every optimal system marginal. Disjointness of the resulting locked set and the free marginal set rules out resource-free optimality, whereas overlap alone does not establish attainability. For the diagonal torus in dimension $d\geq 2$, optimal testing without coherence is possible only with a single query. We determine both the exact optimal type-II error over all protocols with incoherent system marginals and the minimum system-marginal coherence required to attain the unrestricted optimum. For the orthogonal subgroup in dimension $d\geq 2$, a real protocol attains the optimum at every query number. For the qutrit Clifford group, Wigner-positive optimal protocols exist at three and four queries but not from five through nine; whether they exist beyond nine queries remains open. Together, these results relate the subgroup- and query-dependent resource requirements of optimal symmetry testing to structural constraints on optimal system marginals.

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

We study average-reward weakly-coupled Markov decision processes (WCMDPs), where a WCMDP consists of $N$ smaller MDPs, called arms, that share multiple per-step budget constraints. We consider the setting where the arms have identical model parameters, multiple actions, and state- and action-dependent costs. For restless bandits (RBs), a well-studied special case of WCMDPs, prior work has developed policies that achieve an $O(1/\sqrt{N})$ optimality gap under general conditions, and has further identified conditions under which policies can achieve a better-than-$1/\sqrt{N}$ optimality gap. However, for general WCMDPs, no prior result achieves an optimality gap better than $1/\sqrt{N}$. In this paper, we identify conditions analogous to those for RBs under which a better-than-$1/\sqrt{N}$ optimality gap is achievable, and design a policy that attains an $O(1/N)$ optimality gap. Notably, unlike prior approaches based on generalizing priority orderings, our policy is not priority-based but rather is designed to induce locally linear mean-field dynamics.

We study Ore extensions $R[t;\sigma,\delta]$ of rings graded by an arbitrary group $\Gamma$. The grading of $R$ extends with $t$ of degree $\gamma$ if and only if $\sigma$ is compatible with conjugation by $\gamma$ and $\delta$ with left translation by $\gamma$. The extended grading is then unique. For nonabelian $\Gamma$ the degree of $t$ need not commute with the degrees of $R$, and this twist cannot always be removed. If $R$ is gr-simple and $\sigma$ is an automorphism, then $R[t;\sigma,\delta]$ is gr-simple if and only if it has no homogeneous normal element that is monic of positive $t$-degree. The quantized Weyl algebra shows that the graded forms of the classical necessary conditions do not suffice. Over a group algebra $kG$, these extensions correspond to actions of $G$ on the affine line, and gr-simplicity means that the action has no finite orbit. In characteristic zero this is the nonvanishing of a class in $H^1(G,k_\chi)$, and simplicity forces $G$ to be metabelian. We prove the analogous results for Poisson polynomial rings and relate the two settings by semiclassical limits.

We consider conformal boundaries and defects in Euclidean conformal field theory (CFT) at finite temperature and infinite volume. We distinguish defects that wrap the thermal circle and defects that are localised at a point on it. In both set-ups, and for any dimension and co-dimension, we classify bulk one-point functions of scalar, vector and spin-2 primaries. We relate the low-temperature expansion of bulk scalar one-point functions to zero-temperature defect CFT data and new finite-temperature data of defect primaries. For localised defects, we derive one-point bootstrap sum rules using periodicity and the defect operator expansion. We consider several examples in free bulk CFTs: unitary and non-unitary boundary CFTs, a wrapping monodromy defect, and a localised magnetic line. We determine thermal defect CFT data in all examples. For defects wrapping the thermal circle, we compute thermodynamic observables. For localised defects, we observe a Hurwitz zeta function decomposition of one-point functions suggestive of an underlying dispersion relation.

Reliable multistep quantum lattice-Boltzmann evolution requires controlling computational faults. When ideal collision preserves encoded mass and momentum exactly, changes in those charges can provide syndromes for selected faults at the post-collision checkpoint. A fault that shifts one population then leaves a unique mass-momentum residual labeled by the lattice velocity. A coherent reference register stores the expected charges, so the same test remains valid while the physical fluid charges vary across the lattice. Single bit flips on population number registers occupy disjoint syndrome sectors and satisfy the Knill-Laflamme condition. A state-vector demonstration on eighteen data qubits of the two-dimensional nine-velocity lattice (D2Q9) recovers that single-bit family to double-precision roundoff. Conservation still leaves a fifteen-dimensional kinetic nullspace on the three-dimensional nineteen-velocity lattice (D3Q19). Exact multiple-relaxation-time (MRT) streaming analysis ranks those charge-preserving modes by the order at which they return to density or momentum. A classical D3Q19 decaying-flow simulation at moderate Reynolds number then injects about $1.75\times10^4$ selected single-population shifts per realization. Recovery of that alphabet returns the trajectory to floating-point roundoff. The quantum statements assume an ideal charge-preserving collision and a reliable reference. The result is an inner recovery map for a stated charge-changing alphabet together with a kinetic classification of the unresolved sector.

