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The Quantum Internet is commonly envisioned as a network that transports quantum states and distributes entanglement as the key resource underpinning distributed quantum applications. This view is necessary but incomplete if quantum phenomena are confined to what the network carries or manages, while network functionalities remain grounded predominantly in classical abstractions. This Perspective advances a broader thesis: quantum phenomena can also participate directly in the realization of network functionalities. We first establish the architectural baseline by introducing entanglement as a stateful network resource whose operational condition is non-locally distributed across remote nodes, evolves through manipulation or consumption, and degrades over time through decoherence. Its evolving state must therefore remain visible to the functionalities acting on it. We then move beyond resource visibility and use two mechanisms as proof points of a broader quantum-native functional design space: entanglement generation during propagation through coherent spatial-path superposition, and operational connectivity induced by shared entanglement that can depart from the physical graph. These examples show that paths, neighbors, or participating nodes may become operationally relevant in ways determined by quantum coherence and shared entanglement, rather than by physical connectivity alone. We identify Quantum Addressing as a transversal abstraction capable of representing such relations while complementing, rather than replacing, classical addressing and signaling. The resulting perspective broadens the Quantum Internet from transporting quantum information and distributing entanglement to exploiting quantum phenomena in network functioning, opening a coupled frontier spanning routing, forwarding, control, and functionality placement.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO combines multi-answer prompting with a set-level reward to train the LLM to produce sets of solutions that specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes standard, diversity may need to become the default post-training objective.

Health-misinformation analysis presents a dual challenge: misleading claims can affect public well-being, while systems designed to detect them may expose sensitive user-submitted text. This motivates privacy-preserving inference for public-health applications in which user queries may contain confidential medical information and trained models and reference databases are maintained on organizational servers. We design a privacy-preserving text inference framework based on CKKS homomorphic encryption for health-misinformation classification and semantic retrieval. The classification pipeline fuses BioBERT embeddings, PCA-reduced MPNet embeddings, and SVD-reduced TF-IDF features, while the retrieval pipeline combines MPNet embeddings with ISCC-SCT semantic fingerprints through late fusion. We evaluate predictive performance and benchmark plaintext versus ciphertext-based execution. The hybrid classifier achieved an accuracy of 0.971 and a macro-F1 score of 0.950, with identical reported metrics under plaintext and ciphertext-based inference. The hybrid late-fusion similarity model achieved a Pearson correlation of 0.8691 with human sentence-pair similarity scores on STS-B. For ciphertext-based retrieval, we evaluated naive and optimized implementations. The optimized implementation uses CKKS single instruction, multiple data (SIMD) packing to compute and return multiple similarity scores together, reducing single-query latency over 7,128 indexed items from 222.028 to 5.168 seconds and communication overhead from 6.11 GB to 2.13 MB. These findings demonstrate the technical feasibility of privacy-preserving text inference for health-misinformation applications and characterize its predictive utility and efficiency trade-offs.

Robot-mediated rehabilitation has the potential to deliver high-intensity, individualized therapy, but existing systems (which have not consistently improved outcomes) typically prescribe kinematic trajectories rather than explicitly targeting the neuromotor activations thought to support recovery. To address this gap, and ultimately enable activation-optimizing rehabilitation robot behavior, we present a personalizable transformer-based model mapping individuals' muscle activations (as measured via surface electromyography) to prescribed contact force trajectories when interacting with an end-effector rehabilitation robot. The model uses a transformer encoder-decoder leveraging rotary positional embeddings (RoPE) to generate a latent representation of trajectory-relevant and user-specific neuromotor factors, and augments trajectory prediction with flow matching to produce a distribution over plausible prescriptions biased toward the training distribution. Using data from 16 healthy participants completing 15 isometric trajectory tracking tasks, we evaluate generalization across held-out tasks and users, as well as the feasibility of user-specific fine-tuning within a therapy-session timescale. The model achieves mean trajectory prediction errors of <8% on held out tasks and users, with effectively instantaneous deterministic inference and sub-second sampling of trajectory distributions. An initial test using the model during live rehabilitation tasks demonstrates that, on average, participants reach the target neuromotor activations with just 15% error accumulated throughout the task. These results provide a proof of concept for data-driven, activation-targeted trajectory prescription in robot-mediated rehabilitation and establish a foundation for future validation in clinical populations. Data and code have been open-sourced as part of the OpenRobotRehab project on SimTK.

