Papers

We obtain a characterization of finite non-$p$-groups with five automorphism orbits. In the solvable case of Fitting height $3$, the groups are precisely $S_4$ and $C_2^4\rtimes D_{10}$. Moreover, the corresponding fixed-point subspaces form a spread in a finite projective space. For Fitting height $2$, we distinguish the possible structures according to the number of prime divisors of $|G|$.

Flow matching (FM) learns generative transport by fitting continuous-time motion from a simple source distribution to the data distribution. Most existing methods use first-order bridges: once a source and a target sample are paired, the path is a straight motion with constant velocity. FM with optimal transport (OT) improves the pairing, but the bridge itself remains linear, limiting its ability to model curved motion, acceleration, and changing directions. A natural remedy is to use second-order phase-space dynamics; however, learning the bridge requires target-side terminal-velocity information that static datasets do not provide. We propose Variational Terminal-Velocity Flow Matching (VTV-FM), a second-order FM framework that derives the missing velocity by minimizing acceleration energy, yielding a closed-form closure for static data. The same minimum-acceleration variational construction also defines the OT pairing cost and the acceleration targets used for training. Experiments on low-dimensional datasets, PDE-governed physical fields, and CIFAR-10 show that VTV-FM improves transport geometry and generation quality over first-order and high-order FM baselines.

We study the measure of restrictiveness proposed in Fudenberg, Gao, and Liang (2026) to evaluate complexity of economic models using synthetic data. We show that Rademacher complexity is an affine transformation of a particular case of a consistent finite-sample estimate of restrictiveness. Our results show that restrictiveness inherits a cardinal interpretation as a bound on generalization error while avoiding the inability of limiting Rademacher complexity to distinguish between some falsifiable models.

Control and readout systems for superconducting quantum computing support real-time control and high-fidelity qubit-state discrimination. We examine when additional digital processing improves readout fidelity. A common baseline for dispersive readout uses a boxcar averager to compute a uniformly weighted average over a fixed window followed by threshold-based state assignment. We evaluated an adaptive finite-impulse-response (FIR) filter trained in real time using the least-mean-squares (LMS) algorithm on a field-programmable gate array (FPGA) quantum controller. We also analyzed measured readout shots offline to compare the frozen filter with boxcar averaging, and evaluate per-sample weighting plus sequential detection. For the fixed FIR filters tested, summing the filtered samples gives the boxcar sum multiplied by one complex number apart from a small edge correction. We call this the kernel collapse. The multiplication scales the state separation and noise equally without improving state discrimination, and we call this the boxcar limit. The frozen LMS filter reduces trace noise, but shows no resolved improvement in readout fidelity. On a 2D transmon, optimizing the readout window accounted for much of the improvement over full-window integration. We then examined how changing the decision method could reduce calibration effort and decision time. On a higher-fidelity 3D ancilla readout, our modeled template estimation reached the same fidelity target as direct averaging with 89.8% fewer labeled shots per state. Offline sequential replay assigned most shots before the acquisition window ended. These results distinguish waveform denoising from state-discrimination improvement, and motivate direct control of decision weights and assignment time in dispersive readout.

Artificial-intelligence weather prediction (AIWP) models have made it possible to produce high-quality tailored forecasts with limited computational resources. This advance has the potential to benefit hundreds of millions of farmers in low- and middle-income countries who lack access to forecasts of critical weather phenomena. However, it can be difficult for key stakeholders to evaluate forecast quality, risking a "race to the bottom" as cheap but low-quality forecasts crowd out forecasts that would benefit farmers. We propose a set of principles and protocols for evaluating agriculturally-relevant forecasts as a starting point for standards that would let forecasters credibly convey their forecasts' quality.

