Papers

It is known that on complete Riemannian manifolds with nonnegative Ricci curvature, the space of harmonic 1-forms of polynomial growth is finite-dimensional. In this paper, we extend this finiteness phenomenon to some manifolds whose Ricci curvature is allowed to be negative. More precisely, under a scale-invariant $L^2$-Sobolev inequality, a weak Hardy inequality, and quadratic Ricci curvature decay with a sufficiently small coefficient, we prove that the space of polynomial-growth harmonic 1-forms is finite-dimensional. We also construct a counterexample showing the necessity of the smallness condition. Our result is closely related to an earlier theorem of L.F.Tam \cite{tam1998note}, where the finite-dimensionality of polynomial-growth harmonic 1-forms was established under a faster curvature decay assumption, without any smallness condition on the coefficient. In comparison, our result treats the critical quadratic decay regime, at the expense of requiring the corresponding coefficient to be sufficiently small. As a byproduct, we obtain an analogous finite-dimensionality result for polynomial-growth solutions to the Schrödinger heat equation, which generalizes the finite-dimensionality results in \cite{lin2019ancient},\cite{colding2021optimal} and \cite{lin2026space} to some extent.

We present a repertoire-free benchmark for soft-robot damage recovery under nine online trials. The protocol pairs damage masks within each morphology, retains a measured nominal fallback, and separates method development from evaluation on new bodies. A Gaussian-process expected-improvement (GP-EI) reference controller adapts actuator phases using three initialization probes and six feedback-selected rollouts. Across two disjoint 75-body cohorts, it outperforms random search, Sobol, CEM, and CMA-ES under equal budgets. GP-EI improves the worst-mask gain on 69/75 confirmation bodies and exceeds these four baselines by 0.235-0.310 mean worst-mask reward. A TuRBO-style local GP is the closest comparator; the paired confidence interval includes zero. Post-confirmation fixed-controller replay finds 5.06 voxel widths of mean recovery together with a 0.0031 increase in worst-mask p99 geometric edge strain; a strict no-added-demand deployment gate retains 48.7% of mean gain. In a frozen development stress test that physically removes 10% of occupied voxels, GP-EI improves 71/75 bodies and exceeds official BoTorch TuRBO by 0.356 mean worst-mask gain. Together, the replayable controllers, body-level inference, and frozen-cohort evaluation provide a reference for measuring the added value of learned damage priors and future adaptation methods.

Active Feature Acquisition (AFA) is a classification problem in which an agent decides which costly features to acquire before predicting each sample's label. Unlike batch AFA, which trains a fixed policy and classifier offline on fully observed data, online AFA updates its predictor from revealed labels as samples arrive. Existing online methods either use deep reinforcement learning (RL) without performance guarantees or maximize cost-adjusted reward rather than enforce a global budget. We formulate online AFA as a combinatorial Bandits with Knapsacks (BwK) problem that couples acquisition and prediction. Unlike prior bandit-based AFA and classical BwK, our setting has combinatorial complexity, evolving rewards, a global budget, and structured side information. We obtain an improved regret upper bound over standard BwK bounds in this framework, leveraging a cardinality-aware confidence bound and the subset update structure. To avoid an exponentially large action space, we propose LP-Chain, a variant that searches a cost-aware chain of feature subsets with a size that grows linearly with the number of features. While the regret upper bound is specific to the combinatorial framework, LP-Chain empirically achieves comparable predictive performance. On synthetic data, LP-Chain outperforms HEDGE-based BwK and deep RL-based online AFA baselines and scales favorably to more features.

We evaluate whether AI agents can match the reported findings of published biomedical studies using public data. Existing evaluations do not consistently separate analysis from prior knowledge or retrieval of the published answer. We introduce BioStudyBench, a benchmark of 25 long-horizon analysis tasks drawn from studies first published between July and September 2026, after the developer-reported knowledge cutoffs of the models we evaluate, semi-automatically filtered down from 404,019 PubMed records. In each task, the agent receives a neutral research question but no data files, so it must find and download the relevant public data, search the literature through tools that return only records dated before its cutoff, and report findings through data analysis. To measure gains over prior knowledge, we run every task both with and without access to data and tools. Across eight models, access to data and tools raises the pass rate by 47 percentage points on average over the no-data baseline. Open-weight models across sizes trail closed-weight models, with the best open-weight model passing 81.3% of tasks against 94.7% for the best closed-weight model.

