Papers

Scientific discovery begins where known problems end. There, AI systems must engage in exploration: framing hypotheses, designing experiments, and iterating on the results. However, evaluating this ability is difficult: (1) how to verify whether a genuinely new hypothesis holds, and (2) how to determine whether a system has discovered it through exploration or merely recalled related knowledge from pre-training data. To this end, we introduce ExplorationBench, which turns the wicked problem of evaluating scientific exploration into a concrete and tractable framework built on verifiable Alien Worlds: their rules are executable, so every answer can be checked exactly, and they conflict with familiar knowledge, so recall alone cannot solve the tasks. The benchmark contains two sandboxes, AlienCode (31 discovery targets, 70 tasks) and AlienLogic (24 discovery targets, 70 tasks). Each sandbox provides a flawed manual, task-specific environmental feedback, and a dedicated tool-call schema. Systems use these resources to explore the sandbox, then solve held-out tasks. We evaluate 10 AI systems and find that the strongest systems can acquire and apply unfamiliar rules, while performance varies substantially across trajectories and continued exploration can stall or reverse earlier gains. ExplorationBench represents a step towards AI systems that can acquire and apply genuinely new knowledge through exploration in unknown environments.

Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving full-resolution fields directly. In principle this reduces computational cost and simplifies learning, but in practice errors often accumulate rapidly during long autoregressive rollouts, limiting predictive utility. We show that this instability does not stem from the latent representation itself, but arises when it is trained solely for reconstruction, producing representations poorly suited to long-horizon forecasting. We systematically evaluate training-level interventions that align latent representations with long-horizon rollout: Koopman operator learning and Hamming noise injection during autoencoder training to improve compression, together with noise injection and multi-step rollout fine-tuning to improve dynamics. Interventions that improve long-horizon rollout stability often degrade conventional training metrics, including reconstruction and one-step prediction accuracy. Collectively, these interventions reduce long-rollout error by approximately 40% and match or exceed the accuracy of full-resolution models on two physics benchmarks, while requiring 2 orders of magnitude fewer floating point operations and half the GPU memory. Applied to mesoscale crystal-plasticity simulations of high-cycle fatigue, the resulting surrogate achieves stable extrapolation over horizons orders of magnitude beyond those observed during training. More broadly, these results show that neural compression should be designed not merely to reduce dimensionality, but to restructure the solution space for stable dynamical evolution, a key requirement for reliable, efficient neural surrogates in scientific applications.

This paper studies the three-dimensional Muskat problem for two immiscible fluids in a porous medium subject to gravity and surface tension. We consider the setting in which one fluid forms a bounded bubble surrounded by the other. For any value of the physical parameters, we prove the global-in-time nonlinear asymptotic stability of a translating spherical bubble for small initial perturbations in the critical Lipschitz class. This enlarges the class of critical spaces considered in previous two-dimensional bubble results. The proof combines spectral analysis of the linearized operator on $\mathbb{S}^2$ with multilinear singular integral estimates that exploit a crucial null structure in the nonlinear terms.

High-dimensional, unbinned neural simulation-based inference often relies on neural ratio estimation, which uses expressive supervised models to estimate density ratios, but a learned ratio by itself provides neither an explicit normalized density nor a generative model. Flow-based surrogate models instead enable tractable density evaluation and efficient sampling, but residual density-estimation errors can limit precision for complex implicit distributions. We propose hybrid neural density estimation, which uses a flow to define a parameter-independent reference distribution, and classifiers to estimate target-to-reference density ratios. Multiplying a learned ratio by the reference density gives an evaluable target density surrogate. The ratio also provides importance weights for integration and resampling. We show how this representation defines an exact Asimov dataset, whose maximum likelihood fit returns the generating parameters. We also show how the tractable reference supplies renewable samples for pseudo-experiments and how it enables methods to reduce the Monte Carlo variance of expected test statistic calculations. We demonstrate the construction in a toy statistical model motivated by high-energy physics measurements, but for which the exact densities are known analytically.