Teleoperated demonstrations are a primary source of data for robot manipulation, and teleoperated interventions are a primary mechanism for correcting policies at deployment. Yet most teleoperation systems close the loop through vision alone and are built around parallel-jaw grippers, limiting both what the robot can execute and what the operator can express through it. This is most damaging in shared autonomy, where the operator sees the scene only through occluded cameras and must take over a dexterous hand mid-task, often with an object already grasped. We present DITTO-X, a hand-agnostic dexterous teleoperation interface that renders joint-level force and fingertip contact events from sensing already on the robot hand, and drives three commercial dexterous hands (Sharpa, Wuji, and Inspire) without per-hand redesign. Because the exoskeleton is actuated, DITTO-X also supports reverse teleoperation, in which the robot back-drives the operator's fingers into its own configuration before control is transferred, so the human enters the loop already matched to the state they inherit. Our results show that DITTO-X improves demonstration quality and throughput over a commercial hand-tracking glove, both in regular data collection and in human intervention during policy deployment for contact-rich manipulation tasks. More information can be found from our website: https://tml.stanford.edu/ditto-x/.

Image watermarking supports provenance and attribution by embedding verifiable identity information into images. Practical deployments, however, must jointly satisfy requirements for attack resistance, false-positive rate (FPR), image quality, and latency. Existing watermarking methods are robust to different classes of transformations, so combining complementary methods can provide broader protection than any single watermark. Such composition is challenging, as additional fragments increase distortion and decoding cost and must share the same FPR budget. Therefore, we propose **TAILOR**, a request-conditioned watermark composition framework with three stages: (1) *offline characterization* measures fragment recovery, distortion, and runtime as response curves over embedding strength; (2) *joint configuration selection* encodes the request as an SMT model over these curves and solves for the lowest-distortion composition of fragments, strengths, order, and geometric recovery; and (3) *live calibration* validates the selected configuration on the user's images and refines predictions that fail to transfer. Experimental results across 7,321 distinct requests spanning five scenarios and 20 attack settings show that **TAILOR** achieves **96.21%** scenario-averaged request satisfaction with a mean PSNR of **41.02 dB**, outperforming existing methods in robustness while achieving consistently better image quality. Code is available at [https://github.com/aaFrostnova/Tailor](https://github.com/aaFrostnova/Tailor).

Synthetic data now is essential to LLM training, used to strengthen advanced capabilities such as autonomous and long-horizon task execution. Yet recent work shows that training on it at scale can degrade model generation, making it important to decide what synthetic data is worth training on. While current data curation practices do so with individual-level signals (i.e., estimates of each data sample's training utility in isolation), across pre-training and post-training settings we show that this is insufficient for synthetic data, and that group-level signals (i.e., estimates of utility that account for interactions among data samples) are necessary for effective data curation. First, we show that individual-level signals are blind to how samples jointly affect training: synthetic datasets with different compositions can be indistinguishable under individual-level influence yet differ sharply under group-level influence, and curating by the latter yields better downstream performance, particularly in generative capability. Second, we find that group-level signals matter more as training pipelines become increasingly synthetic: among widely used data curation methods, only those incorporating them improve over baseline, with gains increasing when weights capturing relations among samples are amplified. Finally, we translate these findings into practice – for model developers under a compute budget, we offer a cheap diagnostic that prioritizes which groups of synthetic data most need group-level estimation, recovering much of the benefit of full group-level scoring at a fraction of the compute cost.

In goal-conditioned reinforcement learning (GCRL), quasimetric learning models goal-reaching costs as quasimetric distances, connecting local constraints to global value geometry. Its local constraints, however, should reflect the direction- dependent effects of control composition over a finite horizon together with environmental feasibility. We propose ReQRL, which constrains the critic's value gradients through finite-horizon reachability. Drawing on state-constrained optimal control, we decouple dynamical reachability from boundary geometry, estimating both from data. On OGBench, our method outperforms or rivals existing quasimetric approaches and other offline GCRL methods.