In mill yards, log loaders clear dense piles by a sequence of bundle grasps: hundreds of logs rest in contact, and each removal changes the pile available to the next grasp. A learned policy chooses where to place and orient the grapple from unsegmented point clouds and runs on a trailer-mounted hydraulic forestry crane. The policy classifies at which observed point to grasp and predicts depth and grapple orientation there. The same network outputs support behavior cloning (BC), reinforcement learning (RL), and deployment. BC learns from successful top-of-pile demonstrations; RL explores for improvements by fine-tuning the cloned policy (BC$\to$RL) or by training from scratch. In simulation, BC clears 98 of 100 piles of 200 logs, while BC$\to$RL improves load stability. Twelve field trials compare a geometric heuristic, RL from scratch, BC, and BC$\to$RL through complete grasp-transport-deposit cycles. BC and BC$\to$RL deposit 93.8% and 88.9% of pooled inventory, against 80.4% for the heuristic. BC$\to$RL deposits logs on 83.6% of its cycles, against 79.6% for the heuristic and 65.7% for BC, while its simulated stability gain does not carry over to the crane testbed. Trained entirely in simulation and run unchanged on the crane, the learned policies clear more than the hand-filtered heuristic while observing unfiltered clouds that still contain the storage rack's rails and poles.

Inverse inequalities are essential for controlling derivative growth and ensuring stable sampling in kernel approximation. Existing whole-space and single-scale estimates provide an established analytical basis, but their extension to multiscale analytic spaces on finite intervals requires uniform control of boundary effects and cross-scale cancellation. This paper establishes unweighted interval \(L^2\) inverse inequalities for spaces generated by primitives of kernels with positive exponential spectra. By retaining exterior diagonal energy and controlling off-diagonal interactions through one-sided estimates with endpoint-distance weights, we derive uniform coefficient bounds for normalized high derivatives. A synthesis-operator perturbation argument extends these bounds to positive spectral mixtures, while adjacent-derivative comparison and interval interpolation yield an inverse bound of order \(h_*^{-1}\), where \(h_*\) is the smallest scale. Under geometric scale separation and within-scale centre separation, the constant is independent of the number of scales and centres and their distances from the endpoints, allowing endpoint centres and coincident centres across scales. The coefficient lower bound approaches the optimal limit \(1/2\). Two-centre constructions establish the sharpness of the scale exponent for every fixed kernel in the class and, for a single exponential spectrum, a sharp deficit of order \(q^{-1/2}\) from \(1/2\) for the best uniform coefficient lower bound, where \(q\) is the derivative order. Numerical illustrations for Cauchy and logistic kernels demonstrate coefficient stability in several multiscale configurations. These results extend interval inverse estimates to multiscale analytic kernel spaces with endpoint centres and provide quantitative conditions for deterministic sampling stability.

For a non-degenerate braided fusion category $\mathcal B$, we study the Grothendieck $\mathbb Z_+$-ring of $\mathcal B$-module categories. We define a convolution of étale algebras in the Drinfeld center $\mathcal Z(\mathcal B)$ and show that the full center of a relative tensor product of module categories is canonically isomorphic to the convolution of their full centers. The module Grothendieck ring has a canonical upper-triangular grading by the poset of localizations of $\mathcal B$. We describe each localization stratum by double-coset endpoint blocks and a group-ring-valued transition matrix, obtaining an explicit sandwich multiplication formula. When $\mathcal B$ is the center of a fusion category, the transition matrix of the maximal stratum is the Gram matrix of the Lagrangian algebras, so linear relations among their classes give rise to radicals. We compute stratum rings and the radicals of their complexifications in examples from classical finite geometry, Drinfeld doubles of finite groups, exceptional WZW categories, and the Haagerup center. The examples exhibit noncommutative module Grothendieck rings with semisimple complexifications, as well as nonzero radicals in both intermediate and maximal complexified strata.