Manim supports precise, programmatic video generation, but a successfully rendered educational animation can still have visual defects, missing explanations, or incorrect content. Rendering does not directly identify the code changes needed to correct these visual failures, so feedback-driven revision is needed. Existing agentic frameworks use iterative rendering and revision but typically rely on large models, often proprietary. Existing Manim datasets primarily contain final programs and often lack quality verification and the trajectories of feedback and revisions needed to learn this refinement process. We introduce ManimData and ManimCode, a data and training framework for feedback-driven educational animation generation. We construct ManimData through a render-guided pipeline that iteratively generates, executes, reviews, and revises Manim programs with retrieved API documentation. Its 24,034 render-verified, quality-filtered records preserve intermediate programs, execution errors, visual critiques, and corrective revisions. We use role-conditioned supervised fine-tuning on these trajectories to train ManimCode, a single 4B model, to write, review, and revise animation programs. To improve correction of errors that differ from those in the collected trajectories, we then train the Reviser with reinforcement learning on self-generated states, using rendering outcomes and reference-free quality feedback. ManimCode achieves 96.6% and 97.0% render success on ManimData-test and ManimBench, compared with 52.6% and 82.0% for the untrained 4B model under the same inference setup, while also improving video quality scores from 2.48 to 2.94 and from 3.00 to 3.44. Integrating ManimCode into two long-form educational video generation systems increases completed videos from 19/117 to 107/117 and from 53/239 to 239/239, alongside improvements in educational effectiveness and visual quality.

Online 3D Gaussian Splatting reconstructs a scene during capture: each keyframe spawns primitives once and refines them for only a few dozen iterations, leaving little chance to fix poor initialization or missing detail. Gaussians are also inherently soft, needing many overlaps for solid surfaces. We present Hierarchical Incremental Beta Splatting (HIBS), which brings beta kernels to incremental reconstruction. Their shape parameter interpolates between a soft, Gaussian-like profile and a flat-topped, near-opaque surfel, acting as a confidence dial for geometry. Our confidence-aware spawning uses geometric observability and multi-view depth agreement to initialize both opacity and shape, producing solid primitives where geometry is verifiable and soft, correctable primitives where it is not. As online densification, error-driven relocation recycles stale primitives into photometric-error hotspots. Bounded beta kernel support enables exact tile culling and faster rasterization, and a closed-form, shape-preserving merging formulation provides a level-of-detail (LOD) hierarchy for fast optimization and real-time rendering. On Mip-NeRF 360 in the on-the-fly protocol, HIBS improves PSNR by up to 0.8 dB while reducing optimization time by up to 40%. Project page: https://linus-franke.com/hibs/

Visual interaction models that support users during ongoing physical tasks require evaluation in closed loop, where assistant responses can change subsequent user behavior and task outcomes. Existing benchmarks largely rely on offline replay and therefore cannot capture these effects. We introduce Interactive Visual Gym, a framework for closed-loop evaluation and training of visual interaction models through joint simulation of executable task environments and human users. We contribute three simulators that recreate everyday tasks and human-aligned action spaces across cooking, household manipulation, and mobile-interface domains, together with a persona-conditioned user simulation harness that collaborates with the assistant while incorporating controlled execution errors and other out-of-plan behaviors. We instantiate the framework as IVG-Bench, a benchmark with 315 interaction scenarios. Evaluating state-of-the-art VLMs as visual interaction models reveals substantial limitations: the best-performing model, Gemini 4 Argon, completes only 53.4% of tasks within the time limit, exhibits significant weaknesses in factual grounding and actionable guidance, and is often too slow to prevent errors when response latency is considered. We verify our evaluation protocol with a human study which finds 78.5% agreement between our interaction-quality metric and participant preferences. We further show that the environments provide useful learning signals: in a proof-of-concept GRPO experiment, closed-loop training improves both task success and interaction quality for Qwen3.5-4B model in our cooking environment.

