Papers

Large language models are stochastic by nature. Repeated executions under the same experimental conditions may produce different responses. We propose a framework that can be applied across the model lifecycle, from task design to residual behavior and continuous monitoring. The method consists of building an empirical response distribution estimated through Monte Carlo simulation. Semantic interventions are introduced to study how these distributions change. We illustrate the framework with two different tasks, borrower classification and music album recommendation, and quantify the resulting distributional changes. The framework is linked to model risk management and governance by measuring robustness and control effectiveness, and characterizing residual behavior. Since it relies only on observed responses, it can also be applied to black-box models accessed through commercial APIs.

Instructions to assemble flat-packed furniture rely on visuals, making them inaccessible to Blind and Low Vision (BLV) individuals. Consequently, BLV individuals depend on caregivers or external services (e.g., Be My Eyes), limiting their autonomy. We explore how to empower them to assemble such furniture themselves, by providing eight BLV participants in our study with accessible instructions consisting of a high-level roadmap and stepwise procedural guidance. We use a technology probe, AssemblyLens, which converts visual assembly instructions into screen-reader-accessible text. We derive insights into converting instructions, empirical observations of BLV assembly strategies, and the role the roadmap played in them. Our observations yield three themes: spatial cognition and mental mapping, embodied ergonomics and kinetic semantics, and assembly workflow and user agency. We present eight design recommendations for instruction system design. Our findings are a step toward an agenda for inclusive instruction in physical tasks.

Hybrid-abandonment systems, where jobs abandon from certain stages of service but not others, occur frequently in medical, service, and computing systems. Abandonment affects the heavy-traffic behavior of both the stages with and without abandonment. In contrast to existing heavy-traffic works that focus on cases where there is abandonment at either all stages or no stages, we focus on the heavy-traffic behavior for these hybrid-abandonment systems. We provide the first heavy-traffic characterization of the second queue length in a two-stage tandem queue with abandonment only in the first stage. We characterize the scaled mean of the second stage queue length and prove that the scaled second queue length is asymptotically exponentially distributed and asymptotically independent of the first stage queue length. We derive our results by analyzing Markovian arrival process queues with countably infinite phases. We do this by extending techniques used to analyze queues with Markov-modulated arrivals to the broader class of infinite Markovian arrival process queues. We prove asymptotic results for a more general infinite phase process condition, an infinite birth-death phase process, and the hybrid-abandonment tandem case. We also empirically demonstrate that our heavy-traffic approximations are good approximations across various system settings.

Theory predicts that H I emission from photoionized clouds should lie close to the Case B limit established by Menzel and Baker, and observations of nearby nebulae have largely confirmed this expectation. However, recent observations of more distant high-redshift systems have revealed a small fraction with striking departures from Case B. What additional physics might be at work in these objects? This paper is part of a series exploring the physical processes that can produce such departures. In Paper I (D26), we show that Case B remains remarkably robust over a broad range of physical conditions, consistent with observations of nearby nebulae. Here, we explore one additional ingredient: a soft, non-ionizing radiation field. Such a continuum can strongly perturb the Balmer spectrum. The largest effects occur for radiation fields resembling log(Teff K)\sim 3.2-4.2 blackbodies, where photoexcitation from the metastable 2s level alters the hydrogen level populations and subsequent radiative cascade. The resulting Halpha/Hbeta and Hgamma/Hbeta ratios follow a different trajectory from dust reddening, allowing the two effects to be distinguished using multiple Balmer lines. In unresolved systems, a cool source located near the line-emitting gas may provide an additional radiation field distinct from the hot stars responsible for ionization. Balmer decrements may therefore carry information about otherwise hidden components of the radiation field surrounding the emitting gas.

