Papers

Biomedical machine learning papers often compress model performance into one headline number. That number can look like a property of the model even when it depends strongly on how the benchmark was evaluated. We study this problem on the widely used Kermany pediatric chest radiograph dataset using nine image classifiers and a controlled evaluation protocol. Under the same protocol, the eight pretrained backbones differ by only 0.026 AUROC. In contrast, changing whether the backbone is frozen or fine-tuned changes AUROC by 0.044 on average, and changing the decision threshold changes balanced accuracy by 0.090 on average. The official test split is also measurably different from the training pool: a partition classifier distinguishes them at AUC 0.697, rising to 0.898 for normal radiographs. Most strikingly, a classifier using only file properties, with no image anatomy, reaches 0.992 balanced accuracy within the training pool but falls to 0.496 on the official test split. Validation-fitted thresholds and calibration also transfer imperfectly. These results show that a high benchmark score can support different conclusions when the split, training policy, threshold, metric, calibration, and uncertainty are not communicated with it. We end with a seven-item reporting recommendation in which each item is tied to an effect measured in the study

If $T$ is an optimal transport map between bounded convex domains $\Omega$ and $\Omega'$, we characterize the regularity/singularity dichotomy for $DT$ at $(x,T(x)) \in \partial \Omega \times \partial \Omega'$. This is obtained through a new approach to the regularity theory based on affine degenerations of the tangent cones to $(\Omega, \Omega')$ at $(x,T(x))$. We formulate a general principle relating the optimal boundary regularity to a stability criterion and an $\mathrm{SL}(n)$ moduli space of pairs of convex cones. Among other results, we establish geometric criteria for existence and non-existence of homogeneous optimal transport maps between convex cones.

A sequence of non-linear iterations with non-identically distributed random perturbations is studied. The asymptotic behaviour of the sequence is described via its visitations measures, which are deterministic measures that allow one to estimate the time spent by the sequence in the neighbourhoods of its partial limits. The results obtained are compared with statements regarding the statistical convergence of the sequence of iterations under study

Honeybee queen loss is a major threat to colony health, yet queen-status assessment remains largely manual and disruptive. Acoustic monitoring offers a non-invasive alternative by enabling continuous analysis of hive sounds. In this paper, we benchmark conventional and learned acoustic representations for automated detection of queen absence, comparing task-specific convolutional neural networks with pretrained audio transformers. Experiments are performed on 5,129 audio recordings from 3,285 hives across 47 apiaries collected between October 2024 and August 2026, evaluated using hive- and apiary-independent splits. Results show that models relying on modulation spectrograms achieve the best performance, reaching an Area Under the Receiver Operating Characteristic (AUROC) of 0.81 and Area Under the Precision-Recall Curve (AUPRC) of 0.37 on unseen hives; performance decreases under unseen-apiary evaluation. Overall, our results highlight the promise of modulation-based audio representations for non-invasive queen-status monitoring and highlight the challenge in cross-apiary model generalization.

Rounding errors in finite element computations can lead to a complete loss of accuracy, stalled convergence, and incorrect results. Moreover, the effects of rounding errors accumulated within automatically generated and compiled kernels are difficult to analyze a priori. We present the first software framework for automated rounding error estimation within finite element kernels. The proposed methodology is based on an a posteriori technique called Running Error Analysis (REA), where a forward error estimate is automatically computed concurrently with the value. An open-source implementation is provided for the FEniCS Form Compiler (FFCx), based on a C++ backend for generating type-generic templated kernels over a custom arithmetic type that tracks both the value and its error estimate. We demonstrate REA on two examples. First, we use it to detect catastrophic cancellation in the assembly of a Neo-Hooke hyperelastic model in the small deformation regime. A series expansion circumvents the cancellation problem and the computed error estimates show this. Second, we study the assembly of the Laplace operator on a near-degenerate mesh. We demonstrate that our REA implementation typically incurs only 2-4x performance overhead. Applications of this work include robust reduced-precision computations in embedded systems, numerical debugging of new, possibly ill-conditioned or unstable PDE formulations, and guiding the design of mixed-precision kernels.