Loan portfolio optimization (LPO) seeks portfolios that minimize credit risk while satisfying practical selection constraints. Accounting for portfolio-level risk requires modeling not only expected losses but also loss variability and borrower-default correlations, leading to a large-scale combinatorial optimization problem whose complexity grows rapidly with portfolio size. In this work, we formulate LPO as a Quadratic Constrained Binary Optimization (QCBO) problem that jointly captures expected and unexpected losses and transform the resulting formulation into a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for variational quantum optimization. To address the limited qubit resources of current quantum hardware, we employ Pauli Correlation Encoding (PCE), which enables a large number of portfolio-selection variables to be represented using comparatively few qubits. The proposed framework is evaluated on a real-world microfinance dataset comprising 2012 borrowers. For problem instances with up to 1000 portfolio-selection variables, we benchmark classical simulations of a variational quantum algorithm (VQA) against Google OR-Tools under matched time budgets, obtaining feasible portfolios with an objective-value gap of about 40% across all sizes. We further implement the framework on superconducting quantum hardware for instances containing up to 1500 variables. Across these instances, the experimentally obtained objective values are within 10% of the corresponding simulation results. These findings demonstrate the feasibility of applying PCE-based variational quantum optimization to large-scale loan portfolio optimization under current quantum hardware limitations.

We prove that every bounded stable solution of the Allen–Cahn equation in $\mathbb R^3$ is one-dimensional. As a consequence, this shows the validity of De Giorgi's conjecture for monotone solutions in dimension four.

The Lempel-Ziv (LZ77) factorization decomposes a text into the least possible number $z$ of phrases that each refer to an earlier occurrence. It is this phrase count, rather than the encoded size, that governs the size of LZ-based compressed indexes, and computing a factorization with few phrases is a time and space bottleneck in their construction. In practice, computing LZ77 quickly typically requires the suffix array. In theory, the exact LZ77 factorization, and a 3-approximation of it, can be computed more space-efficiently without the full suffix array [SPIRE 2023]. These algorithms have remained unimplemented, because two of their components resist a direct implementation: a lookup table that degenerates to patterns of length at most two for realistic inputs, and an orthogonal range reporting data structure that is impractical. We replace both, fine-tune every remaining stage, and obtain the first practical implementation, which runs in space close to the text rather than to the suffix array. On one thread, our 3-approximation factorizes 12-19x faster than the classical LPF algorithm while using 14x less memory; on 32 threads, even our exact algorithm is 1.4-2.9x faster than parallel LPF, at 9x less memory. In practice the approximation ratio stays far below 3. As a side result, passing only the perfect phrases of our 3-approximation to a downstream compressor yields a precompressor that is on par with the state of the art [Dinklage, SEA 2026] in compression ratio, and better in memory consumption and parallel throughput.

Long-horizon reasoning remains a central challenge for large language models (LLMs) under sparse-reward regimes. We argue that this brittleness arises from two biases induced by complex reasoning spaces: an exploration bias, where models are drawn toward locally plausible but structurally unstable branches, and a compounding bias, where small local deviations accumulate across depth and suppress rare rewards. We introduce Symbolic Closure Analysis (SCA) as a theoretical lens characterizing how branching structures and sparse rewards induce these biases in long-horizon reasoning with local admissibility, and as a design principle for structural priors in less formal reasoning tasks. Motivated by this analysis, we propose SAGE (Structural Admissibility-Guided Exploration), a unified framework that injects structural guidance to alleviate exploration bias and compounding bias in long-horizon reasoning. SAGE combines two complementary structural guidance: algebraic sparsification, which projects locally admissible candidates onto operator-indexed algebraic subspaces to suppress spurious branching and mitigate exploration bias, and hyperbolic structural guidance, which embeds reasoning states into a negatively curved space to provide dense depth-wise signals and mitigate compounding bias. Across 12 benchmarks and 7 model families, SAGE outperforms competitive baselines. In particular, SAGE achieves up to an 8-fold improvement on the Andrews-Curtis problem, an open real-world long-horizon task. Code is available at: https://github.com/Susan571/SAGE-NeurIPS2026.

A $d$-set mapping is a function acting on a domain $X$ equipped with a partition into $d$ disjoint subsets. While standard functions represent $1$-set mappings, generalizations to arbitrary $d$-partite structures appear naturally across discrete mathematics. In this paper, we develop an analytic combinatorial framework to quantify the functional graphs of these mappings. By leveraging generating functions and singularity analysis, we derive exact asymptotic expansions for macroscopic graph properties as the cardinality of $X$ tends to infinity, including the expected number of connected components, cyclic nodes, and tail lengths. We demonstrate the efficacy of this framework by recovering the classical bipartite mapping results of Hansen and Jaworski, and successfully generalize these mechanisms to arbitrary $d$-set mappings, providing the foundational architecture to establish their probabilistic limit laws.