Bilayer graphene (BLG) is a unique electronic material offering electrostatic tunability of its band gap. Here, we study how charge disorder in the dielectric environment modifies band-edge states by binding electrons and holes to Coulomb centres, taking into account the in- and out-of-plane dielectric response of Bernal bilayers. We apply this framework to (a) hBN-encapsulated medium-size-gap BLG used for gate-defined quantum dots, and (b) BLG under double n/p ionic gating. In hBN/BLG/hBN, we find that single remote charges produce only weakly bound states, with binding energies generally small compared with the BLG gap. Under ionic gating, we find that the bound states are too large to be trapped by individual ions – localisation arises from fluctuations in the ion density, whose magnitude is limited by Coulomb charging energy at the freezing temperature $T_f$ of the ionic configuration. Thus, in both regimes, charge disorder does not produce deep midgap states, with the bound states remaining closer to the conduction and valence band edges.

Stochastic dual dynamic programming (SDDP) and its variants are run in practice with forward passes that sample the noise at random. Recent iteration-complexity results favour another choice: when the trial points are selected deterministically, for instance along the scenario with the largest gap, the number of iterations is polynomial in the horizon $T$, whereas every bound we know of for randomly sampled forward passes is exponential in $T$. We show that this is not intrinsic to random sampling, for a broad class of trajectory-following dynamic programming algorithms, which includes SDDP, stochastic dual dynamic integer programming and stochastic Lipschitz dynamic programming. With random sampling, and with Lipschitz constants, diameters and per-stage loss ranges bounded independently of the stage and of the horizon, the expected number of iterations whose policy is not $T\varepsilon$-optimal is $O(T\varepsilon^{-(d+1)})$, where $d$ is the state dimension: linear in $T$, as for deterministic selection rules. The proof needs no particular scenario to be sampled: the gap between the expected cost of the current policy and the current lower bound equals the expected sum of one-step Bellman residuals along the sampled path, and Lipschitz cuts that are tight at the visited states turn the positive residuals into permanent increases of a bounded potential. The results extend to noise without finite support, to backward passes on a sample average approximation, and to stationary and periodic infinite-horizon SDDP with geometric pass lengths.

The current state of the art for batch selection and noise addition in differentially private training is a combination of DP-BandMF (informally, DP-SGD where the noise added in two different steps can be correlated if the steps are within $b$ of each other) and privacy amplification by sampling via Monte Carlo accounting. First, whereas prior batch selection strategies for DP-BandMF were inspired by Poisson sampling, random allocation is known to outperform Poisson sampling for DP-SGD. We therefore propose and analyze new batch selection strategies for DP-BandMF inspired by random allocation, improving RMSE by up to $1.85\times$ over previous work. Second, Monte Carlo accounting typically requires drawing $\Omega(1/\delta)$ samples from a privacy loss distribution, making accounting costly. We increase sampling and scoring throughput by two orders of magnitude through a carefully optimized GPU implementation. Finally, previous work chose the DP-BandMF strategy matrix and the batch selection strategy independently. We give a simple framework for choosing these parameters jointly, reducing RMSE by up to $13.4\%$ over fixed strategy matrices.

Federated Large Language Models (FedLLMs) are promising to deliver privacy-preserving, collaborative intelligence. The decentralized training process is vulnerable to Byzantine attacks that corrupt semantic consistency and factual resilience through malicious model updates. This paper presents a new resilience strategy that prevents semantically corrupted knowledge from propagating during federated aggregation. A defense problem is formulated to jointly maximize global accuracy and suppress manipulated model updates, enabling trustworthy knowledge aggregation without accessing private local data. To strengthen the resilience of FedLLMs, we develop a novel Hypergraph Message Passing Graph Autoencoder (HMP-GAE) framework, where low-rank model updates are represented as nodes in a hypergraph and high-order semantic relationships among multiple agents are exploited through iterative message passing. By leveraging historical checkpoints and cross-agent relational reasoning, HMP-GAE identifies and suppresses semantically inconsistent updates while preserving knowledge alignment among agents throughout federated training. HMP-GAE is implemented using Qwen-2.5 and Llama-3.2 as pretrained FedLLM backbones and evaluated on AG News and Yahoo! Answers datasets. Compared to existing defenses, HMP-GAE improves global accuracy by $1.21$%, reduces final-model classification semantic entropy by $44.08$%, and lowers perplexity by $13.34$%. HMP-GAE outperforms the GAE-based defense by improving the accuracy $1.39$%, reducing the semantic entropy by $54.5$%, and lowering perplexity by $35.5$%.