Neural theorem proving increasingly uses retrieved premises and project context to support proof generation. Evaluating these resources requires measuring the advantage of target-selected declarations over comparable alternatives and how this advantage depends on training. We introduce LeanContext, a benchmark of 129,826 Lean whole-proof generation problems, to investigate these questions. We group selected complete preceding mathematical declarations as Mathematical Context (MC) and the remaining selected local source commands as Environment Context (EC). Four aligned input views support crossed training and inference evaluations with shared targets and original Lean verification environments. For both diffusion- and autoregressive-based models, selected declarations outperform comparable alternatives by a larger margin when training includes MC. Final-input audits identify omitted declarations referenced by the target. Prioritizing these dependencies improves Pass@32 by 1.40% and 1.70% for LLaDA and Llama, respectively, on 2,000 targets. The selection experiment operates without access to target reference proofs and holds checkpoints, EC, and inference budgets constant. The code and dataset are available at https://github.com/haaaardcvZ/LeanContext.

We investigate the problem of scaling safe reinforcement learning (safe RL) to massively parallel training regimes, where a large number of environments are exe- cuted with short rollout horizons. Although this setting improves data throughput and wall-clock efficiency, it creates a mismatch with constrained Markov decision processes (CMDPs), whose safety constraints are defined over full-episode cost returns. We address this mismatch by analyzing staggered environment resets as a phase-mixture distribution over short trajectory segments. This analysis charac- terizes the bias induced by phase coverage and motivates a phase-aggregated cost estimator that reconstructs episode-level cost estimates from short rollout batches. We further incorporate finite-sample uncertainty and distribution mismatch into a constraint-tightening framework, yielding a scalable Safe RL method compatible with on-policy optimization. Using an MJX-based implementation of Safety Gym, our experiments show that the proposed method achieves performance comparable to non-massively parallel implementations while substantially reducing wall-clock training time.

Transformers use the same forward computation stream to both predict the next token and store useful state for future token predictions. We formulate the state-prediction separation hypothesis: disentangling the two roles yields better language modeling performance. We design a Transformer variant that uses separate computation streams to separate the two functions, and conduct pretraining experiments across various scales. Our experiments show that state-prediction separation consistently offers better data- and compute-efficiency, improving validation loss and outperforming standard Transformers by 2-3 percentage points on average on downstream tasks. We also conduct extensive empirical analysis that rules out potential confounders and demonstrates the fundamental difference in the gradients our design entails.

Generalist Anomaly Detection (GAD) aims to detect anomalies in unseen domains using only a few reference samples. Recent normal-abnormal guided methods improve this setting by exploiting abnormal references, but their residuals often mix transferable anomaly cues with domain-specific appearance factors such as texture, geometry, and acquisition conditions. This residual domain entanglement limits cross-domain transfer and may produce spurious activations on novel domains. We propose DART, a plug-in framework for normal-abnormal guided GAD that learns to separate residuals into anomaly-relevant and domain-specific components. DART combines a Residual Disentanglement Module, which preserves anomaly-discriminative information while suppressing domain information, with Cross-Domain Meta-Training, which forms episodes across source domains to make the separation effective. The method is architecture-agnostic and can be inserted between residual computation and the detection head of existing GAD pipelines. Experiments on MVTec AD, VisA, and BraTS show consistent improvements over multiple base methods, with the largest gains under stronger domain shifts. https://github.com/aqeeelmirza/DART