Here, I give a brief history of the theory, with twists and turns, and list possible predictions for the spectra of the direct cascade of gravity waves on the water. The description of long waves is straightforward within the weak-turbulence theory developed by Zakharov and his school. As the energy cascade proceeds to shorter scales, the mean surface steepness grows, and wave-breaking events appear with increasing frequency. Considering surface cusps, Phillips suggested a wavenumber spectrum (with a wrong magnitude, as I argue here) and a frequency spectrum whose whole form is incorrect. The right form for the frequency spectral slope due to breaking waves was suggested by Kuznetsov. Here we estimate the magnitude and argue that the frequency spectrum is expected to continue unchanged through the whole cascade. The transition from weak to strong turbulence in the wavenumber and spatio-temporal spectra is due to spectrally nonlocal interactions and happens earlier (at larger scales) than the dimensional estimate suggests. As a result, the magnitude of the strong-turbulence spectrum is not universal but depends on the pumping for a sufficiently long weak-turbulence cascade. The reason for nonlocality is likely that breaking of shorter waves is determined by the magnitude of the longest wave on whose crest they are running.

High-momentum ratios measured in the CaFe experiment using high-energy electron scattering off the CaFe nuclei $(i.e.~ {}^{40}\mathrm{Ca}, {}^{48}\mathrm{Ca}, {}^{54}\mathrm{Fe})$ have revealed a surprising correlation between the nuclear shell structure and the high-momentum components generated by short-range and tensor correlations (SRC). The non-local dispersive optical model (DOM) successfully describes the experimentally measured high-momentum ratios while simultaneously describing the nuclear bound-state properties and scattering observables for these CaFe nuclei. The experimentally measured average high-momentum ratio of ${}^{48}\mathrm{Ca}$/${}^{40}\mathrm{Ca}$ and ${}^{54}\mathrm{Fe}$/${}^{48}\mathrm{Ca}$ are $1.10~\pm~0.02$ and $1.49~\pm~0.03$, respectively. The corresponding DOM results are $1.05~\pm~0.05$ and $1.52~\pm~0.08$, which is the first successful description of these experimental results. The present DOM analysis of CaFe nuclei relied on an extended version of the DOM incorporating a shrinkable geometry to provide a more localized and stronger volume absorption at higher missing energies to correctly represent the SRC physics. The success of the DOM can be attributed to its simultaneous treatment of structure and reaction data, the latter requiring a depletion of the mean-field accompanied by the proper admixture of high-momentum components in the respective ground states.

We study two Riordan arrays associated with the Motzkin-prefix sequence (\href{https://oeis.org/A005773}{OEIS A005773}). By connecting their production matrices through a simple boundary factorization, we obtain a period-three transformation on Motzkin endpoint distributions and exact formulas for paths by final height modulo~$3$. In addition, a unified factorization for the shifted Hankel matrices leads directly to explicit closed forms for the third and fourth Hankel determinants, $\Delta_n^{(3)}$ and~$\Delta_n^{(4)}$.

Branching fundamentally modifies nonlinear localization by introducing vertex degrees of freedom absent in one-dimensional lattices. We investigate localized states in a PT-symmetric four-edge star graph described by the discrete nonlinear Schrödinger equation. We identify a discrete vortex state with a fixed topological charge, supported by the branching geometry. Constructed by continuation from the anticontinuum limit, the vortex evolves into a current-carrying state in the presence of balanced gain and loss and exhibits stability windows absent for the conventional branches. A possible electric-circuit realization of the proposed model is discussed.

A $k$-arrangement of pseudolines is a set of bi-infinite curves in the plane such that any two of them intersect each other in exactly $k$ points, at which they cross, and it is simple if no three curves meet at a common point. Cyclic arrangements are the only simple $1$-arrangements of pseudolines that are unavoidable, in the Ramsey spirit: for each fixed $m\ge 1$, every sufficiently large simple $1$-arrangement of pseudolines has a cyclic subarrangement of size $m$. We show that, for every $m\ge 3$, the number of unavoidable simple $k$-arrangements of pseudolines of size $m$ grows exponentially with $k$, independently of $m$. For even $k$, we prove an analogous result for $k$-arrangements of pseudocircles.