The nerve theorem provides a combinatorial model for the homotopy type of a topological space from a suitable open cover. We extend this local-to-global approach by replacing the intersections of the cover with compatible categorical models. These local models are assembled through the Grothendieck construction, yielding a small category whose classifying space has the weak homotopy type of the original space. Under suitable hypotheses, the resulting category is finite and acyclic. We develop two versions of this construction. The first is indexed by the usual poset of nonempty finite intersections of the cover. The second uses the membership poset, inspired by the finite-space construction of Sancho de Salas, which retains only the membership patterns realized by points of the space and is defined for point-finite covers. The classical nerve theorem and its componentwise variant are recovered as particular cases. The construction is recursive: categorical models of local pieces, together with functors representing their inclusions, can be combined to produce categorical models of more complex spaces.

Influence functions estimate how individual training examples affect the behavior of large language models (LLMs). Analyzing how training data influence different behaviors of an LLM involves repeated influence computation. Reusing stored training gradients reduces the computational cost, but storing full gradients is prohibitively expensive at LLM scale. We study how to compress these gradients while preserving influence estimates for future queries that are unknown at storage time. Through a worst-case analysis, we characterize the optimal fixed-dimensional linear representation and propose eigenbasis-corrected one-bit gradient projection (EOGP) to approximate it at scale. Specifically, EOGP uses EK-FAC to reduce gradient dimensionality, then applies PCA within the retained subspace to learn compression directions from the training gradients. We then apply one-bit quantization to the resulting coordinates, allowing more coordinates to be retained within a fixed storage budget. On GPT-2, EOGP predicts retraining outcomes more accurately than the evaluated compression baselines while using one-sixteenth of their per-example storage. On OLMo 2 SFT models from 1B to 32B parameters, EOGP remains competitive with the baselines allocated over 100 times as much storage per example.

Masked generative models offer parallel token prediction, but accurate parallel sampling must account for dependencies among tokens. When dependencies are unknown, finding safe batches also costs model evaluations. We study whether total evaluations, including discovery, can be sublinear in sequence length $N$; sublinear sequential depth then follows. We consider discrete distributions with hidden forest structure, accessed through a fixed approximate conditional oracle. Under explicit regularity conditions and uniform Hellinger error bounds, for any fixed target accuracy $\varepsilon\in(0,1/8]$ and sufficiently large $N$, our sampler achieves seed-averaged total-variation error at most $\varepsilon$, with total masked-state submissions and sequential depth both bounded by $\widetilde{O}(N^C \varepsilon^{-a})$ for constants $0<C<1$ and $a>0$. These guarantees use polynomial vocabulary size and an edge-response lower bound set by $N$ and $\varepsilon$. The sampler shares evaluations of hypothetical reveals across dependence tests to identify safe parallel batches without requiring full recovery of the hidden forest. A tunable parameter trades probing cost against irreversible commit rounds. In the same class, any admissible irreversible product-commit sampler attaining the same seed-averaged accuracy requires $\Omega(N^c \varepsilon^b)$ counterfactual submissions or commit rounds in the worst case, for constants $c,b>0$.

This paper addresses the stabilization of switched affine systems under dwell-time constraints around a desired operating point that is not a common equilibrium of the subsystems. Since asymptotic stabilization is generally unattainable in this setting, the objective is to ensure that trajectories converge to and remain within a prescribed region containing the desired operating point. The main contribution is the development of Lyapunov-based tools that accommodate target regions more general than those induced by quadratic Lyapunov functions. In particular, we establish a constructive Lyapunov characterization for a broad family of weighted $p$-norm functions, which generalizes the classical quadratic Lyapunov equivalence and underpins the proposed hybrid-control and dwell-time developments. Focusing on the case in which the desired region is a polytope, and building on existing Lyapunov-based methods, we develop a constructive two-step method that starts from a polytopic Lyapunov certificate for the average system and yields a smooth weighted $p$-norm Lyapunov function for all sufficiently large $p$. We prove that this extension guarantees practical asymptotic stability of the desired operating point and yields a Lyapunov-certified invariant region under minimum dwell-time switching. Numerical examples illustrate the effectiveness of the proposed method.