After a runtime or API migration, an LLM-repaired procedure can run cleanly yet return wrong results, and a release check on typical test inputs ships it. We report a preregistered study of 73 tasks covering 60 documented changes in CPython, Node.js and SQLite. Every candidate is executed on the real runtimes against withheld contracts. Over the complete repair space, the all-assertions gate on typical inputs released 0.410 of wrong repairs. One edge input written from the release note cut this to 0.065, and to 0.061 on 15 unseen clusters. Three inputs from a blind GPT-5.6-luna writer that never saw the program reached 0.070. Two further frozen stages enlarged the menu to 1491 fragments and then added 233 hard distractors that match the legacy output on typical inputs. The edge input (0.058) and the frontier-model writer (0.058) passed their preregistered tests. Yet 0.168 and 0.153 of the hard wrong programs still passed. Two local-model writers failed their preregistered tests. Across four model families, the edge input cut wrong releases per attempt in all three open-weight families on all three menus, for example from 0.233 to 0.057, without lowering correct completion. Self-tests helped less. A blind AI audit flagged 34 contracts as stricter than their requirements. Dropping the disputed checks changed 0 verdicts, but class-label disputes remain open. No model-written code was executed. Artifacts are available from the authors on request.

Recent neural decoding approaches achieve strong performance by training on large collections of paired neural-behavioral recordings, but such datasets are expensive, invasive, and difficult to scale. In contrast, behavioral data is abundant and easy to collect, raising the question of whether neural decoding can benefit from decoupling behavioral and neural representation learning. We introduce BEEMO, a flexible multi-session framework that enables training with arbitrary mixtures of paired neural-behavioral recordings and unpaired behavioral data. A behavior decoder learns movement dynamics directly from behavioral trajectories, while neural activity is incorporated through cross-attention layers when available, allowing behavioral and neural supervision to scale independently. Across multiple intracortical motor datasets and tasks in nonhuman primates, we show that incorporating unpaired behavioral data improves decoding performance, particularly when transferring to new tasks, and that adding even a small amount of behavioral data from the target task further improves transfer. By decoupling neural and behavioral data, we unlock a new dimension for scaling: unpaired behavioral data, which is substantially cheaper and easier to collect than paired neural recordings, can be used directly to improve decoding performance. We further show that behavior-only pretraining, without any neural pretraining, achieves performance comparable to models pretrained on substantially larger neural datasets. Together, our results suggest that scaling behavioral data offers a practical and cost-effective path toward neural decoding models that generalize across subjects and tasks. Code is available at https://github.com/nerdslab/beemo.

Multimodal language models can simulate different observers, yet it remains unclear how assigned perspectives reshape their internal representations and whether these changes govern their judgements. Here, we investigate the representational geometry of persona-conditioned visual interestingness in Qwen3-VL-8B-Instruct. Across 100 images and 53 prompting conditions, we systematically vary persona content and the linguistic framing used to introduce it, while recording behavioural ratings and layer-wise hidden states. We observe a systematic reorganisation of representational geometry across processing depth: early layers primarily encode image identity, whereas persona-specific structures emerge in later layers. Strikingly, prompt framing reshapes internal representations more strongly than persona identity, whereas persona content has a greater impact on behavioural judgements. This dissociation is further illustrated by minimal identity statements that alter representations even without changing responses. These findings demonstrate that representational distance does not necessarily reflect behavioural relevance. More broadly, they reveal how simulated perspectives emerge as distinct structures within the representational space of artificial cognitive systems, highlighting a fundamental distinction between the geometry of internal representations and their functional consequences.

Egocentric human video offers a scalable source of manipulation priors for robot learning, yet translating raw data scale into generalizable robot policies demands rigorous data curation and training recipes. We introduce Open-HumanWAM, the first fully open recipe for scaling egocentric pretraining to 50,000 hours, anchored by Open-HumanWAM-50K---a curated egocentric video corpus densely annotated with hand motion and natural language. Leveraging this corpus, we systematically investigate pure human pretraining via closed-loop simulation evaluations and uncover an empirical log-linear scaling law linking pretraining data hours to downstream robot success rates. Grounded in these findings, we develop HumanWAM-Vanilla, a world--action model pretrained exclusively on 50k hours of egocentric human video. Upon robot post-training, HumanWAM-Vanilla reaches 92.08% success on RoboTwin 2.0 Clean2Clean and 68.88% on Clean2Random, alongside a 14.17% mean success rate and a 19.00 mean progress score on RoboDojo. To push the capability frontier further, we explore joint human--robot pretraining with HumanWAM-Goal, a visual-goal-conditioned world--action model. Hybrid data scaling unlocks broad zero-shot generalization across both simulation and physical benchmarks, propelling post-trained RoboTwin 2.0 performance to new state-of-the-art levels: 92.70% on Clean2Clean and a substantial leap to 84.60% on Clean2Random. On physical robots, HumanWAM-Goal further exhibits emergent embodied in-context learning, dynamically adapting its manipulation behavior to unseen visual goals without parameter updates. To support reproducible scaling research in embodied AI, we open-source the Open-HumanWAM-50K corpus, data curation and pretraining pipelines, alongside the pretrained and post-trained HumanWAM checkpoints, inference code, and simulation evaluation suites.