We establish duality relations for conditional entropies relative to subalgebras of arbitrary von Neumann algebras, including the Umegaki relative entropy as well as the sandwiched- and Petz-Rényi divergences. Even in finite dimensions, these results extend the familiar dualities for conditional entropies from tensor-product subsystems to general subalgebras, while also lifting the framework to the fully infinite-dimensional setting. As an application, we establish an infinite-dimensional extension of quantum Stein's lemma when the alternative hypothesis is the state space of a finite-index subalgebra, which gives an operational interpretation of the relative entropy to a subalgebra as the optimal asymptotic error exponent in composite quantum hypothesis testing-the first beyond finite dimensions.

A central puzzle in transfer learning is why pre-training on one task can accelerate training or improve performance on another task, and what mechanisms underlie this transfer. In this work, we examine the transfer between memorization tasks of random input-output mappings. We find two surprising transfer patterns: equivalent transfer, where each additional pre-training epoch saves approximately one downstream fine-tuning epoch; and non-equivalent transfer, where pre-training on a mismatched task can be even more efficient than directly training on the downstream task itself. Through ablation experiments, we decompose and localize the transfer into two separate effects: a "trivial" magnitude-driven transfer in the last layer, and a "non-trivial" structure-driven transfer, partially attributable to the covariance of the other layers. These results advance our understanding of the underlying mechanisms of transfer learning and have the potential to lead to principled pre-training strategies.

We summarize recent developments in the theory of the Benjamin-Ono equation, a well-known long-wave asymptotic model for internal waves in deep water, focusing on results obtained by means of an explicit formula for the solution of the Cauchy problem in terms of given initial data. We give a full description of this formula, and provide simple examples, with the aim of bringing it into the realm of applied mathematics. We also show how the formula simplifies further upon restriction to rational initial data. We then show how the formula and its rational restriction explain in great detail, and in a strikingly simple fashion, the asymptotic behavior of solutions of the Benjamin-Ono equation in the small-dispersion and long-time limits. In the setting of long-time asymptotics, we prove some new results related to soliton resolution yielding pointwise convergence with a concrete decay rate under the assumption of rational initial data. The first half of the paper is a stand-alone general survey and user's guide, while the appendices constituting the second half are intended for readers who want to explore the topics in greater depth, and it includes the proofs of our new results.

We consider the augmentation of randomized experiments or trials with data from observational studies for the purpose of improving statistical precision. In particular, we focus on the Hybrid Augmented Inverse Probability Weighting estimator, designed to integrate predictions from several foundation models while preserving valid statistical inference. In this article, we extend the Augmented Inverse Probability Weighting framework to the estimation of the risk ratio, the quotient of the absolute risk of an exposed to an unexposed group. Our approach allows one to use information from black-box foundation models trained on external and possibly unstructured data, yielding an estimator of the risk ratio whose asymptotic variance is never larger than the one of the default estimator based on experimental data alone.

A graphene slit junction is investigated as a compact geometry for directional electron-beam formation, coherent interference, and symmetry-controlled spin filtering. Atomistic tight-binding calculations combined with the nonequilibrium Green's function formalism show that trigonal warping in monolayer graphene produces strongly directional electron beams near E~2.7eV. Boundary reflections redirect these beams toward a common drain, where the transmission exhibits magnetic flux-dependent oscillations consistent with an h/e Aharonov-Bohm period, whose modulation is characterized by Fourier analysis and harmonic fitting. A local electrostatic gate provides additional control of the interference phase. In separate self-consistent mean-field Hubbard calculations, the pristine antiferromagnetic ground state is shown to have spin-degenerate transmission, whereas structural or electrostatic breaking of the left-right symmetry enables spin filtering. Complementary valley-resolved calculations using a four-band continuum model demonstrate analogous beam formation in bilayer graphene at E = 50meV. The results identify the slit junction as a common geometry for electron-optical and spin-dependent transport and motivate further investigation of low-energy bilayer implementations.