Let $R = S/(f)$ be a complete local hypersurface ring and let $A = S[\![u,v]\!]/(f+uv)$. Pfister and Popescu showed that the stable categories of maximal Cohen-Macaulay modules over $R$ and over $A$ are equivalent, with no assumption on the characteristic. We give a short proof. If $(\Phi,\Psi)$ is a matrix factorization of $h$ and $\partial$ is a derivation, then $(\partial\Psi,\partial\Phi)$ is a null-homotopy for multiplication by $\partial h$. Since $u$ and $v$ are partial derivatives of $f+uv$, they act as zero on the stable category of $A$, so the Koszul complex on $u$ and $v$ splits in the singularity category, and this gives density. For the double branched cover $S[\![z]\!]/(f+z^2)$ the same argument yields $2z$: it recovers Knörrer's lemma up to free summands on the double branched cover when $2$ is a unit, and we show by an example that this lemma, and periodicity for the iterated double branched cover $S[\![z,w]\!]/(f+z^2+w^2)$, fail in characteristic two. We also compute the second syzygy over $A$ of a maximal Cohen-Macaulay $R$-module by an explicit resolution, and show that the change of basis used there cannot be given by a universal matrix formula.

Correlations between optical modes, ranging from classical fluctuations to quantum entanglement, are a cornerstone of modern optics and emerging quantum technologies. However, probing these correlations on the natural timescale of electronic motion - the attosecond regime - remains a major challenge. Here, we generate and characterize correlated attosecond extreme-ultraviolet (XUV) emission by perturbing gas-phase high-harmonic generation with two-mode bright squeezed vacuum. The signal and idler fields imprint their correlated amplitude and phase fluctuations onto two families of harmonics, thereby transferring these correlations from the infrared to broadband XUV modes. Even harmonics serve as an intrinsic attosecond phase-sensitive probe of these correlations through interference between indistinguishable XUV pathways. Shot-resolved covariance measurements reveal the amplitude correlations, while even-harmonics resolve the phase correlations with sub-cycle precision. Time-domain reconstruction of the correlated emission reveals a transition from maximal fluctuations to near-silence within only 30 as. Whereas the signal and idler driven attosecond pulse trains exhibit excess fluctuations individually, their joint reconstruction shows strongly suppressed fluctuations, reflecting their shared correlations. These results establish a framework for generating and probing quantum correlations on attosecond timescales, opening the door to quantum attosecond science.

Vision-Language Models (VLMs) remain vulnerable to cross-modal implicit risks: visual and textual inputs that appear benign in isolation can jointly elicit unsafe responses. Existing safety methods often require large preference datasets, costly multi-rollout training, or additional safeguards at inference time. They may also sacrifice helpfulness by directly refusing requests that could be answered safely. In this paper, we propose Intent-Privilege On-Policy Self-Distillation (OPSD), which leverages evidence-grounded intent as privileged supervision during training to help VLMs recognize implicit risks and provide safe, useful responses instead of blanket refusals. OPSD distills a teacher's intent-conditioned preferences over responses into a student using a single rollout per prompt; the student then responds without intent annotations or an additional safety module. With only 1,447 safety-specific examples - 95% fewer than standard preference datasets - OPSD reduces training time by 5x relative to multi-rollout GRPO-style training and average inference length by 7%. It attains the highest ratio for joint safety-helpfulness success, which measures the proportion of responses that are both safe and helpful, across all five evaluation groups. Remarkably, on pooled SIUO+HoliSafe, this success ratio rises from 43.9% to 53.5%. These results show that training-time intent supervision can improve both safety and helpfulness while substantially reducing data, training, and inference costs.