Phase I cancer trials seek the maximum tolerated dose (MTD) while protecting patients from excessive toxicity. Dose assignments must therefore balance patient safety with learning the dose–toxicity relationship as data accrue. We model continuously measured toxicity outcomes using two forms of Bayesian additive regression trees (BART): isotonic BART projects posterior response curves onto nondecreasing functions, whereas monotone BART constrains the model. Joint curve and variance draws induce an MTD posterior that guides dose selection through escalation with overdose control (EWOC). We compare these methods with three parametric procedures across seven dose–toxicity curves in simulation. We assess dose-limiting toxicity (DLT) counts, above-MTD assignments, signed last-dose error, and relative absolute error. The tree procedures attained the lowest mean RAE on four nonlinear curves and jointly minimized mean DLT counts and above-MTD assignments on four curves. A Bayesian reinforcement learning perspective formulates these sequential decisions as a finite-horizon planning problem. Dose restrictions yield a lower bound on last-dose error; under exact posterior-predictive evaluation, an EWOC-based rollout policy has no greater expected weighted loss than its baseline. Dose Trial Lab, a desktop simulator for all five procedures, accompanies the supplementary material.

A standard question in computational real algebraic geometry is to compute all real solutions to a system of polynomial equations with real coefficients. One classical and promising approach is to track along a connected component of a real curve defined by a Newton homotopy, which is dependent upon the selected start point. As the start point varies, different subsets of real solutions may be obtained. This yields a partition of the space of start points into cells, and it is important to understand the structure of this partition in order to develop efficient algorithms based on Newton homotopies. The structure of the boundary of such cells and the number of cells in the corresponding partition are investigated for bivariate systems. Several examples are included to demonstrate the results.

Questionnaire-based patient-reported outcomes (PROs) are discrete, bounded and overdispersed, yet joint models relating them to survival may ignore these features or estimate both processes sequentially. We propose a Bayesian joint model combining a beta-binomial mixed-effects submodel with a Weibull proportional hazards submodel, linked through the subject-specific response probability. Simulations show that simultaneous estimation reduces bias in the longitudinal slope and yields practically unbiased association estimates, unlike two-stage estimation. In a cohort of 543 patients with chronic obstructive pulmonary disease, the model identified associations for all eight SF-36 dimensions and for two of three SGRQ dimensions, including several associations not detected by the two-stage approach, and provided dynamic survival predictions.

Ego-Exo4D is a large-scale dataset providing synchronized egocentric and multi-view exocentric video, a rich resource for skill learning and assessment, procedural activity understanding, and embodied AI. However, the dataset ships with only sparse 3D human pose annotations, and reconstructing dense human motion from its multi-view captures is nontrivial. To this end, we present Ego-Exo4D-HM, a large-scale dataset of 4D human motion reconstructions for Ego-Exo4D's captures, and release the accompanying reconstruction pipeline. The code, dataset, and documentation can be found at https://abhiram824.github.io/egoexo4d_human_meshes.

Vision-language models (VLMs) have become a common foundation for autonomous mobile GUI agents, but most existing systems rely on the VLM for both planning and action grounding at nearly every interaction step, leading to substantial latency and model-serving cost. We introduce Jev-Mobile, which shifts this paradigm to low-frequency VLM planning and high-frequency lightweight execution: the VLM specifies local goals, the accessibility tree defines a structured executable action space, and Jev, a fast typed decision model, repeatedly selects actions within this space. This design allows multiple GUI actions to be executed under a single VLM decision, reducing expensive VLM inference while preserving adaptive interaction. On the full AndroidWorld task suite, Jev-Mobile achieves 79% task success, compared with 78% for SeeAct-V and 84% for a Step-wise VLM baseline. Among successful trajectories, it reduces mean end-to-end execution time by 32.7% and mean model API cost by 73.4% relative to Step-wise VLM. These results show that decoupling high-level VLM reasoning from low-level action execution can substantially improve mobile GUI agent efficiency while maintaining competitive task performance.