Long-horizon manipulation requires robots to retain task-relevant history while revising conclusions no longer supported by physical evidence. Retaining observations alone does not specify which completed conditions should be withdrawn after a disturbance or which obligations require repair. We introduce REMM, Revisable Embodied Memory for Manipulation, a supervisory memory layer for a frozen G0.5 vision-language-action executor. REMM separates an append-only evidence history from revisable task state and explicitly links derived relations and completed conditions to their supporting facts. When accepted evidence changes a supporting fact, it withdraws dependent conclusions and schedules targeted recovery at verified skill boundaries without updating the executor. Across 51 physical trials, including operator-assisted runs, REMM improves mean recorded task progress over the strongest baseline from 57% to 91% in intervention recovery and from 43% to 70% in sequence recall. Complementary video diagnostics show improved grounding of retained history into the next instruction, including comparisons with $\pi_{0.5}$-compatible high-level planner adaptations. These results support revisable memory as a practical interface for continued manipulation without policy retraining. Project: https://revanthsenthil.github.io/remm/.

Turbulent conjugate heat transfer (CHT) in pipes with azimuthally non-uniform heating is studied theoretically and numerically with a focus on low-$\mathrm{Pr}$ fluids. While the influence of the solid properties is well documented for uniform heat flux, their effect under azimuthally non-uniform heating has not been explored systematically. We address this gap by combining spectral analysis of the problem – which reduces arbitrary boundary conditions to a discrete set of azimuthal wavenumbers – with well-resolved numerical simulations of thermally and hydraulically fully developed turbulent pipe flow at $\mathrm{Re}_\tau \approx 180$ for $\mathrm{Pr} = \{0.025, 0.71\}$, representative of liquid metals and air. Two principal results emerge: (i) the global Nusselt number is independent of the azimuthal heat-flux distribution and exhibits only a minor dependence on the solid properties, resolving an open question for low-Prandtl-number fluids; (ii) CHT nevertheless strongly affects the azimuthally resolved mean temperature at low $\mathrm{Pr}$, where azimuthal conduction in the solid homogenises the interface heat flux, and governs the level of temperature fluctuations through the effusivity ratio (thermal activity ratio) $K$. Finally, an analysis of the turbulent Prandtl number $\mathrm{Pr}_{t}$ shows a strong anisotropy, particularly near the wall, and a dependence on the azimuthal wavenumber.

This manuscript demonstrates that the Schwarzschild and Kerr metrics can be derived fundamentally from the Einstein Equivalence Principle (EEP) without explicit reliance on the Einstein field equations. We show that the EEP implies a gravitational stretching of length in the direction of acceleration, a spatial counterpart to time dilation. In the static case, this effect yields the constraint $g_{00}g_{11}=-1$, from which the Schwarzschild solution is recovered by taking the Newtonian limit. For the stationary case, we employ oblate spheroidal coordinates and construct a physically motivated tetrad to implement the EP, introducing gravity through three unknown functions. By applying the EEP-induced constraints and showing that the principle requires the preservation of the spacetime volume determinant ($g = g_0$), the system is reduced to a single unknown function that yields the Kerr metric. These results suggest that classical tests of General Relativity are, at their core, fundamental validations of the EEP. We further argue that the EEP leads naturally to Unimodular Gravity, implying that the existence of the cosmological constant is a direct consequence of this foundational postulate.