Partial single-motor loss of effectiveness (LoE) changes the remaining control-authority geometry of a quadrotor and can change which control allocator performs best during emergency landing[cite: 11]. We compare three allocators in Crazyflie software-in-the-loop simulation: bounded weighted least squares (reported as PINV), a finite-candidate residual allocator (QP-lite), and the same residual allocator with scoring parameters tuned offline by the Cross-Entropy Method (CEM)[cite: 11]. For this study, fault geometry is represented by the known failed-motor index[cite: 11]. At $η=0.496$ remaining effectiveness, matched development trials select CEM for M1, M3, and M4 and PINV for M2; the M3 selection is a one-trial margin (29/30 versus 28/30)[cite: 11]. After freezing this routing map, the policy achieves 117/120 safe first-contact touchdowns on fresh seeds and 115/120 in a separate randomized-order integrated-supervisor evaluation[cite: 11]. For the critical M2/PINV branch, Firth regression gives a nominal $η_{50}\approx0.4956$ with a within-model 95% bootstrap interval of approximately [0.4955, 0.4956][cite: 11]. One-factor-at-a-time $\pm10\%$ plant perturbations shift $η_{50}$ by up to 0.05495 for thrust coefficient and 0.04974 for mass; the most frequent violated first-contact criterion also changes from vertical speed in many conditions to angular rate for mass -10% and thrust-coefficient +10%[cite: 11]. At fixed $η=0.496$, PINV has a higher M2 safe count than frozen CEM in 9/11 tested plant states and ties in 2/11; the two ties are both 0/30[cite: 11]. The experiments therefore distinguish motor-conditioned allocator selection from sensitivity to plant-model mismatch[cite: 11].

We give a deterministic, strongly polynomial algorithm running in $\tilde{O}(km+k^4n)$ time that finds $k$ arc-disjoint arborescences of minimum total cost in a directed multigraph with $n$ vertices and $m$ arcs. This significantly improves upon the state of the art for $k \ge 2$ with $k=n^{o(1)}$: the prior fastest weakly polynomial and strongly polynomial algorithms take $\tilde{O}(km\sqrt{n}\log C)$ and $\tilde{O}(kmn)$ time (Gabow and Xu, 1989; Gabow, 1995), respectively. Roughly, our technique can be viewed as a way to apply a linear number of \emph{shortest} augmenting paths in near-linear total time for the special case of the weighted matroid intersection problem between the $k$-fold graphic matroid and the indegree partition matroid. This was previously done in the unweighted case by Gabow (1995), but our approach is different. As an extension, we also obtain a deterministic $\tilde{O}(km^{1+o(1)}+k^5n)$-time algorithm for minimum-cost maximum-cardinality packing of $k$ forests in undirected graphs. In particular, this finds $k$ edge-disjoint spanning trees of minimum total cost, if they exist. The previous fastest algorithm takes $\tilde{O}(kn^2+m)$ time (Gabow and Westermann, 1992).