Pre-training interventions are critical to alignment research, since beliefs formed during pre-training shape how a model generalizes from later training. One recently popular technique for such interventions is synthetic document fine-tuning (SDF), which aims to alter what the model believes. Ideally, synthetic documents would be mixed into pre- or mid-training, but every change to a pre-training corpus must be followed by a full post-training run before its effect can be measured, making iteration slow and expensive. Common practice instead applies SDF to an already post-trained model. This is known to leave artifacts and degrade capabilities, and, as we show, it makes the model treat fabricated entities unrelated to the documents as real, a failure we call reality drift. We propose grafting: train the SDF adapter on the pre-trained checkpoint, then add the learned weight update to the post-trained model, which approximates the faithful approach while reusing the existing post-training. We demonstrate this by installing false facts, training misaligned model organisms and applying a constitutional mid-training intervention, across model families up to 284B parameters. Grafting installs the target belief as strongly as SDF on the post-trained model while reducing both reality drift and the loss of preference coherence by more than half on average, and it stays closer to a faithful mid-training run. Because grafting requires no post-training, the same adapter can be applied to any later checkpoint, enabling researchers to iterate quickly on pre-training interventions at the cost of a single fine-tuning run.

Factor modeling provides a framework for extracting common components from high-dimensional time series. We develop an estimator of the factor loading space that combines contemporaneous covariance with lagged autocovariance information. Under cross-sectionally heteroskedastic white noise, the contemporaneous covariance contains heterogeneous diagonal noise contributions. We apply the existing HeteroPCA algorithm to the combined estimation matrix to correct this contamination while retaining information from serial dependence. The framework also accommodates noise contamination on a known set of entries subject to sparsity and incoherence conditions. Under regularity conditions for dependent observations, we establish consistency and derive convergence rates, identifying regimes in which incorporating contemporaneous covariance improves the rate relative to the lagged-autocovariance estimator. Simulations evaluate loading-space estimation error and the effects of contemporaneous covariance inclusion and diagonal correction. An application to S&P 500 stock returns illustrates the method.

Let $k$ be a positive integer, and consider the sequences of positive rationals with $x_0\in\N$ and $x_{n+1}=k/(x_0+x_1+\dots+x_n)$. Write $x_n=a_n/b_n$ in lowest terms. We show that there is a rational constant $c>0$ such that $c\,a_n+b_n$ is a perfect power for every such sequence and every $n\ge2$ if and only if $k=h^2$ and every prime factor of $h$ is congruent to $3$ modulo $4$; in that case $c=2/h$ and the powers are squares. The proof rests on the observation that $t_n=(x_0+\dots+x_n)/h$ satisfies $t_{n+1}=t_n+1/t_n$, a recursion under which reduced fractions never cancel. This yields an exact formula for $c\,a_n+b_n$, shows that along any single sequence each prime factor of $h$ spoils at most one term, and leads to two generalizations. For arbitrary $k$ the invariant $b_n^2-\frac4k a_n^2$ is always a rational square, and it is always an integer square exactly when the primes dividing the square part of $k$ satisfy an inertness condition in $\Q(\sqrt{-k})$. For the recursions $x_{n+1}=h^2/(x_0+\dots+x_n+n\mu h)$ the role of the Gaussian integers is played by the quadratic fields $\Q(\sqrt{\mu^2-4})$, which include $\Q(\sqrt{-3})$ and every real quadratic field.