Semi-supervised learning typically assumes that labeled and unlabeled data share an identical class distribution and label space. However, this setting is often violated: unlabeled data may be imbalanced and contain unknown class samples, causing mismatches in both class distribution and label space. Such dual mismatch leads to majority classes dominating the latent space and unknown class samples being overconfidently misclassified, degrading feature discriminability and pseudo-label quality. To address this, we propose a hub-spoke latent geometry, where known classes are uniformly distributed around a central hub and each class forms compact clusters around its prototype, while the hub provides an anchor for a low-evidence region specifically designed for high-uncertainty unknown class samples. Integrated with an evidence-based classifier, this geometry ultimately enhances feature discriminability and uncertainty separation by mitigating majority-class domination through structured feature organization and guiding high-uncertainty unknown class samples toward the hub. Extensive experiments show that our method outperforms state-of-the-art methods, with a maximum improvement of 3.25% across various settings.

Neural simulation of high-fidelity deformable bodies is a foundational challenge in computer graphics and physical AI. Long-horizon prediction for high-resolution 3D volumetric meshes is hard: autoregressive methods are prone to error accumulation, while direct multi-frame prediction at native resolution is computationally prohibitive. This motivates a compact spatiotemporal latent representation, which is largely unexplored for mesh-based volumetric physics. Meanwhile, it remains unclear whether deterministic regression or generative diffusion is the more suitable predictive paradigm. To address these coupled challenges, we introduce PhysLDM, a unified latent-diffusion paradigm for one-shot deformable simulation. Its core is a holistic spatiotemporal VAE that avoids the "staircase" artifacts of standard temporal compression (e.g., video VAEs), achieving ~2.48 mm reconstruction precision on meter-scale scenes at up to 78x token compression. Based on this reliable latent space, we systematically compare regression and diffusion methods. Our experiments uncover a key modeling insight: complex deformable dynamics are often chaotic, and in this regime deterministic regression tends to produce non-physical averages, whereas diffusion better models their distribution. Accordingly, we employ a latent diffusion model that effectively learns from chaotic data to generate physically plausible trajectories. Trained purely kinematically on an Objaverse-scale dataset, a single PhysLDM generalizes zero-shot to unseen OOD datasets. Its differentiability further enables efficient solution of inverse problems and higher-order design optimization. To our knowledge, PhysLDM is the first high-fidelity spatiotemporal autoencoder and latent-diffusion paradigm for volumetric deformable dynamics, offering a scalable and robust approach to neural simulation. Project Page: https://yucrazing.github.io/physldm/

We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on the interiors of certain 4-manifolds using Seiberg–Witten theory. In particular, no punctured blowups of a homotopy K3 manifold admit complete metrics of uniformly positive scalar curvature. Further, let $X$ be a compact oriented smooth manifold of dimension $5$, $6$, or $7$. We show that if $\operatorname{Int}X$ admits a complete metric of uniformly positive scalar curvature, then $X$ admits a positive scalar curvature metric with minimal boundary. In dimensions $6$ and $7$, the metric may moreover be chosen to be a product near the boundary. In dimension 5, under additional hypotheses and after possibly changing the smooth structure on $X$, one can likewise obtain a positive scalar curvature metric that is a product near the boundary.

Model-guided directed evolution seeks to identify high-fitness protein variants under limited oracle budgets. Protein language models (PLMs) provide rich representations for this task, but task-agnostic zero-shot scores can be misaligned with a target assay, while supervised search in high-dimensional embedding spaces can make surrogate modeling and uncertainty estimation sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: within mutation-induced residue-level representation changes, a compact, assay-specific set of directions makes fitness variation linearly accessible from few labeled variants. This is a local, supervision-recoverable statement rather than a claim that protein fitness landscapes or global PLM geometry are universally linear. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which estimates an LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition in the learned subspace. Across 10 core ProteinGym assays, 87 extended static-validation assays, and an 18-assay budgeted-search evaluation, SGES improves fitness prediction and search efficiency over zero-shot PLMs and recent ML-guided protein optimization baselines. Controlled comparisons with PCA, random projections, label-shuffled PLS, classical mutation features, and acquisition ablations further isolate the benefit of a fitness-aligned site-delta coordinate.