As one of the most important underwater sensing technologies, forward-looking sonar exhibits unique imaging characteristics. Sonar images are often affected by severe speckle noise, low texture contrast, acoustic shadows, and geometric distortions. These factors make it difficult for traditional teacher-student frameworks to achieve satisfactory performance in sonar semantic segmentation tasks under extremely limited labeled data conditions. To address this issue, we propose a Collaborative Teacher Semantic Segmentation Framework for forward-looking sonar images. This framework introduces a multi-teacher collaborative mechanism composed of one general teacher and multiple sonar-specific teachers. By adopting a multi-teacher alternating guidance strategy, the student model can learn general semantic representations while simultaneously capturing the unique characteristics of sonar images, thereby achieving more comprehensive and robust feature modeling. Considering the challenges of sonar images, which can lead teachers to generate a large number of noisy pseudo-labels, we further design a cross-teacher reliability assessment mechanism. This mechanism dynamically quantifies the reliability of pseudo-labels by evaluating the consistency and stability of predictions across multiple views and multiple teachers, thereby mitigating the negative impact caused by noisy pseudo-labels. Notably, on the FLSMD dataset, when only 2% of the data is labeled, our method achieves a 5.08% improvement in mIoU compared to other state-of-the-art approaches.

Large language models (LLMs) hold significant potential for psychological support, capable of generating empathetic responses and simulating therapeutic conversations. However, existing LLM-based approaches often lack sufficient grounding in structured diagnostic reasoning and diverse therapeutic strategies, limiting their effectiveness in complex counseling scenarios. To address these limitations, we propose PsyLLM, the first large language model designed to incorporate diagnostic- and therapeutic-oriented reasoning for mental health counseling. To develop PsyLLM, we design a novel automated data synthesis pipeline that processes real-world mental health posts collected from Reddit, where users frequently express psychological distress and seek community support. The pipeline transforms these posts into multi-turn counseling dialogues and leverages LLMs guided by international diagnostic standards (e.g., DSM/ICD) and multiple therapeutic frameworks (e.g., CBT, ACT, psychodynamic) to generate structured, clinically informed reasoning traces. A rigorous multi-dimensional filtering mechanism further improves the quality and clinical fidelity of the synthesized dialogue data. In addition, we introduce a new benchmark and evaluation protocol, assessing counseling performance across four key dimensions. Our experiments, along with evaluations by professional counseling experts, demonstrate that PsyLLM consistently outperforms various baseline models on this benchmark. Code, data, and models are available at https://github.com/Emo-gml/PsyLLM.

We compute Cunningham's canonical decomposition of a symmetric submodular function on $n$ elements in $O(n^3)$ time. The decomposition represents all minimum cuts in linear space. For the pair $s,t$ produced by Queyranne's algorithm, we construct in $O(n^2)$ time a digraph representing exactly the minimum $st$-cuts of the function. Using this construction in Chekuri and Xu's decomposition algorithm gives the cubic bound.

We consider the problem of cross-validation (CV) in time series forecasting, with a focus on global forecasting models based on deep learning. The prevailing CV strategy in forecasting is to partition data across time with the last part of each series used for testing. With global models trained on collections of time series, however, a fundamentally different approach becomes possible: partitioning across series and time. We formalize series-wise CV for global forecasting models and benchmark several instantiations, including K-fold CV, bootstrapping, and Monte Carlo CV, on 11 datasets with 10 neural network architectures. We evaluate CV procedures along five dimensions: performance estimation, overoptimism rate, model selection accuracy, regret, and downstream forecasting performance. We withhold a random fraction of series from training so that they appear only in the test set. This protocol simulates the emergence of new series not seen during training, a common scenario in global forecasting. Under this protocol, our results reveal a nuanced trade-off: series-wise CV yields better downstream forecasting accuracy by guiding model selection toward configurations that generalize across both time and series, while time-wise CV retains a slight advantage for estimating out-of-sample error.