Vision-language reward models are trained on annotated preference pairs, which are expensive to collect, can disagree, and are ranked by benchmark accuracy. We build one with no human preference label: a linear head on an intermediate layer of a frozen Qwen3-VL backbone, trained to score a web caption above a perturbed version of the same caption; labeled data enters only to select the layer. The layer is the decisive choice, worth 5.8 points over the last layer, and one recipe transferred without re-tuning beats or at least matches GPT-4o on three benchmarks at 32B, 6.6 points ahead on VL-RewardBench, from a few thousand parameters at about a thousandth of fine-tuning compute. At an equal pair budget, perturbations teach a frozen head 3 to 5 points more than curated RLAIF-V pairs. Because the backbone is frozen, the objective is convex, and the perturbation sampler specifies the reward, which the benchmark does not identify: two heads trained on disjoint halves of the same perturbations tie on the benchmark and differ by 6.4 points in hallucination judging. Retraining the head on the policy's own verifier-labeled candidates cuts caption hallucination by 5.1 CHAIR points and lifts image-generation pass rate by 5.4, while scoring lower on every reward benchmark. Together, an intermediate-layer probe, free same-image perturbations, and a verifier-driven bootstrap turn give a recipe for multimodal reward modeling that needs no annotator, costs a fraction of fine-tuning, and is specified by the comparisons it is trained on rather than by a benchmark rank.

Concerns about falling and potential resulting injuries prevent many older adults from participating in forms of health-improving exercise such as walking, dance, and tai chi. Existing passive devices like walkers require use of the arms for support, and active devices like exoskeletons and robotic frames are often rigid, bulky, and stigmatized, which limits their use. The FallGown is a soft wearable support structure consisting of pressurized pneumatic pouches within a fabric shell; it can support the full weight of a user's body and aims to prevent falls. It is portable (6.9 kg and 0.051 m3 when stored), minimally burdensome (7.24-20.8 N drag force depending on floor type and whether an optional rolling base frame is used), and convenient (less than 2.5 minutes on average to don and less than 0.5 minutes on average to doff). The optional rolling base lowers friction with the floor, but reduces portability and skirt deformation (which can be useful to fit through doors and other tight spaces). Fall prevention testing with a single user revealed a tradeoff between device size and stability against tipping; a skirt with 12 pneumatic pouches and a floor diameter of 1.4 meters with a base frame prevented all falls except in one case with a mechanical failure. On-board pressure sensors can sense the user's weight distribution, providing an opportunity for monitored exercise and adaptive support.

We combine the universal polynomial matrix identities of Larsen–Nguyen with Trost's arithmetic lemmas to obtain polynomial parametrizations of $\text{SL}_2(\mathcal{O}_{K,S})$ for every global function field $K$ and every nonempty finite set of places $S$. The additional ingredient is a function-field cancellation lemma, proved using ray class fields and Chebotarev in odd characteristic and the perfectness of finite residue fields in characteristic two. The proof also gives a polynomial matrix over $\mathbb{Z}$ that works simultaneously for all these rings.

Federated learning allows dispersed oilfield sites to train a shared intrusion detector without pooling network traffic, yet its aggregation step forces a choice between privacy and robustness. Byzantine-robust rules must read each update in the clear, whereas secure aggregation hides updates from the checks that detect poisoning. We present PVBRF-ID, a two-server protocol in which sites secret-share their updates and the servers jointly test each update's norm and its cosine similarity to a reference computed on a small clean root set, revealing one accept bit per site. Commitments, Merkle roots and a homomorphic audit make the inclusion of accepted updates publicly verifiable. On a 15-class Edge-IIoTset task with ten sites holding differently distributed data and ten random seeds, PVBRF-ID matched FedAvg on clean data (macro-F1 0.708 vs. 0.706) and withstood sign-flip attacks (0.696 vs. 0.091). Against an adaptive attacker controlling 30% of sites, PVBRF-ID with secure clipping reached 0.641, whereas FedAvg fell to 0.046; plaintext multi-Krum remained higher by 0.052. An update-inference attacker recovered each site's class mix from plaintext updates (Spearman correlation 0.81) but not from one server's view. Backdoors passed the filter, and noise-based mitigation gave only heuristic protection. The implementation uses Python 3.13, NumPy 2.3, 30 rounds and 10 seeds.