Time-variable stellar heating may create new climate states, such as permanently hot or cold hemispheres, on asynchronous planets. Planets on eccentric orbits, circumbinary planets and planets on polar orbits around gravity-darkened stars all receive variable irradiation, yet variably irradiated planets (VIPs) have not been studied from a fundamental dynamical perspective. We present the first generalized study of the atmospheric response of variably irradiated tidally locked planets, using a 1.5-layer shallow-water model forced towards a time-dependent radiative equilibrium. We derive linearized analytic expressions for the mean, amplitude and phase lag of the response, which is that of a forced damped harmonic oscillator, and recover the established trends of tidally locked planets in the limit of steady forcing. When the instellation variation and wave timescales match and the damping is weak, a resonance occurs because waves propagate and interfere freely. The resonance produces a global standing wave mode and consequently a temporarily warmer nightside. Linear and nonlinear simulations reproduce these results and show that the hotspot oscillates longitudinally at the forcing frequency and reaches the antistellar point at resonance. The oscillation is eastward or westward of the substellar longitude depending on the rotation rate and the nonlinearity of the system. Synthetic phase curves carry signatures of this variability and invert in shape at resonance because of nightside warming. Among observed systems, we find 11 planets with at least 10% phase curve modulation from variable irradiation. Eccentric, pseudo-synchronous giants are the most promising targets, with HAT-P-2b having the largest predicted modulation.

Multimode optomechanical scattering is ubiquitous in free-space imaging protocols, but its radiation pressure counterpart is challenging to detect with extended objects. Here we demonstrate radiation pressure actuation of a nanomechanical membrane using dynamically structured light from a spatial mode demultiplexer (SPADE). Using single- and two-mode illumination, we directly image the position-dependent intermodal coupling between Hermite-Gauss (HG) modes as mediated by the membrane's motion. As an application, we use multimode radiation pressure feedback to simultaneously cool two nearly degenerate membrane modes. Our results are applicable to diverse mechanical systems and serve as a stepping stone to SPADE-based quantum optomechanics.

We prove that the exotic smooth $8$-sphere and both oriented homotopy $10$-spheres representing elements of order three admit Riemannian metrics with strictly positive sectional curvature. The construction combines Sperança's special $S^3$-$S^3$ bundle models with the compatible-disk construction of He, Liu and Yau. We show that the relevant bundles admit equivariant polar normal forms, with transition functions that are constant along meridians and conjugation-equivariant. We also show that the representation-dependent part of the He–Liu–Yau construction requires only a uniform bound on the infinitesimal action fields. Sperança's $8$- and $10$-dimensional examples satisfy this bound. The resulting northern and southern metrics have matching boundary metrics and compatible second fundamental forms, so the Reiser–Wraith gluing theorem gives the required positively curved metrics.

Quaternary mixed-metal chalcohalides (MMCHs) are a promising mixed-anion semiconductor family, but their thermodynamic accessibility remains largely unexplored. We combine density functional theory with the Alexandria Materials Database to carry out a rapid and reliable evaluation of the thermodynamic accessibility of 54 M(II)$_2$M(III)Ch$_2$X$_3$ compounds. All evaluated MMCHs are predicted to be thermodynamically unstable, but a considerable fraction of MMCHs lie within computational uncertainty of the convex hull. Their predicted decomposition follows five distinct reaction pathways, most commonly into M(III)$_2$Ch$_3$, M(II)X$_2$, and M(II)Ch. Solution processing of six Sn-based MMCHs supports our analysis. Notably, this includes the first synthesis of the previously unreported Sn$_2$InS$_2$Br$_3$ in a multiphase film. Our approach identifies convex hull proximity and competing phase formation as key constraints on MMCH synthetic accessibility during solution processing, thereby guiding future MMCH exploration.