Diffusion-based molecular docking requires learning a corrective score field across a broad corruption distribution, yet individual pose errors can differ substantially in their structural consequences. This creates a post-training conflict between preserving broad score-field coverage and concentrating supervision on corrections that appear more relevant to docking geometry. Using DiffDock, a fixed-budget study compares broad continuation with torsional supervision focused on Cartesian consequence or conditional target consistency, and with a broad/focused mixture. Evaluation separates fixed score fidelity, generated-pose quality, best-of-10 sampling capacity, and confidence-selected Top-1 docking performance. At <5 Angstrom, broad continuation had the highest mean Top-1 success among trained policies, and focused or mixed supervision showed no consistent advantage under the tested budget. The starting model had better fixed score fidelity, whereas the evaluated broad-continuation model had higher mean Top-1 success with the same aggregate best-of-10 recovery. Focusing supervision on structurally consequential or more consistently specified corrections did not consistently improve returned-pose success over broad continuation.

We give a new rounding technique for spreading-metric linear programs, called Greedy Region Growing, which adapts the classical technique of region growing to min-max graph layout problems and flow-expander decomposition. Using this technique, we obtain state-of-the-art approximation algorithms for several fundamental problems. (1) An $O(\log n)$-approximation for Cutwidth and Pathwidth, improving upon the previous bound of $O(\log n\exp(O(\sqrt{\log\log n})))$ due to Bansal, Katzelnick, and Schwartz (FOCS 2024). This matches the $Ω(\log n)$ integrality gap of the standard LP relaxations. (2) An $O(\log n)$-approximation for their directed analogues, Minimum Storage and Minimum Register Sufficiency on directed acyclic graphs, improving the previous bound of $O(\log^{3/2} n)$. (3) A $φ$-flow-expander decomposition that cuts at most an $O(φ\log n\log\log n)$ fraction of the edges. This improves the $O(φ\log n\exp(O(\sqrt{\log\log n})))$ bound of Bansal, Jambulapati, and Saranurak (ICALP 2026), and is within an $O(\log\log n)$ factor of the graph-theoretic lower bound. The vertex version of our algorithm also gives an $O(\log n)$-approximation for Treedepth. In particular, our results answer several open problems of Bansal, Katzelnick, and Schwartz (FOCS 2024). Technically, we also solve the conceptual question raised by their work: our technique shows how to adapt Seymour recursion to min-max objectives, and constructs $O(1)$-weak local partitions in spreading metrics.

Wind farm power control can help the system maintain balance and avoid blackouts. In Europe, this can be achieved through implicit balancing, where a wind farm adjusts its power setpoint in anticipation of the imbalance price using information published by the Transmission System Operator. Thereby, the wind farm helps restore system balance while also reducing its own imbalance costs resulting from forecast errors. However, implicit balancing is a challenging problem since the settlement price is unknown in advance and can be impacted by the pursued control strategy. Reinforcement learning methods could help to solve this problem, but lack the interpretability needed to be deployed on real wind farms. Therefore, we propose a policy distillation framework using explainable boosting machines (EBMs), a variant of generalized additive models, to obtain a transparent control policy. To increase the value captured by the EBM model, we introduce a value-oriented perspective to policy distillation inspired by research in the field of energy forecasting. Furthermore, we suggest to include expert knowledge during model design, such that the control strategy is also justifiable to stakeholders. Using real data of the Belgian grid and an offshore wind farm, we find that our value-oriented and expert-based controller can reduce imbalance costs by 82%, while outperforming a price threshold controller as well as a policy distillation baseline using decision trees.

When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, $P_g - b_g$, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM). The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or, in simulation, from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a $g\times g$ map takes $1 + 2g^2$ runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9% (one seed), as occlusion and gradient $\times$ input do, while plain gradients remove much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at one wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask computed classically before approximate loading, 300 test pictures were classified at 37.7% against 10% chance (56.3% in exact simulation), and $2\times2$ maps of the filtered input of 30 test pictures drawn at random in advance, measured on the chip, agreed with the exact ones ($r = 0.88$; standard estimator 0.82). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.