High-risk applications of deep learning require precise characterization of model decision-making. We conduct a systematic explainability evaluation across Convolutional Neural Networks (CNNs), Vision Transformers (ViTs), and Vision Mamba (ViM). Unlike predominantly qualitative studies, we quantify the alignment between model attention and human visual perception using eye-tracking ground truth. We formalize this comparison via a standardized normalization pipeline mapping post-hoc attribution maps and gaze heatmaps onto spatial probability distributions. Alignment is evaluated across fine-grained classification, medical imaging, and emotion recognition using architecture-specific XAI methods. We measure fidelity using Jensen-Shannon similarity, Chi-square similarity, and Pearson correlation, three complementary estimators capturing support overlap, mass discrepancy, and structural co-variation. Our results reveal distinct attention dynamics: CNNs tend to exhibit a more global focus, with spatially more diffuse saliency maps that correlate well with human perception in general contexts, while ViTs demonstrate fine-grained, patch-level attention, often focused on discriminative microfeatures. The Mamba architecture shows biased behavior: it achieves strong explainability in medical tasks but exhibits divergent intensity distributions in natural images; our analytical characterization of the metrics makes this dissociation explicit, since near-unit support overlap is attained simultaneously with a vanishing linear correlation. We further analyze the effect of backbone freezing and ensemble strategies on model interpretability. The results highlight how architectural and training choices influence the alignment between model saliency and human visual attention.

Aggregating independently computed sub-sample inferences is a well-known challenge in large-scale Bayesian computation, federated learning, and opinion pooling. The core problem is to approximate a distribution whose density is proportional to a product of individual densities. We propose Product Monte Carlo (PMC), an algorithm for computing arbitrary expectations under a product of densities using only Monte Carlo draws from individual densities. We turn the intractable product expectation into a regression problem by expressing it through a family of computable conditional expectations. Besides the point estimate, our fully Bayesian regression formulation provides coherent uncertainty quantification and principled diagnostics. We establish theoretical guarantees on consistency and characterize convergence rates for the PMC estimator. Across simulated and real-data experiments varying the number, dimensionality, and heterogeneity of the component distributions, PMC achieves higher estimation accuracy, better-calibrated uncertainty coverage, and improved scalability at a lower computational cost than existing methods. In addition, PMC requires no density evaluation, making it applicable to simulation-based inference, as we demonstrate in an application with protein images.

Perspectivist NLP has established that annotator positionality shapes labels for subjective tasks, but the field still lacks methods for operationalising it. Positionality is typically operationalised as a demographic form completed at recruitment: a static attribute recorded once and treated as a covariate, on the assumption that the knowledge it indexes is active when the annotator reads an item. This paper treats that assumption as a design problem and asks whether lived experience can instead be primed by the task itself. We introduce AXLE, a pre-annotation stage in which a scenario vignette anchors a short, axis-guided conversation that is synthesised into a first-person micro-narrative and returned to the annotator before labelling begins. In a 2x2 between-subjects study (104 annotators, 30 items, 1,040 annotations) on ambiguous hate speech spanning immigration, religion and gender, elicitation was associated with higher identity resonance and higher sensitivity to harm. It also increased label entropy and lowered inter-annotator agreement: the stage appears to surface plurality rather than manufacture consensus, which distinguishes it from annotator training, whose success criterion is convergence.