This paper establishes a theoretical framework for vertical adaptive layer skipping, proving three foundational results: (i) an Expected FLOPs formula (theorem 2) giving a closed-form expression for the computational cost of arbitrary per-sample skip schedules as a function of layer-wise skip probabilities; (ii) function-space superset (theorem 10) and strict inclusion (theorem 11) theorems showing that skip-layer models are strictly contained in—yet meaningfully approximate—the full-layer function space, with an explicit separating example; and (iii) a structural duality between VALSE and Mixture-of-Experts architectures (proposition 6), positioning vertical depth-wise sparsity as the orthogonal counterpart to horizontal width-wise sparsity. Building on this theory, we propose VALSE (Vertical Adaptive Layer Skipping for Efficiency), a per-sample, non-contiguous layer skipping method: a lightweight difficulty estimator scores each input from the first few layers, and per-layer gates selectively skip redundant layers—including arbitrary middle layers while retaining deeper ones—so that only the necessary depth is activated for each input, whose feasibility is preliminarily assessed at prototype scale.

In this study, the lean extinction behaviors of CH4 and a 16% cracked ammonia surrogate fuel, CR16, in counterflow premixed flames were compared. Experiments were conducted along with one-dimensional simulations using OPPDIF; the GRI-Mech 3.0 and UCSD mechanisms were applied to CH4 and CR16, respectively. CR16 exhibited higher extinction strain rates and resilience to strain-induced blow-out (RSIB) than those of CH4 under lean conditions. At Phi = 0.66, although both flames had the same extinction strain rate, CR16 showed a higher RSIB because of its longer flame time. Near its extinction, CR16 sustained H2 consumption, radical reactions, and heat release through the interflame region toward the stagnation plane. Hydrogen oxidation coupled with nitrogen-related pathways, including NH2 + NO and HNO reactions, supported this behavior. These results clarify the chemical basis for the superior extinction resistance of economically favorable low-cracking-ratio ammonia fuel.

A very-high-frequency (VHF) electron gun operating at a resonant frequency of 216.667 MHz has been developed at Tsinghua University for the Shenzhen Superconducting Soft X-ray Free-Electron Laser ($\rm S^3FEL$) facility. Building upon the SHINE gun design, the cavity profile was optimized to achieve a higher cathode electric-field gradient and a higher accelerating voltage at comparable input power. The revised cavity geometry also yields improved multipacting performance. In addition, thermal analysis was carried out to guide the water-cooling design, and enhanced cooling was implemented in the vicinity of the cathode. During high-power conditioning, 82 kW of continuous-wave radio-frequency power was successfully coupled into the gun, corresponding to a cathode gradient of 29.9 MV/m and an accelerating voltage of 856 kV. The gun voltage surpasses the previous world record for room-temperature VHF guns. The maximum dark current measured by the Faraday cup at the gun exit was only 6.8 nA.

This article proposes Selective Affective Layer Fine-Tuning (SALFT), an efficient adaptation framework for Video Vision Transformers in player arousal recognition from gameplay. To bypass computationally expensive full fine-tuning, SALFT introduces a selection criterion based on the L2-norm change in layer parameters after brief adaptation, directly measuring representational shifts and providing a more stable basis than gradient-based alternatives. Evaluated via five-fold cross-validation on the Arousal Video Game AnnotatIoN dataset, SALFT achieves performance comparable to full fine-tuning across all games without statistically significant degradation ($p>0.05$), while updating only $\approx$8% of parameters (over 92% reduction). Notably, in one game, SALFT consistently outperforms both full fine-tuning and the best baseline across all metrics and folds, reaching the theoretical minimum p-value (p=0.0625, exact two-sided Wilcoxon signed-rank test). In addition, we introduce an interpretability method to trace attention patterns, enhancing model transparency. These results establish SALFT as an effective and efficient approach for affective game computing.