Neural networks trained toward the same final objective can reach similar predictive performance while retaining internal representations shaped by earlier training history. We study this effect using controlled sequential-training experiments in which paired convolutional networks start from identical weights, experience reversed task orders, and then receive the same deterministic common-relaxation distribution. Across 20 paired MNIST runs, 16 satisfy a predeclared behavioral-matching criterion, yet their matched representations retain a mean history score of 0.139 (95% bootstrap CI: 0.127-0.153) and approximately 3.1% prediction disagreement. Extending common relaxation to 50,000 optimizer updates does not erase the measured difference: across five paired seeds, the representation-history score remains 0.190 (95% bootstrap CI: 0.161-0.219) at the end of the measured horizon while the mean accuracy gap is only 0.18 percentage points. Fresh linear probes show that, with sufficient labeled data, the two histories retain practically equivalent linearly accessible class information. A same-label rotated-MNIST control reproduces the effect: all five paired seeds reach behavioral matching while retaining a mean representation-history score of 0.162. Finally, a matched-learning-rate ReLU-LeakyReLU control reduces the 50,000-update representation residue by 0.040 on average in all five paired seeds, providing directional evidence that activation-mediated plasticity contributes to the persistence of training-history effects. These results provide protocol-scoped evidence that behavioral convergence need not imply representational convergence and that optimization history can leave measurable internal traces after prolonged common training.

We report a comprehensive high temperature structural investigation of the B-site ordered double perovskite SrLaCoNbO$_6$ using combined Raman spectroscopy and x-ray diffraction (XRD) over the range 25–900~$^\circ$C. Two distinct temperature-driven anomalies are identified at $T_\mathrm{OD} = 300\pm 25~^\circ$C and $T_\mathrm{PT} = 750\pm 25~^\circ$C through pronounced renormalizations in the phonon frequency and linewidth, accompanied by the evolution and suppression of characteristic XRD reflections. The low-temperature anomaly at $T_\mathrm{OD}$ is associated with an isostructural octahedral distortion within the monoclinic $P2_1/n$ phase. At $T_\mathrm{OD}$, the radial and angular distortion parameters of the CoO$_6$ and NbO$_6$ octahedra decrease to near-zero values before reversing upon further heating due to an inversion of the in-plane Co–O and Nb–O bond-length hierarchy. The high-temperature anomaly at $T_\mathrm{PT}$ corresponds to a symmetry-breaking structural phase transition from $P2_1/n$ to the monoclinic $I2/m$ phase, confirmed by group-theoretical analysis and Rietveld refinement. These results demonstrate that integrating temperature-dependent Raman spectroscopy with laboratory-based XRD, complemented by quantitative octahedral distortion analysis, provides a robust approach to disentangle isostructural octahedral distortions from symmetry-breaking phase transitions in complex double perovskite oxides without recourse to synchrotron or neutron diffraction facilities.

Harness optimization provides a practical setting for recursive self-improvement (RSI), where agent-generated modifications inform subsequent changes through execution feedback. Recent work such as Meta-Harness implements this process through iterative code generation and evaluation, but retains a fixed development set and proposal policy. These constraints channel evolution along a single search trajectory, increasing the risk of converging to a local optimum. We make the improvement process itself adaptive by organizing search into branches with evolving development subsets and proposal policies. Each branch retains development cases solved by more of its leading harnesses than by those of other branches, drops cases solved by every leading harness across all branches, and revises its proposal policy using its own search history. To deploy the resulting complementary harnesses, we propose a router to select one development-selected branch head for each new input before execution. Across mathematical reasoning and agentic coding benchmarks, our system achieves relative improvements over Meta-Harness of 34.8% on Olympiad-level mathematical reasoning, 11.6% on Terminal-Bench 2.0, and 3.8% on SWE-bench Lite, with harness selection and router configuration based solely on development data. These results show that evolving branch objectives and proposal policies can yield complementary harnesses whose strengths a router combines without access to test outcomes.