A learner's current observations need not determine its response to further training. We formulate intrinsic-extrinsic coupling through the continuation-conditioned value of a constrained learning-state intervention, with observation-relative fibers describing present agreement. An executable finite-frame classifier-head write protects current logits while repairing specified historical margins under finite-precision acceptance checks. We distinguish local admissibility, continuation-conditioned intervention value, and complete-policy performance. A matched four-cell contrast identifies readout-specific non-additivity between the same intrinsic intervention and alternative external continuations. In a CLINC-derived class-incremental setting, replay changes the write's 32-update contribution from five correct predictions to zero. Nonzero interactions also occur under output distillation, with a RoBERTa backbone, and under optimizer-native SGDW dynamics. Under SGDW, correct-count interactions are negative in all three activated roots at 128 updates, showing that coupling need not imply positive synergy. The mathematical analysis distinguishes feasible local repairs and favorable terminal outputs from training-reachable repair regions. Separate coordination tests show that content controls match or exceed the development gain, while a five-root fresh-test comparison with Fiber present in every arm shows root-dependent rather than uniformly beneficial correct-count effects. On the secondary cross-entropy readout, guided allocation yields lower mean loss than standard replay in all five pairs. Together, these results make intrinsic-extrinsic coupling operational by connecting executable state geometry to continuation-conditioned value, matched interaction identification, and closed-loop coordination, while separating identified coupling from complete-policy performance.

U.S. employment-discrimination complaints describe complex event sequences that are not explicitly captured by lexical or embedding-based representations alone. We present ARGUS, a source-grounded pipeline that combines a 5W1H-inspired schema, legal-domain models, and LLM-based structured generation to construct document-level Event Knowledge Graphs (EKGs) from CourtListener complaints. ARGUS extracts fact-bearing statements, builds chunk-level event graphs with participant, temporal, and causal structure, and merges them into document-level representations. We evaluate graph quality through human and multi-model assessment and test downstream utility on claim classification and legal QA. The graph-structured classifier outperforms raw and linearized baselines on the held-out set, and EKG-only retrieval improves document-scoped QA, while open-retrieval gains remain limited by low first-stage candidate recall. These results suggest that EKGs are most useful for organizing and reasoning over evidence once relevant material has been retrieved.

High-performance optical systems, including space telescopes, require wavefront-sensing and correction capabilities to achieve resolution near the diffraction limit. Existing wavefront-sensing approaches span a broad range of architectures, but many require dedicated interferometric hardware, rely on computationally intensive nonlinear or iterative reconstruction algorithms or provide only limited wavefront information. Focal-plane wavefront-sensing methods are particularly attractive because they can operate without dedicated metrology hardware, and among these, Double Blind Fourier Holography (DBFH) stands out as a robust and computationally light alternative to nonlinear and iterative solvers. Here we introduce differential Double Blind Fourier Holography (diff-DBFH), a two-image variant of DBFH based on a small pupil-plane amplitude perturbation. Inspired by differential Optical Transfer Function (dOTF), diff-DBFH leverages the linear framework of DBFH to produce a more precise wavefront estimate. We derive the diff-DBFH formalism, compare its performance against dOTF using numerical simulations on a segmented aperture geometry inspired by the Habitable Worlds Observatory, analyze its sensitivity under noisy conditions, and demonstrate the method experimentally using an optical bench model of the same aperture.

We import the theory of $R$-links and derivative links into contact topology in both the Legendrian and transverse setting. This framework is used to characterize various forms of Lagrangian and symplectic sliceness, and more generally establishes one approach to what we call the Lagrangian slice-ribbon conjecture. Our main theorem asserts that a Legendrian knot with Thurston-Bennequin invariant $-1$ is Lagrangrian slice (resp. regularly Lagrangian slice) if and only if it supports a tight transverse (resp. Legendrian) $R$-link derivative.

We address the inverse problem of reconstructing the initial temperature distribution in a one-dimensional non-homogeneous heat equation with Dirichlet boundary conditions from a finite number of pointwise-in-time measurements at a single spatial location. We propose an explicit approximation scheme that incorporates the source term and utilizes a refined sequence of measurement times. Unlike previous approaches that often rely on exponentially growing observation times, our chosen time sequence allows for efficient recovery within a fixed time horizon. We establish algebraic convergence rates under suitable regularity assumptions on the initial data and the forcing, and we validate the theoretical sharpness with numerical experiments for varying numbers of measurements.