We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal transport. Each update is parametrized by a spatial map and a mass-changing factor, allowing spatial redistribution and local mass creation or loss to be treated jointly within a single variational step. Their cone action bounds the squared HK distance from above, yielding a sufficient condition for discrete energy dissipation through comparison with the identity pair. Minimizing the pair objective over all admissible pairs recovers the exact JKO minimum when the source and a minimizer have positive densities. We establish existence and mass bounds for JKO minimizers and, under additional assumptions, obtain positivity and regularity together with a discrete Euler-Lagrange equation and a metric-dissipation identity. The self-consistent chemical potential is then nonincreasing along an optimal map. There exist parametric pairs whose endpoint densities and objective values converge to those of an exact JKO minimizer, provided a regular-pair approximation hypothesis holds. Finally, we show that a primal-dual gap controls objective suboptimality and, for Boltzmann entropy, the $L^1$ density error, assuming exact-step regularity, positive-semidefinite interactions, and global dual feasibility. Numerical experiments examine pointwise agreement with the PDE, energy dissipation, and the roles of transport, reaction, and fully implicit interactions.

Reinforcement learning with verifiable rewards (RLVR) provides a natural framework for adapting pretrained models to video temporal grounding, where generated temporal intervals can be scored directly against ground truth intervals. Yet existing overlap verifiers typically score each rollout independently, leaving the joint structure of the rollout group unused. We introduce SUTURE, which conditions verification on the rollout group and exploits its structure at two complementary scales: disagreement across rollouts controls how strongly the target is reweighted, while coverage at each position determines where reward mass is redistributed. We show that the resulting verifier admits an exact decomposition into the standard IoU term and a covariance correction determined by the rollout group. A local gradient diagnostic finds a preference for responses covering relatively less supported target regions in the analyzed groups. Across five temporal grounding benchmarks, SUTURE improves grounding performance at every reported IoU threshold. Its trained policy also shows less video-start anchoring in reasoning traces: for later events, the first temporal mention more often overlaps the annotated target. Together, these results show that the joint structure of a rollout group can support a more informative temporal verifier.

Useful-skew schedules can satisfy timing constraints yet remain unrealizable by a fixed clock tree with discrete tuning choices. We formulate this mismatch as exact membership in a finite relative-latency set and develop a checkable feedback interface between the scheduler and the tree model. Arithmetic certificates explain unrealizable targets, while tree-specific contraction reduces the structural size of the exact relations projected onto selected sinks. These relations become realizability cuts that can exclude more candidates than a no-good on the same certificate support, including discrete holes that linear inequalities cannot separate. Controlled experiments confirm fewer oracle calls and faster projection construction. They also expose important limits: globally minimum certificates can cost more than they save, compact arithmetic feedback can fail on non-parity obstructions, and direct monolithic optimization remains faster on the tested additive models. The contribution is an exact, independently verifiable scheduler–tree interface, rather than a claim of universal solver acceleration or physical signoff.

In this paper, we study robust decision-making in the latent space of world models (WMs). Robust optimization is a mathematical framework where, given explicitly specified dynamics and physically meaningful disturbances, a robot can select actions that remain effective even under worst-case disturbances. However, applying this principle to the learned latent space of WMs introduces a fundamental challenge: because WMs have fully learned state spaces and dynamics inferred from high-dimensional observations, it is unclear how to define latent-space disturbances that faithfully represent uncertainty in the underlying system. Our key idea is to model a latent-space disturbance as a perturbation to the learned latent dynamics that induces pessimistic but plausible transitions. Specifically, we construct a set of plausible latent dynamics by combining a dynamics-aware similarity metric that captures plausible transitions with out-of-distribution detection that excludes implausible latent states. We calibrate this uncertainty set over latent dynamics using conformal prediction, ensuring that WM imaginations induced by the latent disturbance remain plausible without becoming overly pessimistic. We then jointly optimize robust robot actions and the worst-case latent disturbances through game-theoretic optimization. We leverage this latent-space robust optimization to robustify policy steering, considering two paradigms: latent safety filtering and sample-and-verify steering of a generative control policy. Our controlled simulation experiments show that our latent disturbance enables robust decision-making directly in WM latent spaces, and hardware experiments with a Franka manipulator show that modeling latent disturbances enables robust policy steering, reducing failures by 70% in safety filtering and 54% in sampling-based policy steering. Project website: https://junwon.me/LatentDisturbance/.