Thin fluid-filled channels in porous media are prevalent in a wide range of environmental settings including fractures in geological formations. Transport of fluid in such multi-domain systems is commonly described by Darcy's law and formulated either in a fully dimensional framework or through a hybrid-dimensional approach, where fractures are represented as inclusions of co-dimension one enclosed in the porous matrix. These mixed-dimensional models enable accurate representation of the corresponding full-dimensional systems while significantly reducing computational complexity. Models available in literature usually do not properly account for channel-wall roughness while applying coupling conditions on the fracture-matrix interface and are usually developed for flow directions parallel to the fracture. The goal of this work is to advance and study the hybrid-dimensional Stokes-Darcy model developed by the authors in their previous work. We consider a thin open channel embedded within a porous matrix, where the channel walls are in contact with porous regions of distinct permeabilities. We incorporate channel-wall roughness effects into the model and improve it to accommodate arbitrary flow directions. We prove existence and uniqueness of the weak solution for the new model and demonstrate its advantages over existing hybrid-dimensional Stokes-Darcy models using pore-scale resolved simulations.

Certo is a small non-generative decision model (Qwen3-4B): it scores candidate actions from their text and returns a probability, instead of generating an answer. The accurate design reads the state, the rules, and each candidate together (a joint scorer), so cost grows with the menu. Independent encoding lets each candidate be encoded once and reused across states (about 5x cheaper at 77 candidates), but separates state from candidate. We ask how much rule-sensitivity survives that move, and whether it can be trained back. Four experiments on Certo: (1) the tested conversion to cacheable scoring loses rule-sensitivity (recall@1 1.00 -> 0.24) while the joint scorer holds 1.00, and a shortlist+rerank rescue fails; (2) targeted counterfactual supervision restores strong performance on held-out synthetic rule tasks (paraphrase, counterfactual, composition; reproducible across seeds), though we do not isolate whether predictions depend on the supplied rule; (3) on real rules the added benefit is not established – after fixing a truncation confound, the joint scorer wins significantly on the short tier (0.861 vs 0.500) and directionally on the hard tier (0.655 vs 0.483, n=29); (4) a matched cross-domain real-prose mixture did not help and reduced contract accuracy (-9.3, -16.2 points). A cacheable encoder can be made rule-sensitive on its training distribution, but transfer to unseen-source real rules is not established; the joint scorer keeps an edge at the cost of caching.

Real-time diffusion-based video super-resolution (VSR) is in high demand for online streaming, yet stringent latency requirements often compromise generative fidelity. We propose ReCaVSR, a Wan2.2-based, one-step framework for streaming VSR that builds on two observations: recycled SR latents retain local temporal context, reducing the need for full historical Key-Value (KV) caches; and individual transformer layers benefit from distinct temporal scopes. ReCaVSR combines three complementary designs: (i) layer-wise cache routing with recycled SR latents: each DiT layer learns its KV-cache temporal scope under a cache budget and exports a static inference schedule, while recycled SR latents propagate local context by conditioning each new block on the model's own preceding predictions. (ii) Multi-Scope Query (MSQ) Discriminator: a compositional discriminator combining global, spatial-window, and temporal-tube feedback for holistic realism, local texture generation, and temporal stability. (iii) LR-conditioned adaptation of FlashDecoder: a VAE decoder that incorporates LR observations for efficient latent decoding. ReCaVSR enables streaming VSR without iterative sampling or full historical KV-cache materialization. Experiments on synthetic and real-world VSR benchmarks show better perceptual quality, temporal consistency, and streaming efficiency than representative VSR baselines. At $1080{\times}1920$ output resolution on a single NVIDIA A100-80GB, ReCaVSR achieves 21.20 FPS with 15.16 GB peak allocated GPU memory, running 2.72$\times$ faster while using 38.0% less peak allocated memory than FlashVSR Tiny. The code is available at https://github.com/kopperx/ReCaVSR.

We study the $q$-matroids associated with nondegenerate $\F_{q^m}$-linear near-MRD codes, which we call near-uniform $q$-matroids. Using the correspondence between rank-metric codes and their associated $q$-systems, we determine explicitly their rank functions and characterize their cyclic flats. We show that near-uniform $q$-matroids form a class of representable paving $q$-matroids. and prove an upper bound on the number of their cyclic flats, which is shown to be sharp for certain parameters. Finally, when $n>m$, exploiting the rank distribution of near-MRD codes, we obtain an exact count of the nontrivial cyclic flats of the associated $q$-matroids.