Could a collider become the symbol of everything that must be abandoned to save the climate? In the summer of 2026, this question ran through discussions within the Particles and Fields Division of the French Physical Society. An unacceptable carbon footprint, two EPR nuclear reactors, five hundred deaths, billions to be reallocated and, to top it all, unclear scientific objectives: the objections to CERN's Future Circular Collider (FCC) appeared to form an overwhelming indictment. This essay examines each charge in turn. Grounded in a clear and compelling scientific vision, it confronts emotionally charged imagery with orders of magnitude, distinguishes a project's footprint from its full balance sheet, considers the costs of postponing or abandoning it, and explores ways of reducing its impacts-including the still uncertain prospect of natural hydrogen. The climate alone does not decide the future of the FCC; it requires us to judge the available choices by their real consequences. Developed for the public debate organised by France's National Commission for Public Debate (CNDP) and for the Swiss consultation, this essay is intended for the broadest possible readership, well beyond particle physics and the scientific community. It frames the FCC debate as a choice about the kind of society we want to build: should we organise society around renunciation and ever-shrinking horizons, or transform how we produce and choose a future worth wanting?

Hyperbolic metamaterials (HMMs) are widely used to enhance spontaneous emission through their exceptionally large photonic density of states, yet large Purcell factors (>100) rarely translate into brighter emission, exposing both a practical limitation of HMMs as brightening platforms and a flaw in the Purcell factor itself as a figure of merit. Here we systematically evaluate spontaneous emission enhancement and photon outcoupling in metal-dielectric HMMs (TiO$_2$/Ag and phase-change Sb$_2$S$_3$/Ag) using effective medium theory, transfer matrix calculations, and full-wave FDTD simulations. We show that planar HMMs with Purcell factors exceeding 100 have external quantum efficiencies below 0.01, yielding an actual radiative Purcell factor (PF$_{rad}$) of only 1-2. Nanopatterning the HMM into a photonic crystal efficiently couples trapped high-k modes into free space, raising PF$_{rad}$ by an order of magnitude. Incorporating the phase-change material Sb$_2$S$_3$ further enables dynamic tuning of the hyperbolic spectral window and active control over emission brightness: an optimized nanostructured design reaches PF$_{rad}$ ~ 10-15 in the near-infrared, with switching contrast exceeding a factor of 15 upon phase transition. These results establish the radiative Purcell factor as a more reliable figure of merit than the conventional Purcell factor for engineering quantum emitters, and provide a practical route toward actively tunable, bright single-photon sources based on hyperbolic metamaterials.

Ensuring high structural coverage remains a fundamental challenge in automated test generation, particularly for complex software systems where reaching specific lines or branches requires satisfying intricate control- and data-flow constraints. Large Language Models (LLMs) have recently demonstrated strong capabilities in producing human-like test cases; however, they often struggle to generate inputs that satisfy precise path conditions. Conversely, symbolic execution can systematically derive such constraints, but it often fails to construct realistic, executable test cases and is constrained by scalability limitations. In this paper, we introduce NEUROTESTGEN, a hybrid approach that integrates symbolic execution with LLM-driven test synthesis to generate test cases targeting on-demand code coverage. Given a set of target statements within a method, NEUROTESTGEN first employs a symbolic analysis engine (i.e., the Z3 SMT solver) to extract path-specific constraints and construct a symbolic guidance specification for the desired coverage goal. This specification is then used to guide an LLM in synthesizing concrete test cases that are both structurally valid and semantically meaningful. For paths involving complex object-related constraints that are difficult for SMT solvers to handle, NEUROTESTGEN leverages LLMs to infer plausible constraints. Furthermore, NEUROTESTGEN incorporates an iterative feedback loop that validates LLM-generated tests and provides corrective guidance until the target line or branch is covered or a limit is reached. Our empirical evaluation on a widely used benchmark demonstrates that NEUROTESTGEN significantly outperforms the state-of-the-art approach across multiple LLMs, including Llama 3.3 70B1, GPT-4o Mini, Claude 3.5 Haiku3, and Claude Sonnet 4.6.