It is shown that Shannon entropy, Fisher information, and quantum-mechanical kinetic energy may all be viewed as measures of correlation. We begin with a fundamental correlation-destroying map: a joint probability density $\rho(x,y)$ is replaced by $\rho_x(x)\rho_y(y)$, the product of its marginal distributions. In the discrete case, Shannon's entropy is nondecreasing under this map. For continuous distributions, this fundamental map leads to a well-behaved, coordinate-invariant correlation measure, analogous to the discrete Shannon entropy: \[ I[\rho] = h[\rho_x] + h[\rho_y] - h[\rho]. \] In the continuous case, however, another measure appears: Fisher information. The relative Fisher information $J(\rho\|\rho_x\rho_y)$ behaves similarly under the fundamental map. For a normalized real quantum wavefunction, this decrease is exactly proportional to the decrease in mean kinetic energy, \[ \langle T\rangle_\psi - \langle T\rangle_\Phi = \frac{\hbar^2}{8m} J(\rho\|\rho_x\rho_y), \qquad \Phi = \sqrt{\rho_x \rho_y}. \] In Jaynes's language, the result supports a principle of minimum justified correlation: given physical constraints and a set of possible distributions or related amplitudes satisfying those constraints, select from that set those with the least correlation. This is Part I of a two-part paper. Here we develop the entropy, Fisher-information, and kinetic-energy identities above, and state the principle they support. Part II addresses questions which Part I raises but leaves unanswered: multiple solutions, time dependence, the role of spin, a route to the Schrödinger equation itself, and a proposed experimental test. AI has been used.

World simulation is inherently multisensory, demanding synchronized visual and acoustic dynamics in real time. Yet prevailing interactive world models remain strictly silent, focusing exclusively on visual rendering and control while overlooking the acoustic dimension. We present HelixWorld, a real-time interactive audio-visual world model where visual scenes and camera-grounded spatial stereo sound co-evolve natively under user interaction. We curate a high-fidelity spatial audio-visual dataset with true stereo acoustics and metric camera poses, upon which we pre-train a bidirectional teacher conditioned on 6-DoF camera trajectories and user actions. To enable low-latency causal interaction, we distill the teacher into a few-step streaming student via an online trajectory distillation loss, sustaining drift-free joint audio-visual rollouts at 24 FPS on a single GPU. Furthermore, we formalize spatial-acoustic consistency and introduce HelixBench to evaluate whether synthesized sound fields faithfully track dynamic viewpoint motion. Extensive experiments demonstrate that HelixWorld matches state-of-the-art silent world models in visual fidelity and responsiveness, while significantly surpassing existing baselines in camera-aligned spatial-acoustic immersion.

In 2023, pulsar timing array (PTA) collaborations around the world announced evidence for a nanohertz gravitational-wave background (GWB). Beyond increasing the detection significance, the next major goal is to characterize the GWB and identify its source(s). The typical model-comparison metric used in PTA analyses is the Bayes factor (BF). However, BF computation methods used in the PTA literature, such as product-space sampling and thermodynamic integration, are computationally expensive or inefficient if the models compared are dissimilar or non-nested. In this work, we introduce a PTA model-comparison method using a combination of normalizing flows, nested sampling, and a PTA likelihood that is marginalized over all non-GWB parameters. The flows are trained using a newly-developed Python package coppuccino, which learns the data's copula: the dependence structure after transforming to uniform marginals. We validate the method on both analytic targets and simulated PTA data, recovering the analytic evidence within error bars and achieving an area-under-the-curve (AUC) score of 0.996 when treating the BFs as binary classifiers of the injected models. The result is a method to perform Bayesian model comparison of arbitrary GWB spectral models in minutes on consumer hardware.

KV cache memory and bandwidth costs grow with context length and batch size, which limits efficient long-context inference. To address this bottleneck, we introduce WUSH-KV for low-bit KV-cache quantization. It adapts WUSH, which constructs a data-aware transform from the second-order statistics of both factors in a matrix product to reduce quantization error. WUSH-KV uses calibration data to construct separate key and value transforms, with the value transform folded into the model weights and the key transform applied after RoPE. The transforms can be paired with clipped quantizers. For one such quantizer, QuEST INT, we show that, under mild assumptions, the WUSH transform is near-optimal. With this quantizer, WUSH-KV reduces layerwise reconstruction error and achieves the lowest end-to-end perplexity among other tested transforms. For end-to-end evaluation, we integrate WUSH-KV into SGLang using OSCAR-style percentile-clipped affine quantization. At 2-bit, WUSH-KV performs comparably to or outperforms the OSCAR transform across all evaluated models and downstream tasks.

Verifying a vision-based neural feedback system requires a model of the observations its controller acts upon. Such a model must capture the variation the sensor produces, while remaining tractable for closed-loop analysis. Generative adversarial networks (GANs) have served as perception surrogates, but they are large, reproduce complex scenes poorly, and are hard to verify. We explore stochastic world models as a richer class of perception surrogates. We train a world model with physically grounded latents, built from operations that standard verifiers bound. It reproduces held-out frames more faithfully than GAN surrogates with up to 130 times as many parameters. To verify these surrogates, we develop a procedure that combines falsification, adaptive refinement, symbolic, and backward analyses. On an emergency braking benchmark with a GAN surrogate, our procedure resolves the entire state space, 38% of which the state-of-the-art verifier left unresolved. On the RGB version of the benchmark, where no verification results have previously been reported, our procedure resolves over 80% of the state space with a world model surrogate.