Video diffusion transformers (DiTs) increasingly adopt mixture-of-experts (MoE) architectures to reduce active computation, but their full expert storage remains costly. Existing one-shot pruning criteria mainly rely on static activation or routing statistics and cannot capture layer-level re-routing after expert deletion. We introduce DIET, a training-free expert pruning framework based on deletion responses. A single all-expert calibration pass records expert outputs and router states for matched conditional and unconditional tokens. Candidate deletions are then replayed from cached tensors, requiring no additional model forward passes. The resulting deletion-response signatures characterize each expert by the changes induced when it is removed. DIET selects retained experts by minimizing Overall Diversity Loss (ODL), which preserves directional coverage in signature space, and combines intra-layer local search with an inter-layer regression-guided budget search to allocate experts across layers. On LingBot-Video 30B-A3B, pruning 50% of experts (6,144 to 3,072) reduces the checkpoint from 57 GB to 30 GB and enables single-card deployment on a 48 GB GPU without fine-tuning. Under a fixed 284-case VBench protocol, the VBench Total increases from 0.7941 to 0.8115. Across tested retention budgets, DIET consistently outperforms competitive pruning baselines adapted from large language models.

Mixture-of-experts (MoE) models expand capacity via sparse activation, but inference across GPUs introduces tensor-parallel (TP) collectives and expert-parallel (EP) dispatch and combine operations. Completion time depends not just on communication volume but on how logical groups map onto intra-server interconnects, GPU–NIC connections, and the inter-node network. Using ASTRA-sim with the NS-3 discrete-event backend, we build a controlled matrix of 32 GPU ranks with data and pipeline parallelism fixed at one. Workloads are fixed-length 4096-token prefill-like synthetic Chakra traces from four MoE configurations. Experiments cover six server topologies, four TP/EP partitions, two TP collective algorithms, and four network/congestion-control modes, yielding 768 deterministic simulations. In the 144-configuration feedback-enabled subset per model, exposed communication accounts for 89.9%–95.8% of mean completion time. TP16EP2 requires 3.68–4.35x the mean completion time of TP2EP16. With fixed rank mapping, ASTRA-sim Double Binary Tree (DBT) incurs 28.3%–83.2% more time than Ring. InfiniBand-like High Precision Congestion Control (HPCC) is ~0.9% lower than HPCC over RDMA over Converged Ethernet (RoCE), whereas RoCE with Data Center Quantized Congestion Notification (DCQCN) is 23.8%–35.7% slower than RoCE HPCC. Topology effects are conditional: Topology~6 leads at low TP degrees but loses its advantage at high TP degrees, and additional GPUs or NICs help only when rank mapping balances traffic across injection paths. Under uniform 32-way sharding, the largest checkpoint-weight shard is ~48.75 GB per rank, so all configurations meet a 64 GB per-accelerator weight-residency criterion. Within the evaluated workload and simulator semantics, server topology, parallelism, collective implementation, and congestion control jointly determine exposed communication and completion time.

Understanding and controlling charge transfer at graphene-semiconductor interfaces is essential for the integration of two-dimensional materials into silicon-compatible technologies. Here, we combine ultraviolet photoelectron spectroscopy (UPS), Kelvin probe force microscopy (KPFM), angle-resolved photoemission spectroscopy (ARPES), scanning tunneling spectroscopy (STS) and density functional theory (DFT) to resolve work-function modulation and electronic coupling in graphene grown on Ge(001)/Si(001). UPS and KPFM reveal a spatially non-uniform work-function landscape correlated with the nanofaceted morphology of the substrate. ARPES and DFT calculations for the pristine interface consistently indicate n-type doping and electron transfer from Ge to graphene. In contrast, modeling of the oxidized interface predicts a reversal to p-type doping, providing a plausible explanation for the different doping polarities reported in the literature. Machine-learning-assisted classification of the STS data resolves distinct local electronic regimes, ranging from nearly free-standing graphene on nanofacet tops to more strongly coupled inter-facet regions and nanoribbon-like regions with distinct local electronic responses. By identifying the mechanisms governing local graphene-substrate interactions and charge transfer, our study provides guidelines for tailoring the synthesis process and minimizing defect formation during delamination. These insights support the production of high-quality graphene layers for electronic devices and for transfer as protective coatings for air-sensitive materials.