A recent preprint by OpenAI resolved the spherical fermionic Laughlin spectral-gap conjecture for the full $V_1$ interaction by a Fock-space inequality: $H_Q^2\ge \gamma H_Q$ on the lowest-Landau-level Fock space for all large flux $Q$ and every $\gamma$ below $0.0461673\ldots$, so that the gap above the Laughlin state at filling $1/3$ is at least $1/25$. That proof, with its original constant, has also been formalized in Lean. We show that the same argument supports a much larger constant. Two sharper estimates, a product-twirl bound for the three-body tail and a staircase price for the four-body allowance, raise the constant above $0.0601$ without changing the original certificate. Treating the auxiliary operators as the variables of a semidefinite program (SDP) and enlarging the finite set of orbital modes on which they act then gives $H_Q^2\ge\gamma H_Q$ for every $\gamma<\gamma_*=0.2190037845063196\ldots$, certified by exact rational arithmetic. Consequently the gap above the Laughlin state is at least $1/5$ for all sufficiently large spheres, and the untruncated planar $V_1$ Hamiltonian has positive spectrum bounded below by $\gamma_*$, uniformly in particle number and angular momentum. A heuristic extrapolation of the SDP optima suggests that auxiliary operators of the present form can give at most about $0.222$, while exact diagonalization of finite systems places the true gap near $0.4$. A larger family of auxiliary operators could push the bound further towards the true gap, and the SDP formulation makes such families easy to test. The proof of the improvement and the SDP search were completed by the AI model Claude Opus 5.5 (Anthropic) under the author's direction.

We consider the problem of learning to generate data while satisfying a prescribed sample-wise constraint with a user-specified probability of constraint satisfaction. Starting with a population-level constrained negative log-likelihood minimization and using a flow-matching (FM) parameterization, under regularity assumptions and sufficient expressivity of the velocity field family, we derive guarantees on the probability of constraint satisfaction for the corresponding primal-dual optimization algorithm. We provide a practical implementation of this approach, called Primal-Dual Flow Matching (PDFM), which has direct control over constraint satisfaction rate and requires only binary membership oracle feedback for constraint satisfaction, avoiding the need for differentiable distances, projections, or special structure of the constraint set, such as convexity. We show that PDFM improves constraint satisfaction over vanilla FM and achieves competitive performance against constraint-aware baselines while maintaining distributional fidelity. Our code is available at https://github.com/ZhengyanHuan/PDFM.

We prove that if the first Lyapunov exponent of a compactly supported random matrix product is simple, then it is pointwise Hölder continuous for the Wasserstein–Hausdorff distance. By passing to exterior powers, we obtain pointwise Hölder continuity of the first $k$ exponents whenever they are simple.

This paper studies an open network design problem of constructing graph topologies with maximum algebraic connectivity under fixed numbers of vertices and edges. A density-dependent approach is proposed that decomposes the design task into two stages: a high-quality, low-cost structural backbone construction and a reinforcement learning completion stage. The method selects the backbone based on density, using complete multipartite graphs in dense regimes and Cayley graphs in low-to-intermediate regimes, and then refines the remaining edges through a learning-based procedure. Numerical results show that the proposed method achieves high algebraic connectivity with favorable runtime scalability, outperforming existing methods. These results support a structural-family-first strategy for scalable network design.

Vision-language-action models (VLAs) offer a promising route toward general-purpose robotics by transferring semantic knowledge from large-scale vision-language pretraining into language-conditioned control. However, most VLA evaluations emphasize aggregate manipulation success under changes in objects, instructions, or environments, leaving unclear how reliably these policies ground spatial descriptions in the physical scenes where they act. We therefore ask a sharper question: how reliably can current VLAs translate spatial descriptions into appropriate real-robot behavior? To investigate this, we introduce Spa-Bench, a real-robot benchmark that evaluates spatial grounding across six tabletop tasks covering Object State, Relative Size, Referential Description, Relational Placement, Ordinal Position, and Counting. Our primary evaluation compares in-distribution (ID) and out-of-distribution (OOD) spatial configurations while retaining training support for the relevant objects, concepts, and actions, reducing object and motor unfamiliarity as alternative explanations for failure. Four diagnostic conditions further probe physical execution, sensitivity to wording, object-task associations, and recognition that no action is required. We release 4,092 episodes collected on the SO-101 robot arm: 1,200 human-teleoperated demonstrations and 2,892 real-robot evaluation rollouts from five state-of-the-art VLA policies. Across the three fully evaluated policies, success falls from 67.5-73.3% on ID spatial configurations to 40.7-52.0% on OOD spatial configurations, while matched direct instructions improve success by 28.3-40.0 percentage points. These results show that the evaluated VLAs can often execute the required manipulations but lack robust spatial grounding. Project materials, including videos, code, and benchmark data, are available at https://justintiensmith.github.io/Spa-Bench/.

