Papers

We study the decomposed Möbius energies $E_1$ and $E_2$ at the round circle and determine their complete normal Hessians: $H_1(C)=2\pi(|D_s|^3-|D_s|)I_2$ and $H_2(C)=-(4\pi/3)(|D_s|^3-|D_s|)I_2$. Thus $H_1(C)=3H_E(C)$ and $H_2(C)=-2H_E(C)$, where $H_E(C)$ is the Hessian of the full Möbius energy. This exact proportionality singles out the Möbius-invariant combination $F=2E_1+3E_2+2\pi^2$. We prove that $F(C)=0$ and that its first three derivatives vanish on the full space of parametrized variations. For scalar binormal variations, the fourth variation has a Fourier tensor with complete $3+1$ resonance cancellation and finite $2+2$ fixed-sum blocks. Their positivity follows from an explicit weighted-difference tridiagonalization and a closed determinant formula. For arbitrary normal variations in $\mathbb{R}^3$, Möbius invariance in $\mathbb{R}^4$ reduces the radial component to a second binormal direction. The resulting two-component quartic form splits into trace, symmetric-traceless, and antisymmetric blocks, which are positive on the active coordinates. Consequently, $D^4F(C)[u,u,u,u]\geq 0$ for every smooth real normal field $u$, with equality exactly on the normal tangent space of the Möbius family of round circles. This yields a fourth-order nondegeneracy phenomenon that is not determined by the total-energy Hessian alone.

Continuous, second-by-second valence-arousal estimation from physiological signals is typically studied in a subject-dependent setting, where the model sees labeled data from the same person it is later evaluated on. We study the harder zero-shot cross-subject variant on a synchronized EEG-fNIRS dataset: predict raw-scale ([1, 255]) valence and arousal trajectories for subjects whose labels the model never observes, given only their unlabeled EEG/fNIRS recordings while watching the same video stimuli as a disjoint set of training subjects. We decompose the affect trajectory into a structure shared across subjects who watch the same stimuli and an individual structure estimated for each test subject from a label-free EEG marker (alpha-band cross-channel synchrony), which rescales the shared trajectory around the scale midpoint. We validate the per-subject calibration mechanism on four independent axes: leave-one-subject-out correlation between the marker and each subject's true optimal gain, a functional-form comparison against non-linear alternatives, a repeated leave-4-out component ablation isolating each part of the pipeline's contribution, and a ceiling analysis bounding the remaining headroom for per-subject scaling. On held-out subjects, the model reaches an overall MAE of 25.96 / 22.80 across two evaluation batches (valence 21.94 / 19.6, arousal 29.98 / 26.0), well below EEGNet and ASAC-Net baselines reported for the same subject-independent split (raw scale score 60.6 and 55.0 respectively). We further report a systematic negative-result search across model architectures, feature representations, and prediction targets that found no signal able to improve on the single alpha-synchrony marker.

Deep graph learning models deployed in real-world systems often need to cope with non-stationary environments, where the underlying graph distribution drifts continually over time. Prevailing solutions rely on training auxiliary generative modules to synthesize memory graphs for cross-domain adaptation, which incurs substantial computational overhead and scales poorly under prolonged distribution shifts. We argue that a more economical path exists: rather than generating memory, one can crystallize it. To this end, we propose Efficient Memory Crystallization (EMC), a training-free test-time framework that distills each incoming graph domain into a compact, semantically faithful memory through a closed-form solution to a memory-oriented distribution-matching objective, thereby eliminating redundant domain information under continual covariate shifts. To preserve both generalizability and adaptability as the model traverses a long sequence of target domains, EMC further models inter-domain dependencies through state-evolving memories and admits a theoretically grounded, tighter generalization error bound than direct adaptation. Extensive experiments demonstrate the superior performance of EMC over state-of-the-art baselines on graphs under non-stationary distribution shifts, while reducing average runtime by 87.4% and GPU memory consumption by 92.4% relative to the recent competitor, making continual graph adaptation practical at scale.

Controlling noncoplanar spin textures in centrosymmetric magnets remains a central challenge for realizing emergent Berry-phase phenomena. Here, we demonstrate that magnetic (Cr) and nonmagnetic (Cu) substitution at the Mn site provide distinct routes to engineer spin chirality and topological transport in the kagome antiferromagnet Mn$_3$Sn. Cr substitution enhances low-temperature spin canting, stabilizing a dense noncoplanar texture that yields a pronounced topological Hall effect (THE) at low temperatures. In contrast, Cu substitution drives a spin-reorientation transition accompanied by an easy-axis rotation, creating a broad temperature window (150–208 K) where competing magnetic anisotropies stabilize noncoplanar spin textures and generate a large THE. A concurrent carrier-type crossover signals an underlying electronic-structure reconstruction. These results reveal that exchange enhancement and exchange dilution represent two fundamentally different pathways for tuning real-space Berry curvature, establishing chemical substitution as a powerful strategy for engineering topological transport in kagome antiferromagnets.