Query understanding (QU) in production search systems has typically relied on separate models for each subtask, such as search intent classification, attribute extraction, and query rewriting. Large language models (LLMs) now make it possible to consolidate these subtasks into a single model that emits a unified QU output. This consolidation, however, introduces a new optimization challenge. A single model serves multiple components, each with a distinct downstream role within the search pipeline, and the utility of each depends on how the underlying search engine acts on it rather than on agreement with static labels. We present a search-aware reinforcement learning (RL) framework for multi-component QU based on a distill-then-RL paradigm. Teacher-student supervised fine-tuning (SFT) first yields a schema-compliant small policy. The RL stage then starts from this policy, executes each QU plan on the live production search engine, and optimizes every component with a reward tailored to its operational role, rather than relying on a single reward tied to the final search outcome. On a large-scale user-generated game platform, this component-specific optimization raises NDCG@20 by 8.9 points over the SFT policy and by 3.5 points over a single end-to-end reward. The resulting small, low-latency student models also surpass their much larger teacher, and our final model is being incrementally deployed in production.

Low-resolution FMCW radar normally forms a complete range-Doppler representation before detection and tracking. After association, however, the tracker already predicts the target's next range and radial velocity. We propose track-conditioned residual estimation (TCRE), which removes the predicted moving-target phase before spectral formation, summarizes each 64-sample chirp by four coherent complex sums, and estimates the remaining beat-frequency and Doppler-frequency errors from phase progression. We account for the first-order fast-time and slow-time coupling of a moving target and derive the local phase-unwrapping region and three-receiver local information bound. Four summaries retain 93.77 percent of the zero-residual fast-time information while reducing the retained representation by a factor of 16. In 5,000 matched 60-GHz cluttered simulations, TCRE reduces range RMSE by 32.8 to 46.3 percent and velocity RMSE by 58.6 to 71.0 percent relative to a fully specified same-prior residual ZFFT.

Suppressing decoherence and crosstalk systematically across large networks of qubits is a pressing concern as qubit counts increase rapidly. General multi-qubit dynamical decoupling (DD) has historically been based on Hadamard matrices and orthogonal arrays, with instantaneous-pulse sequences whose circuit depth scales linearly with the number of qubits. Chromatic-Hadamard DD (CHaDD) improves upon these methods by properly coloring the hardware graph and assigning to each color a row of a Hadamard matrix, resulting in a circuit depth that scales linearly with the number of colors $C$, which can be as low as the chromatic number of the graph. Here, we explore the tradeoff between circuit depth and the pulse repetition rate (PRR), the average fraction of time steps in which a qubit is pulsed, i.e., a measure of pulse density. We introduce two single-axis sequences based on binary and Gray matrices, Chromatic-Binary DD (CBDD) and Chromatic-Gray DD (CGDD), which, for $C>2$, are special cases of non-minimum-depth CHaDD and achieve PRR $<2/C$ and PRR $=1/C$, respectively, compared with a PRR above $1/4$ for CHaDD, at the price of a circuit depth of $2^C$. In state preservation experiments on a $127$-qubit IBM processor with $C=3$, the less dense sequences outperform CHaDD at short times when the pulses are not robust; this advantage is largely eliminated by robust versions designed to compensate for coherent pulse errors, and among the robust sequences, CGDD uses the fewest pulses over a fixed protection time. Across non-robust $C=3$ and $C=5$ schedules, equal PRR on a fixed qubit subset is empirically associated with similar state preservation. Thus, the PRR serves as a practical figure of merit for chromatic DD whenever coherent pulse errors dominate.