Reinforcement learning (RL) has become a standard post-training method for diffusion models, but most RL objectives roll out the current policy at every iteration, and with a many-step sampler these rollouts typically dominate the cost of training. Few-step models cut this cost, yet they model an average velocity over an interval, whereas existing RL objectives are built for an instantaneous velocity with a many-step sampler. We adapt RL objectives to few-step models systematically in three phases, namely a transformation, a decomposition and an adaptation. The transformation to $x$-space expresses each objective we consider through a common policy prediction, at the clean end by default and at an explicitly marked level for transition or flow-map objectives, so that objectives stated over densities, velocities or rewards become comparable. The decomposition writes the gradient of each of these objectives as the sum of a self-regression toward a reference and a reward augmentation, so that a method reduces, at the gradient level, to a choice of anchors and weights. The adaptation computes each anchor from a few-step model at the end of its transport or along its tangent, with the instantaneous velocity recovered from the network itself or from an auxiliary network. This yields few-step versions of FlowGRPO, AWM, DiffusionNFT, DiffusionOPSD and ReFL in one modular codebase. In our experiments, reward-gradient-based methods are the most effective when the reward is differentiable and its gradient is affordable; otherwise DiffusionNFT-style methods generally reach high rewards in relatively few iterations despite a sometimes higher per-iteration cost. Extra inference steps show no systematic aggregate benefit in our experiments, although selected outputs visibly improve with two to four times as many sampling steps as in training.

Mathematical modeling turns an open-ended real-world problem into assumptions, a model, a solution, and a defended recommendation, and its answers matter only if they are both close to a credible reference and physically feasible; existing benchmarks either score solver fragments or grade reports with an LLM judge, leaving those numbers unchecked. We introduce TB-MathModel (the Terminal-style Mathematical Modeling Bench), the first benchmark to make complete contest-style modeling problems agentic, verifiable, and terminal at once, over 18 real CUMCM and MCM problems (2023--2025). Each task ships the verbatim statement, official attachments, and figures in a containerized terminal; the agent returns one JSON artifact, scored on the numeric core of the final question against a reproduction of the Outstanding-award paper. Two design choices distinguish it: direction-aware, one-sided scoring, which never penalises beating the anchor, and two-layer feasibility verification---a programmatic gate over six decidable invariant forms plus 624 Lean~4 obligations---with a hard gate that zeroes infeasible answers. Each task is scored against a panel of human outstanding papers rather than one, so a model must be close to many accepted answers; across seven multimodal entries (three seeds each) the strongest reach a multi-reference O-Eval of 64.58\%, while the \$2.54 open model holds 59.81\% at $1/100$ the cost. TB-MathModel turns the numeric core of modeling into a reproducible, machine-checkable signal for measuring long-horizon modeling competence and for collecting agent trajectories. The source code is available at https://github.com/wxj630/terminal-bench-math-modeling.

Self-attention carries a quadratic cost in token count, which limits how far Vision Transformers can scale with input resolution. We introduce SSoG, a separable sum-of-Gaussians spatial operator that replaces dense self-attention with a learned mixture of axis-factorized Gaussian kernels, reducing the per-layer cost from $\mathcal{O}(N^2)$ to subquadratic in $N$. Unlike dot-product self-attention, whose Lipschitz constant is unbounded outside a compact input domain, SSoG with fixed kernels is globally Lipschitz continuous, which, via the Picard--Lindelöf theorem, guarantees that the continuous-depth variant has a unique solution on the whole integration interval, a global guarantee that dense-attention counterparts lack in general. On CIFAR-100 at $224\times224$, in a matched discrete-Transformer setting and in the continuous setting, SSoG improves Top-1 accuracy by 2.2--4.1 points across three model widths while using 8.8--16.6\% fewer parameters, with depth and training recipe held fixed. In a looped-Transformer setting, SSoG improves Top-1 accuracy by 5.4--8.1 points. We further probe inference-time scaling by evaluating on inputs up to $1024\times1024$ at matched batch size: in the continuous-depth (Neural ODE) architecture, SSoG reaches up to 154\% higher throughput and over 60\% lower peak memory than dense attention, with the gap widening as resolution grows, consistent with the difference in asymptotic cost. In the discrete and looped settings, SSoG also achieves over 30\% higher throughput than dense attention at this resolution. Together, these results establish SSoG as a practical, parameter-efficient, and theoretically grounded alternative to dense attention across discrete, weight-shared, and continuous-depth Transformer variants.