Research on LLMs continually uncovers model limitations, their causes, and potential solutions. Yet these human discoveries remain largely disconnected from model evolution: an LLM does not automatically learn from new research about its own failures. We introduce PAPER2LLM++, a framework for continual self-evolution of LLMs from research papers. Rather than treating papers merely as knowledge to retrieve, PAPER2LLM++ uses the growing literature as a stream of evidence and supervision for model improvement. For each incoming paper, it extracts evidence-grounded findings, tests whether the reported limitation persists in the current model, and, when needed, converts the findings into candidate learning signals. A try-evaluate-commit procedure integrates an update only when it improves the targeted behavior without substantially forgetting prior improvements or degrading general capabilities. Across a sequential stream of research-discovered LLM failures, we show that models can progressively incorporate new findings while retaining earlier gains. PAPER2LLM++ thus takes a step toward closing the loop between human discovery and model evolution, enabling models to continually learn from research about their own limitations and improvements.

Legal systems are increasingly implemented through software, yet scalable methods for translating legal texts into accurate symbolic representations remain underdeveloped. We study this problem through tax law, where forms and filing instructions define large computational structures involving arithmetic, branching, recursion, and tabular reasoning. We propose Law&Order, a neuro-symbolic framework for automatically formalizing tax forms and instructions into executable symbolic programs. Our approach establishes two forms of correspondence between law and logic: structural correspondence, which aligns legal and symbolic components such as cells and schedules, and denotational correspondence, which requires symbolic components to implement the computations specified by their legal counterparts. We combine large language model synthesis with cell-level verification and iterative localized error repair using human-written OpenTaxSolver tax returns. We then evaluate the resulting formalizations on independently authored, held-out TaxCalcBench returns, that are never exposed during generation or repair. Although the most advanced LLM achieves only 66% accuracy, Law&Order achieves 100% cell-level and form-level accuracy on 51 held-out returns, demonstrating the effectiveness of combining LLM-based synthesis with symbolic verification for scalable and verifiable large-scale legal autoformalization compared with using an LLM alone.

We study the query complexity of finding approximate stationary points under higher-order smoothness using only function values or only gradients. Our results cover different dimensions, oracle models, randomization, and constraints. For constant dimension $d$ and $C^{p,\beta_p}$ objectives, with $\nu:=p+\beta_p$, we give deterministic function-value gradient trapping algorithms with query complexities $O(\varepsilon^{-(d-1)})$ on $\mathbb R^d$ and $O(\varepsilon^{-(d-1)/\nu})$ on $[0,1]^d$. High-order line integration enables gradient-only trapping. For two-dimensional $C^{1,1}$ objectives, randomized integration yields $O(\varepsilon^{-4/3})$ gradient queries on $\mathbb R^2$, breaking the deterministic gradient-only $\Theta(\varepsilon^{-2})$ barrier. For general dimension, we introduce a trapping-or-descent framework that lazily reuses boundary models. For $C^{p,\beta_p}$ objectives with $p\ge2$, it achieves deterministic query complexities $O(d^p+d^{p-1+\beta_p/(\nu-1)} \varepsilon^{-\nu/(\nu-1)})$ using function values and $O(d^{p-1}+d^{p-2+\beta_p/(\nu-1)} \varepsilon^{-\nu/(\nu-1)})$ using gradients. These bounds apply to approximate stationary points on $\mathbb R^d$ and approximate KKT points on $[0,1]^d$. Their dimension-independent accuracy exponent matches the classical AR$p$ exponent $(p+1)/p$ when $\beta_p=1$. For sufficiently high dimension, we prove randomized lower bounds for gradient-only methods. For $C^{1,1}\cap C^{p,1}$ objectives, our lower bound is $\Omega(\varepsilon^{-(3/2+1/(2p))})$, matching known upper bounds for $p=2$ and, up to logarithmic factors, for $p=3$. Without the $C^{1,1}$ assumption, we obtain an $\Omega(\varepsilon^{-5/3})$ lower bound for every fixed $p\ge3$.