Variable selection using information criteria has an explicit statistical target but requires discrete search over candidate models. The smooth information criterion (SIC) replaces the discontinuous model-dimension term by a differentiable approximation, with an $\epsilon$-telescoping continuation strategy progressively sharpening this approximation without data-driven selection of a regularisation-strength parameter. We develop SIC as a general procedure for coefficient-level variable selection in generalised linear models (GLMs) and use it to address a central question: how faithfully does smooth optimisation reproduce the corresponding discrete information-criterion selection problem? Focusing on BIC, we benchmark SIC directly against exhaustive subset selection where feasible, using exact support agreement, BIC difference and selection behaviour across a varying signal-strength boundary. Simulations in Gaussian, binomial and Poisson regression show that SIC closely reproduces exhaustive BIC selection and tracks the exact BIC selection boundary. Relative to stepwise BIC, LASSO, SCAD and MCP, SIC produces competitive variable-selection performance while retaining sparse models, with predictive performance broadly comparable across methods. Computational advantages over stepwise BIC increase with predictor dimension. In a real-data application with 16 candidate predictors, SIC recovers the globally BIC-optimal model among all 65,536 supports at a small fraction of the computational cost of exhaustive enumeration.

We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a $15$ million parameter physics-inspired graph neural network pretrained across $54$ topologies of $500$ to $4{,}000$ buses. Our model attains a $2.45\%$ zero-shot generation-cost error on a $10{,}000$ bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only $100$ solved instances, GridSFM adapts to unseen grids up to $10{,}000$ buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.

We study a robust multiuser framework for simultaneous wireless information and power transfer (SWIPT), where rate-splitting multiple access (RSMA) is integrated with a movable-element simultaneously transmitting and reflecting surface (ME-STARS). By allowing the STARS elements to change their positions in addition to controlling the reflection and transmission coefficients, the proposed architecture provides additional spatial flexibility for improving the cascaded channels toward users in both regions. Meanwhile, RSMA is employed to manage multiuser interference, while power-splitting receivers enable simultaneous information decoding and energy harvesting. The system design further accounts for channel state information (CSI) uncertainty, residual transceiver hardware impairments (HIs), and the nonlinear characteristics of practical energy-harvesting circuits. Accordingly, a robust sum-rate maximization problem is formulated by jointly designing the BS precoders, common-rate allocation, ME-STARS reflection/transmission coefficients, power-splitting (PS) ratios, and movable-element positions. The resulting formulation is highly non-convex because the movable-element positions affect the cascaded channels non-linearly and are tightly coupled with the remaining design variables. To obtain a tractable solution, the joint design is decomposed into active beamforming, passive beamforming, movable-element positioning, and PS-ratio optimization blocks, which are updated iteratively through suitable convex reformulations. Numerical results show that the proposed framework delivers higher sum rates than the considered benchmark schemes, exhibits robust behavior under CSI uncertainty and residual HIs, and achieves stable convergence across the considered system configurations.

We prove that the spectrum of an unknown $d$-dimensional quantum state can be estimated to error $\varepsilon$ in total variation distance using \[ O\!\left(d^2\min\left\{ \frac{1}{(\varepsilon\log d)^4},\; \frac{1}{(\varepsilon\log d)^2} \right\}\right) \] copies. This matches the recent lower bound of Wang. When restricted to unentangled measurements, we give an algorithm with an additional factor of $d$ in copy complexity, which we conjecture to be optimal. We develop a framework for recovering the small eigenvalues of a quantum state by matching Chebyshev moments. We bound the variance of each Chebyshev moment estimate in terms of scalar derivatives of the corresponding polynomial, using classical and quantum Efron–Stein decompositions. Different rescalings of the Chebyshev polynomials balance approximation error and variance, yielding two regimes in our copy complexity bound.

Kehle and Unger have recently shown that self-gravitating charged classical scalar fields can collapse to form extremal Reissner-Nordström (eRN) black holes in finite time, thus violating the third law of thermodynamics (TLT). Reall has subsequently proved that the formation of an eRN black hole in gravitational collapse is impossible if the mass-to-charge ratio of the field exceeds unity, $m/e\geq1$. In the present compact paper we conjecture, using quantum considerations, that the Reall bound is not sharp. In particular, we point out that the electric field of a charged system with charge $Q$ will spontaneously polarize the vacuum in the regime $(eQ/\hbar)^2>(mQ/\hbar)^2+1/4$, thereby creating pairs of charged particles that discharge the black hole and ensure the quantum validity of the TLT in this regime. Motivated by the TLT, we conjecture that the classical Reall bound can be strengthened such that classical considerations would prevent eRN black holes from forming dynamically in the regime $m/e\geq\sqrt{1-\big({{\hbar}/{2eQ}}\big)^2}$, where quantum polarization effects are unable to protect the TLT.