Nitrogen limitation is a key mechanism regulating the mutualism between photosymbiotic cnidarians and their algal symbionts. Algal-derived photosynthate facilitates host assimilation of inorganic nitrogen, specifically ammonium. The resulting competition between symbiotic partners for inorganic nitrogen leads to a negative feedback loop wherein symbiont density is effectively controlled through facilitation of their competitor. However, it is unclear whether this feedback loop is sufficient to stabilize the interaction absent other forms of regulation. Using a generalized modeling approach, we identify the conditions under which cnidarian-algal competition for nitrogen yields dynamically stable symbioses. We show that nitrogen limitation is sufficient to stabilize the interaction through the interplay of intraspecific (symbiont-symbiont) and interspecific (host-symbiont) competition. As host assimilation of inorganic nitrogen increases, the system shifts from being stabilized by intraspecific competition between symbionts to interspecific competition between host and symbionts, necessitating a positive coupling of symbiont density to host nitrogen assimilation via photosynthate translocation for dynamic stability.

Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose $\pi$PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence, $\pi$PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that $\pi$PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Transformer language models build predictions through successive residual updates, but how their representations become specific to an eventual outcome remains unclear. We study this process by comparing intermediate residual states with their own final states and an empirical bank of final states from other contexts. Across six pretrained language models, the own endpoint becomes preferable to the average alternative early, while many individual endpoints remain closer. These competing sets generally shrink with depth, but their membership changes and their surviving endpoints need not become more similar to one another. Directional alignment and endpoint rank can therefore improve while Euclidean distance to the final state changes little. We develop a simple high-dimensional model that separates the roles of norm, alignment, and endpoint geometry, showing how gradual directional changes can produce sharp reductions in competition. We also prove that a straight path toward the own endpoint cannot introduce new competitors under either Euclidean or cosine distance; observed entries thus establish departures from straight-line convergence. Finally, endpoints associated with lower-ranked output tokens tend to lie farther away in cosine distance across all studied models, connecting residual geometry to output organization. Together, these findings characterize increasing geometric specificity during transformer inference and explain why distance, competitor count, and concentration of the surviving endpoints provide distinct views of that process.

Ferroelectric materials are highly attractive for low-power, high-speed electronics and emerging neuromorphic computing architectures. However, the severe physical scaling limits of conventional bulk (3D) ferroelectrics at the nanoscale have shifted attention towards two-dimensional (2D) ferroelectric monolayers. Accurate device-level performance predictions are essential to accelerate the experimental testing and screening of these novel materials. In this work, we present a multiscale simulation framework that bridges first-principles density functional theory with Non-Equilibrium Green's Function (NEGF) transport calculations. Using a 2D Indium Phosphide monolayer as a case study, our approach leverages a continuously interpolated, polarization-dependent Hamiltonian embedded within a self-consistent Poisson-NEGF solver. The model captures the dynamic interplay between ion movement and electronic transport, naturally reproducing macroscopic hysteresis loops and memory windows without empirical parameters. This predictive pipeline provides a computationally efficient tool to evaluate and optimize next-generation 2D ferroelectric field-effect transistors.

The weak value of an operator is the average result of measuring that operator on a quantum system given specified initial and final states. The overlap between these states appears in the denominator of the weak value, and thus if that overlap is small, the weak value can be arbitrarily large. In 1988, Albert, Aharonov, and Vaidman proposed a weak Stern-Gerlach experiment which would be able to measure a so-called anomalous weak value, a measurement result which lies out- side of the eigenvalue spectrum of the operator being measured. Though anomalous weak values have been measured in numerous optical systems, here we present the first such realization of this experiment as originally proposed. By placing a Bose-Einstein condensate of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of a weak magnetic momentum kick (~ 8 $\mu$m/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.