We study the transition threshold problem for the 2D Navier–Stokes Boussinesq equations around the Poiseuille flow on three domains: $\mathbb{T} \times \mathbb{R}$, $\mathbb{T} \times [0, \infty)$, and $\mathbb{T} \times [-1, 1]$. More precisely, we prove that if the initial perturbations of the vorticity and the temperature are assumed size $O(\min\{\nu^{\fr34},\mu^{\fr34},\nu^{-\fr14}\mu\})$ and $O(\min\{\nu^{\fr94},\mu^{\fr94}\})$ in an anisotropic Sobolev space respectively, then for the solution to this system, its size remains so for all time, and the nonlinear enhanced dissipation persists with a rate proportional to $O(\min\{\nu^{\fr12},\mu^{\fr12}\})$.

A robot description does more than specify a physical mechanism: it also encodes arbitrary conventions, such as joint-axis direction, joint-angle zero, and the order and names of links and joints. Morphology-aware policies consume interfaces built from these descriptions, yet cross-embodiment evaluation typically changes the robot while keeping those conventions fixed. This leaves a simple question unanswered: does behavior survive when the robot stays fixed but its description changes? GaugeBench isolates this case by rewriting a fixed mechanism under physically equivalent conventions, verifying that its physics and policy interface are preserved, and then evaluating the same policy weights. The result is stark: three MetaMorph policies score 4030.6 on 80 familiar robots, but only 51.6 when those same robots are equivalently re-described, while 98 genuinely held-out robots score 1489.6. A new description can therefore be more damaging than a new robot. Tracing the failure reveals that axis reversal alone reproduces the collapse, joint-angle zero changes are nearly harmless, and reordering lies between them; moreover, changing joint-state and torque coordinates alone is sufficient to cause the failure, while changing description-derived features alone is not. The same phenomenon appears in ModuMorph and an unrelated PyBullet framework. Yet it is not irreversible: exact two-description transport restores the original controller, and training across equivalent axis conventions raises retained return under axis reversal from 3.6% to 80.6%. Together, these results separate mechanism robustness from representation robustness and show that cross-embodiment evaluation should test both.

Miniaturized magnetic components play an important role in achieving high efficiency and high power density in power converters. Accurate core loss data are essential when optimizing magnetic components, but making accurate core loss measurements remains challenging, especially at MHz frequencies. As a result, many research groups have developed their own testers in pursuit of improved accuracy, and the amount of published core loss data has increased. However, large variations in these data shed light on fundamental barriers to accurate MHz core loss measurement. This paper identifies these barriers and presents methods for overcoming them.

This work presents a comprehensive macroscopic electrodynamic framework isolating the magnetodipole (MD) and electrodipole (ED) contributions to the magneto-optical effects in bismuth-substituted iron garnet. By rigorously incorporating the dispersive magnetic permeability tensor, the dominance of the MD mechanism in the terahertz (THz) gap is demonstrated. In the mid-infrared (MIR) to near-infrared (NIR) domain, a fundamental spectral crossover is revealed where the magnitudes of the MD and ED contributions exactly equalize, invalidating the widespread assumption that magnetic contributions vanish uniformly at infrared frequencies. Furthermore, it is shown that interfacial phase shifts uniquely dictate how these competing mechanisms project onto observable rotation and ellipticity, yielding an inverted spectral hierarchy between transmission (Faraday) and reflection (polar and longitudinal Kerr) geometries. Most notably, the transverse Kerr effect for s-polarized light is established to be exclusively driven by the off-diagonal magnetic permeability. While strictly zero under the conventional ED approximation, the s-polarized transverse Kerr effect emerges as a robust, free of the gyroelectric contribution probe of MD activity in the THz and MIR–NIR regimes, yielding a THz response two orders of magnitude larger than its p-polarized counterpart.