Undergraduate research experiences provide students with an opportunity to apply knowledge learned in the classroom to authentic scientific problems. In this work, we describe the development of a special-topics course in Plasma Physics and Engineering (PPE) at a small liberal arts college using a Course-Based Undergraduate Research Experiences (CUREs). During the first half of the semester, students learned fundamental plasma physics and dusty plasma concepts through traditional lectures and homework. During the second half, they applied this knowledge to investigate an unanswered research question: why does the levitation time of growing nanoparticles decrease in the presence of a magnetic field? Students learned and used Langmuir probe and optical emission spectroscopy diagnostics to characterize an argon plasma over a range of magnetic-field strengths. Their measurements showed a general decrease in electron density with increasing magnetic field strength, while optical emission measurements confirmed a reduction in carbonaceous nanoparticle growth-cycle time from acetylene. Using the measured plasma parameters, students estimated the nanoparticle charge and developed the hypothesis that a reduction in electron density leads to a smaller negative dust charge and consequently a weaker electric force available to levitate the particles as a function of increasing magnetic field strength between 50 and 330 Gauss. Students subsequently disseminated their results through research poster presentations at conferences. Course evaluations and E-CLASS responses also indicated positive student experiences with the laboratory and research components of the course. This work demonstrates one approach for integrating plasma physics education and authentic research in an undergraduate curriculum at a small liberal arts institution.

Molecular neural interfaces that deliver and sense the same neurotransmitter must estimate endogenous release in the presence of their own chemical input. We study two exchanging regions with shared saturable uptake and concentration change measurements. Known delivery and exchange permit identification of apparent uptake at the driven region, but an unknown resting concentration difference leaves the source region's incremental uptake uncertain. We characterize all admissible source histories consistent with both ideal records and show how delivery and baseline information affect release classification. A dopamine-inspired example produces identical ideal concentration-change records for mean release-rate changes of -8.99 and +1.31 nanomolar per second. Stronger delivery changes whether all compatible sources imply suppression, with the true source held fixed. Under a Gaussian observation model, we bound discrimination based on chemical fluctuations. A baseline reference with an assumed standard deviation of 3.3 nanomolar reduces root-mean-square error from 10.41 to 1.21 nanomolar per second compared with an incorrect fixed baseline under exact gain calibration. Classification errors remain substantial with weak excitation, gain errors or responses near the category boundaries.

Early in the 2006 outburst of the recurrent nova RS Oph, Swift detected the onset of the super-soft-source (SSS) phase. An XMM-Newton observation on day 26.1 revealed an unusual soft X-ray spectrum containing transient narrow emission features that could not be identified with known transitions and are atypical of SSS spectra. We analyse a new XMM-Newton observation obtained at a comparable stage of the 2021 outburst and compare it with spectra from other epochs and with similar novae. A blackbody model reproduces the low-resolution 2006 EPIC/pn spectrum but fails to describe the simultaneous high-resolution RGS data. The 2021 spectrum closely resembles that observed in 2006 and consists of a slowly fading shock component and a highly variable soft component containing several unidentified features. While the shock emission evolves on timescales of days, the soft component varies on hourly timescales and dominates the observed variability. Its properties resemble those of the novae V1494 Aql and V1716 Sco, but not those of the persistent SSS Cal 87. No significant 35-s periodicity is detected. The results demonstrate that low-resolution observations can miss the complex line-dominated emission revealed by high-resolution spectroscopy. The rapidly variable soft component, together with radiative recombination continua, Fe X emission, and the previously detected 35-s period, suggests the presence of a hidden photoionising source. We conclude that these enigmatic spectra form an intermediate class between the SSe and SSa categories of Ness et al. (2013), together with V1494 Aql and V1716 Sco. Future modelling will be required to determine the relative importance of photoionisation, charge exchange, and other processes in shaping this class of intermediate SSS spectra.

A model for $\beta$-delayed neutron emission is presented in which the emission of neutrons is allowed to occur before states populated in $\beta^-$ decay have reached equilibrium in the so-called "compound nucleus" picture. The pre-equilibrium neutron spectra are computed using a two-component exciton model, where neutron and proton, particle and hole degrees of freedom are treated independently. This model is implemented in the code BeoH to supplement the existing Hauser-Feshbach model for statistical decay of compound-nucleus states. The effect of a pre-equilibrium component in the total neutron spectrum on the single- and multi-neutron emission probabilities $P_{xn}$ is investigated for $\beta$-decay precursor nuclei in the regions $47\leq Z\leq 49,~83\leq N\leq 86$ and $54\leq Z\leq 58,~N=125,126$. An absolute change in the $P_{xn}$ values of up to 5-10% is observed in the $N=126$ region when including pre-equilibrium emission compared to the values predicted by the Hauser-Feshbach model alone.