Longitudinal studies with functional outcomes subject to truncation-by-death frequently report time-indexed survivor average causal effect estimates, defined among individuals who would survive regardless of treatment assignment. Because the survivor stratum can change over time, the resulting effect estimates may pertain to populations with different characteristics. We propose accompanying survivor average causal effect estimates with measures of covariate divergence between the survivor and baseline populations. We study standardized mean differences (SMDs) and the Kullback-Leibler (KL) divergence as moment-based and distributional summaries, respectively. We show that these divergence measures are identified under a subset of standard principal stratification assumptions and that their identification involves nuisance functions already estimated in survivor analyses. We derive the efficient influence functions, enabling construction of one-step bias-corrected estimators with appealing large-sample properties and allowing machine learning for nuisance estimation. We demonstrate that in randomized studies, one-step estimation of SMDs is robust to arbitrary nuisance model misspecification, whereas the KL divergence and broader density ratio estimands are more sensitive to nuisance misspecification. Additionally, we provide a sensitivity analysis framework that partially relaxes a monotonicity assumption required for identification, and construct one-step estimators for the resulting bounds. Through simulation studies, we demonstrate the finite-sample performance of the proposed estimators and illustrate how divergence measures can improve the interpretability of survivor analyses. Finally, we assess covariate divergence in survivor strata over time in amyotrophic lateral sclerosis (ALS) trials, using data from the Pooled Resource Open-Access ALS Clinical Trials database.

When firms respond to new market opportunities, their capacity choices alter the future discounted free cash flows available to both competitors and investors. In competitive markets, these investment decisions publicized in news articles and analyst reports, measuring the changes in capital structure, product mix, firm leadership, risk exposure and operating procedure made by the firm. Modern search engines rely on Large Language Models to measure the relevancy of source documents to given search query. These measurements let researchers represent these news articles as clouds of dense vectors whose information geometry reflects the dissimilarity of firms over time. Building on Xu et al. (2022), we develop a model of costly competitive adjustment in which firms allocate capacity in which firms make firm capacity adjustment towards free cash flow shocks. Using a novel sandwich estimator, we analyse the sign and magnitude of this predicted adjustment using multi-agent simulation, and validate our findings on a sample of news and analyst reports from Nasdaq-listed companies between 2018-2022.

Electronic invoices are replacing paper invoices worldwide, but today's centralized architectures leave three problems unsolved on the consumption side: an invoice can be submitted for reimbursement repeatedly, authenticity is difficult for recipients to verify, and data is siloed at a central authority that forms both a performance bottleneck and a single point of failure. This paper presents the design, formal analysis, and implementation of a complete blockchain-based electronic invoice system on Ethereum. We formalize the invoice lifecycle as a guarded labeled transition system and prove, under standard cryptographic and consensus assumptions, that the system guarantees: (i) reimbursement uniqueness–an invoice is reimbursed at most once, even across mutually distrusting organizations; (ii) face integrity–any verified invoice matches the recorded one unless keccak256 second-preimage resistance is broken; and (iii) authorization soundness for every lifecycle operation. The core invariants are machine-checked using Solidity SMTChecker, proving inductive validity across all reachable transaction sequences. The architecture models each invoice as a non-fungible, non-tradable token whose state transitions through five guarded subsystems, employing a lock-based protocol that makes duplicate reimbursement unrepresentable rather than merely detectable. We implement the design as a Solidity 0.8 contract with a four-role web application and evaluate it on a private Ethereum network: issuing costs 646,773 gas, full reimbursement costs under 135,000 gas, all operations run in O(1) time, and a single node sustains 137 issuances/s. Finally, the verified contract serves as a safety envelope for LLM-based reimbursement agents, provably rejecting unsafe actions (duplicate, over-limit, or forged-receipt claims) even when the agent's internal policy fails. All code and benchmarks are open-source.