Humanoid household manipulation requires the arms to act while the body balances, steps and changes posture. We present BiGym 2.0, an adaptation of BiGym for the Unitree G1 across 20 household tasks using a unified whole-body controller for demonstration and evaluation. The suite provides 60 native human virtual-reality demonstrations per task with synchronised multi-camera views and full-body execution records. We benchmark vision-language-action fine-tuning, imitation learning, demo-driven reinforcement learning, and cold-start coding agents given the interaction budget of online reinforcement learning. With the same onboard views, proprioception and whole-body controller for every method, vision-language-action fine-tuning has the highest nine-task mean, and agent-developed programs outperform every demo-driven reinforcement learning baseline on this mean and lead on bimanual reaching. Cross-workspace stacking remains open, $\pi_{0.5}$ stays low on pick-box, and multi-object transport is hard for imitation learning, demo-driven reinforcement learning and coding agents. All environments, human demonstrations, and evaluation traces are open-sourced at https://github.com/swirl-uk/BiGym2.

TRANSIT is a transparent scale-in framework to enable multi-node model training on fewer GPUs while maintaining training efficiency by transparently leveraging CPU DRAM as an extension of GPU memory during distributed training. It achieves this through a user-space interposition layer, requiring no modifications to the application, training framework, cluster scheduler, device driver, or operating system. Furthermore, TRANSIT achieves higher efficiency by leveraging a zero-copy data path for CPU-GPU transfers. We evaluate TRANSIT on dense and MoE models across scales up to 64 NVIDIA H100 GPUs and multiple parallelism configurations over a RoCE network. Our evaluation shows that TRANSIT can: (a) outperform state-of-the-art framework-managed offloading techniques, achieving up to 68%, 59%, and 42% higher per-GPU throughput than TorchTitan, ZeRO-Offload, and ZeRO-Infinity, respectively, (b) enables training with 50% fewer GPUs while maintaining over 90% of baseline per-GPU throughput, (c) lower per-node network traffic by up to 33%, and (d) improve per-GPU throughput by up to 35% in communication-bound settings.

Direct Preference Optimization (DPO) has become a standard reward-model-free approach for aligning language models with preference data. However, as the scaled preference margin grows during training, the logistic DPO loss becomes progressively less sensitive to further changes. We study DPO from a loss-level geometric perspective and identify the sigmoid factor as a learning signal that characterizes the local sensitivity of the objective. Based on this view, we propose Learning-Signal-Controlled Direct Preference Optimization (LSC-DPO), which dynamically regulates the learning signal near a target regime. A log-space analysis establishes conditions for stable tracking of the target learning-signal regime. Experiments on AlpacaEval 2, MT-Bench, and Anthropic-HH show that LSC-DPO consistently improves over DPO and strong preference-optimization baselines. We further find that different coefficient initializations induce distinct transient learning-signal trajectories even when their later signal levels become similar. Based on this observation, we derive a signal-budget compensation rule that adjusts the target learning signal to compensate for these transient differences. The resulting compensation substantially reduces performance variation across coefficient initializations.