Large language models are increasingly used as collaborators on deductive-reasoning tasks, but their outputs can hallucinate or pull users away from intended reasoning. Formal proof assistants provide machine-checked verification, but have a steep learning curve and require more granular reasoning than human written proofs. We explore an interface that combines these strengths, allowing users to write and revise free-form natural-language proofs while a verified backend checks their reasoning and returns feedback at the user's granularity. We study this interface in the context of undergraduate mathematics education by developing LeanSide, a formally verified co-reasoning system, which auto-formalizes student reasoning into Lean and informalizes verifier output into understandable feedback. We conducted user studies through classroom deployment and analyzed which system properties helped students make progress and which caused them to get stuck. We use these findings to derive design implications for using a formally verified backend in human-AI co-reasoning systems.

Cyber attack agents are typically trained and evaluated within a single simulator, making it unclear whether learned policies transfer beyond the environments in which they were developed. This limitation hinders both deployment and fair comparison, as cyber simulators differ substantially in their state representations, observation models, and action spaces. In this paper, we study policy transfer across cyber environments and argue that simulator-to-simulator and simulator-to-real transfer can be viewed as instances of the same underlying alignment problem. We propose a framework that separates state alignment from action translation, enabling a policy trained in one environment to operate in another without retraining. We evaluate transfer across four cyber platforms, CyberBattleSim, NetSecGame, CyberWheel, and NASim, including emulated deployments in NASim. Our experiments show that zero-shot transfer is feasible, fully preserving source-policy performance in closely aligned environments and achieving 45.2% win rates when transferring policies whose source performance is 60.5%. In emulated virtual machine environments, transferred policies exhibit a Jensen-Shannon divergence of 0.085 from native policies, indicating strong behavioral similarity. Code and benchmarks are available at: https://anonymous.4open.science/r/RL-Transfer-between-env-4F47/.

By learning transferable rewards, inverse reinforcement learning (IRL) enables counterfactual evaluation of agents under modified environments. Such transfer places strict requirements on coverage since target environments affect agents' state occupancy. We propose a multi-task IRL method that pools data across multiple agents with different rewards in the same environment under a low-rank assumption. In addition to alleviating coverage requirements, so each task need not visit every state as long as others do, the method offers scalable evaluation of multiple tasks under new environments as computationally intensive planning scales with rank rather than the number of tasks. We provide finite sample guarantees on reward recovery and on policy learning in new environments. Experiments show our method is robust to limited coverage, recovers rewards on and off of each task's support, transfers to target environments at lower regret than baselines, with its computational advantage over per-task methods widening as tasks grow.

Long-video question answering is limited by the high cost of visual tokens and by the fixed context width of current VLMs. A long-video question may require broad temporal coverage, but the answer is often supported by only a compact set of moments. To locate these moments efficiently, we propose token-budgeted Video Evidence Indexing (VEI): given a dense low-resolution Video Preview, the model constructs a compact high-resolution Evidence Set for final reasoning. We treat VEI as a policy that must jointly solve evidence localization, which finds question-relevant moments, and budget planning, which decides where to spend the limited high-resolution frame budget. We implement this idea with an inference pipeline: the Video Preview provides cheap global coverage, Video Evidence Indexing constructs the Evidence Set, and Answer Generation combines both inputs for final VQA. To address missing frame-level supervision, we adopt privileged self-distillation, where an answer-aware teacher guides the normal test-time policy on student-generated indexing traces. We explore previews at 1, 6, 12, and 24 visual tokens per frame, training a single policy that supports all four resolutions. Experiments show that Video Evidence Indexing improves accuracy under limited visual budgets, and self-distillation further improves both QA accuracy and temporal evidence localization.