Confidential Virtual Machines (CVMs), such as AMD SEV-SNP, and process enclaves, such as Intel SGX, provide workload protection against cloud threats. However, they strongly differ in TCB, deployment cost and speed, peer workload protection, resource sharing, fine-grained isolation and attestation, and programming capabilities. Nesting process enclaves within CVMs offers an optimal solution and an opportunity to address long-standing SGX limitations: lack of intra-enclave protection, expensive transitions and exception paths, slow enclave cloning, and a restricted programming model that limits Library Operating Systems (LibOS). This paper introduces TEEVisor, a CVM-resident architecture consisting of a security monitor and a kernel driver that leverages AMD SEV-SNP Virtual Machine Privilege Levels (VMPLs) to build hardware-protected, process-level enclaves inside a guest CVM with two modes: (1) an SGX binary compatibility mode to run unmodified SGX applications; and (2) a novel extended SGX~(eSGX) mode optimizing slow execution paths and offering richer enclave programming capabilities. On commercial AMD EPYC hardware, against native CVM execution, TEEVisor incurs under 5% overhead on compute- and memory-bound workloads, around 12% on I/O-heavy applications, and accelerates enclave cloning to a rate of 93~$\mu$s/MB of enclave size, demonstrating that eSGX semantics inside a CVM are practical for production use.

Molecular machine learning evaluates out-of-distribution performance with structure disjoint splits, a construction rule fixed once at the scale its library happened to have: threshold a pairwise distance, then assign whole connected components to folds. For predicting structures from mass spectra, the field has converged on single-linkage clustering under the myopic Maximum Common Edge Subgraph (MCES) distance at a threshold of 10. This convention was set on 29,000 molecules but public libraries now hold 227,690 molecules. MCES is NP-hard per pair over a quadratically growing set, and so the criterion has never been evaluated at that scale. We propose an optimized version of this criterion, allowing for computationally feasible application on the public libraries: Admissible bounds and a union-find skip reduce $2.6 \times 10^{10}$ molecular pairs to only $1.15 \times 10^{7}$ integer programs, a $2{,}259\times$ saving, while provably producing the lossless partition. We find that at this scale the graph percolates. A single component holds $95.5\%$ of the library, capping any test set at $4.5\%$. What remains is not merely smaller, but systematically different: a held-out compound outweighs a training compound 88.1% of the time, because a fixed absolute budget is a tighter relative tolerance on a larger molecule. Large library benchmarks using this splitting rule naively therefore conflate structural novelty with extrapolation to larger, more complex chemistry.

Spatial semantic segmentation of sound scenes (S5) jointly performs audio source separation and tagging on a multichannel audio mixture. Therefore, an S5 system can be decomposed into an audio tagging model and a separation model. The baseline S5 system in task~4 of the DCASE 2025 challenge uses M2D and ResUNet models for tagging and separation, respectively. These are large in overall size and therefore not appropriate for use in embedded devices. The main aim of this paper is to assess the performance loss in an S5 system when using lightweight tagging and separation models instead. To this end, we first compare the tagging performance of lightweight audio tagging models, namely PANNs and DyMNs, in terms of label prediction accuracy against the baseline M2D model. Secondly, we assess separation performance in terms of the scale-invariant signal-to-distortion ratio of the baseline ResUNet separator relative to that of a convolutional-based separator using SuDoRMRF. Finally, we combine the tagging and separation models across various configurations and assess the overall performance of the S5 system using the class-aware signal-to-distortion ratio.