State tracking requires an update at every input, but the depth a Transformer applies to each token is fixed regardless of sequence length. We introduce the Recurrent Looped Transformer (RLT), which splits its layers between a parallel causal encoder and a recurrent decoder. At each token, the decoder merges the encoder output with the previous token's final decoder state, so the computation path grows with sequence length at a fixed per-token cost. On six algorithmic tasks, we compare five splits of eight layers with an eight-layer Transformer over three seeds. Trained on at most 40 bits, two RLT splits generalize parity to 256 bits with 100% accuracy in every seed, while the Transformer stays at chance. On swap-based $S_5$ permutation tracking at eight times the training length, RLT reaches 97% final-state accuracy versus under 1% for the Transformer, and accuracy increases with decoder depth. On modular arithmetic beyond the training lengths, RLT reaches up to 93% versus 33% for the Transformer. Ablations show that these gains depend on the feedback: removing it drops parity and swap-based $S_5$ to chance at every split. Updating the feedback once per four-token chunk lets known tokens in a chunk run in parallel and keeps 64-bit parity at 99%, while permutation tracking depends on per-token feedback: chunking lowers length-64 swap-based $S_5$ from 100% to 20%.

Mobility-on-demand (MoD) platforms can offer exclusive, pooled, and transit-connected services to accommodate different passenger needs. However, determining which services to offer and at what prices is challenging because profitability depends on both passenger choices and operational feasibility. This paper proposes a real-time framework that jointly optimizes service menus, fares, and vehicle trip plans for individual MoD requests. Passenger choices are modeled using a generalized nested logit (GNL) model that captures correlated substitution among service options based on vehicle sharing and transit use. To solve the resulting nonlinear fare-optimization problem, we use Fenchel duality to transform the nonlinear objective from the fare domain to the choice-probability domain, yielding a concave maximization involving a generalized entropy term. We evaluate the framework through operational simulations using real-world New York City trip records. Joint portfolio design and pricing improve operator service margins by 28.4% and 8.5% compared with optimizing only service menus and only fares, respectively. Furthermore, the proposed reformulation is up to 18.8 times faster than solving the original pricing problem directly in fare space, improving computational efficiency for real-time MoD operations.

Joint-event forecasts combine an estimated dependence model with current marginal forecasts. Retaining historical transforms at the marginal fits available when each outcome arrived creates overlapping estimation errors. We derive their joint influence with the terminal estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical correction to harmonically weighted innovation moments. Terminal slope uncertainty remains in the forecast gradient. A feasible covariance estimator yields asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. A same-family terminal refit provides the efficiency comparison. Retaining dated transforms adds a positive semidefinite limiting covariance term, whose event-level cost depends on dependence sensitivity and forecast-state leverage. Monte Carlo comparisons show a small accuracy cost of retaining the transforms and a larger inferential role for current marginal estimation. Allowing Clayton dependence improves downside forecasts relative to Gaussian dependence under each transform rule. A fourteen-variable U.S. real-time forecasting application and simulations with twenty and fifty variables illustrate feasible joint-event estimation and analytic inference for fixed-depth vines.

Modern recommendation is shifting from platform-centric personalization toward user-governed personalization, where a personal LLM agent can act on the user's behalf across services. We formalize this emerging paradigm as Personal-Agent Mediated Recommendation: a platform recommender ranks a candidate set using platform-local information, and a personal agent uses user-authorized cross-platform history to mediate the resulting ranking and produce the final top-K slate. Such mediation is nontrivial: the platform ranking can encode strong population evidence that the personal agent cannot observe, so effective mediation must therefore balance beneficial rescues against harmful overrides. To study this trade-off, we introduce MediateRec, a benchmark that includes scalable proxy cross-platform environments and a real cross-platform test under a controlled platform-agent information boundary. To train the agent to use cross-platform history effectively, we further propose Personal Attribution Mediation Optimization (PAMO), which counterfactually masks that history to estimate personal mediation support and reallocates rank-aware advantage mass under a platform-relative value floor. We theoretically prove that PAMO preserves cutoff-level advantage mass and is locally optimal among first-order reallocations that preserve this mass without lowering average platform-relative value. Experiments on MediateRec show that personal-agent mediation enables meaningful platform corrections, yet even strong proprietary LLMs introduce non-negligible harmful overrides. PAMO consistently improves over matched outcome-only RL across seen and unseen target platforms and on the real cross-platform test, while achieving a better rescue-harm balance.