Scalable logic-based analytics are frequently dominated by cyclic multi-way joins over large relational datasets. State-of-the-art systems evaluate these joins through chains of binary joins, incurring substantial overhead from large intermediate relations that must be materialized and redistributed across the network. Worst-Case Optimal Joins (WCOJ) offer a provably superior alternative by evaluating joins one variable at a time, eliminating intermediate blowup. However, existing WCOJ implementations target either shared-memory machines or one-shot, non-recursive queries on dataflow and big-data platforms, leaving WCOJ-based recursive evaluation on distributed-memory HPC systems an open problem. We present, to our knowledge, the first distributed-memory Datalog engine that uses WCOJ for recursive fixpoint evaluation. Our design builds on HyperCube partitioning, which hash-partitions relations along variable-aligned grid dimensions and replicates them along missing dimensions, and extends it from a single shuffle to iterative execution: in every semi-naive iteration, only newly derived tuples are repartitioned and re-replicated, using MPI all-to-all collectives and per-dimension all-gathers over subcube communicators, while the same layout is reused across iterations so that all WCOJ intersections remain rank-local. We evaluate our system on the Aurora and Polaris leadership-class supercomputers at Argonne National Laboratory using graph mining and program analysis benchmarks, demonstrating strong scalability, outperforming state-of-the-art Datalog engines on most benchmarks, and characterizing how partition dimensionality trades runtime against memory feasibility.

This paper studies formal Laurent series, with particular emphasis on their continued-fraction and Laurent-series expansions. Knowledge of both expansions is important, for example, in the study of Kronecker-type sequences in uniform distribution theory and in the search for potential counterexamples to variants of Littlewood's conjecture over fields of formal Laurent series. Our approach investigates Hankel matrices over a field and relates them to Laurent-series expansions over the same field. We describe such matrices via a block $\mathcal{L}\mathcal{B}\mathcal{U}$ decomposition, using recursive algorithms based on the continued-fraction coefficients of the corresponding Laurent series. The upper-triangular factor $\mathcal{U}$ has several remarkable properties. In particular, it is constructed columnwise from the so-called Ostrowski-type representations of powers of $X$. Applying $\mathcal{U}$ in Niederreiter's digital construction yields an Ostrowski-type van der Corput sequence that can be related to the corresponding Kronecker-type sequence. For ordinary Kronecker sequences, such a relation is known in only one case, that of the $(n\varphi)$-sequence. The original motivation for our study of Hankel matrices was to recast the search for counterexamples to variants of Littlewood's conjecture over fields of Laurent series as the search for specific Kronecker-type sequences. Interestingly, the method developed for the study of Kronecker-type sequences also allows a new perspective on the celebrated Sobol' construction. Our approach yields a short and elegant proof of its excellent distribution properties.

We prove that every finite ordered set of width at most three and cardinality at least four is reconstructible from its deck. This settles the width-three part of an open problem posed by Schröder in Ordered Sets; the separate question concerning ordered sets of height one is not addressed here. The new ingredient is a criterion for recovering the marked maximal deck of an ordered set with exactly three maximal elements from its unmarked maximal deck and the isomorphism type of the suborder obtained by deleting all maximal elements. We express the criterion as an orbital balance condition on the attachment ideals in this common base. Necessity follows by double counting; sufficiency uses the structure of automorphism actions in width at most three. The full-deck theorem then follows from reconstruction results of Schröder concerning maximal cards and marked maximal cards. A local reattachment argument correcting one intermediate step in the two-maximal-element case is included in an appendix.

We revisit the construction of compact liquid drop equilibria from Delaunay unduloids in [Arch. Ration. Mech. Anal. 249 (2025), Paper No. 74]. We evaluate exactly the coefficient arising in the final solvability condition of the Lyapunov-Schmidt reduction, identifying it as the product of the axial period and the normalised Delaunay flux. Using this identity and the monotonicity of the period, we establish the conjectured positivity of the coefficient and prove that its product with the period strictly increases with the neck radius. We also derive an exact relation between the volume and the surface area of one period and prove that both strictly decrease with the neck radius. These results extend the construction throughout the embedded unduloid family and yield compact equilibria of every sufficiently large mass, with reference neck radii converging to any prescribed interior value as the mass tends to infinity.