Let $w_0$ be the positive homoclinic solution of $-w''+w=w^p$ and set $c_p=w_0(0)$. We study bounded positive solutions of \[ -\Delta v+v=v^p\quad\text{in }\mathbb R^N_+, \qquad v=c_p\quad\text{on }\partial\mathbb R^N_+, \qquad v(x',x_N)\to0 \] uniformly as $x_N\to\infty$. This is the threshold boundary value left open by Fernández and Weth [Math.\ Ann.\ 383 (2022), 361–397]. We prove a dimension-dependent rigidity/nonuniqueness picture. For every $p>1$, the profile $w_0(x_N)$ is the unique bounded positive solution when $2\le N\le5$, whereas for $N\ge8$ there is a one-parameter family of bounded positive non-one-dimensional solutions. In the critical dimension $N=7$, nonuniqueness holds whenever a cubic coefficient $\kappa(p)$ of the exact reduced nonlinearity is positive; in particular $\kappa(p)>0$ for all $p\ge2$, and continuity extends this range below $2$. The corresponding amplitudes have Fowler ends, with their limiting energy, neck size, bulge size, and logarithmic period determined to leading order. The case $N=6$, as well as the complementary range in $N=7$, remain open. The proof combines a boundary-adapted Modica estimate, projection onto the kernel of the one-dimensional linearized operator, an automatic tail non-concentration estimate, and a nonlinear cell problem yielding the exact reduced nonlinearity. For $N\ge8$ the reduced linearization is invertible in weighted spaces. In $N=7$ the critical resonance is bypassed by solving the projected radial equation nonlinearly and closing the transverse equation by a Schauder–Tychonoff fixed point.

In their seminal work, F. Ricci and E. M. Stein [Proc. Nat. Acad. Sci. USA 83, 1–3 (1986)] introduced the oscillatory singular integral \[ T_Pf(x)=\mathrm{p.v.}\int_{\mathbb{R}^n} e^{iP(x,y)}\frac{\Omega(x-y)}{|x-y|^n}f(y)\,dy, \] and S. Chanillo and M. Christ [Duke Math. J. 55, 141–155 (1987)] established its weak-type $(1,1)$ inequality for smooth $\Omega$. For the rough variant, however, the weak-type $(1,1)$ inequality remained a long-standing open question. In the present paper, we settle this problem: specifically, we prove that the rough oscillatory singular integral is of weak type $(1,1)$ with $\Omega\in L\log^+L(\mathbb{S}^{n-1})$. Moreover, we establish weak-type $(1,1)$ bounds for the rough maximal oscillatory operator associated with $T_P$, a result of independent interest.

Transferring robotic skills from simulation to reality requires task knowledge that remains usable across differences in perception, dynamics, and embodiment. We introduce Skill2Real, an agentic policy framework that learns executable skills through a shared application programming interface (API). A Proposer-Verifier-Governor (PVG) loop uses privileged simulation evidence to diagnose outcomes and validate updates, while keeping learned skills grounded in public observations and API semantics. The Cerebellum first acquires local manipulation skills; the Brain then learns task-level composition with the Cerebellum frozen. Both memories transfer to the real robot without task-policy fine-tuning or skill-memory updates. As GPT-5.6 Sol learns skills on LIBERO-90, evaluating each frozen checkpoint with GPT-6 Astra raises LIBERO-Pro Long success from 2.0% to 56.3%, without training on Pro Long. Independent Robosuite training reaches 85.1% and 89.4% mean success with Sol and Opus 5 across seven tasks, respectively. Frozen Sol-trained LIBERO-90 skills achieve 78.75% mean completion across four real-world manipulation tasks with Astra. Removing the Verifier or Governor during LIBERO-90 training lowers final Pro Long success by 17.3 and 13.3 percentage points, respectively. These results support learning and transferring a hierarchy of executable skills through a common robot interface.

Let $\mathfrak{g}$ be a finite-dimensional complex semisimple Lie algebra, and let $\mathcal{C}_N\mathfrak{g}=\mathfrak{g}\otimes (\mathbb{C}[t]/t^{N+1}\mathbb{C}[t])$ denote the $N$-th Takiff algebra of $\mathfrak{g}$. We introduce a notion of parabolic subalgebras of $\mathcal{C}_N\mathfrak{g}$ and classify them in terms of $(N+2)$-partitions of a simple root system of $\mathfrak{g}$. We then study the corresponding parabolically induced $\mathcal{C}_N\mathfrak{g}$-modules and establish a necessary and sufficient criterion for their irreducibility, extending Jantzen's criterion for parabolically induced $\mathfrak{g}$-modules. As an application, we derive character formulas for almost all irreducible Harish-Chandra modules in Chari's category $\widetilde{\mathcal{O}}$ over the (centerless) affine Lie algebra associated with $\mathfrak{g}$. In particular, when $\mathfrak{g}=\mathfrak{sl}_3(\mathbb{C})$, we obtain explicit character formulas for all irreducible Harish-Chandra modules in this category.

What does quantum error correction do to relativistic proper time? We show that when two error-corrected quantum memories follow distinct worldlines and are controlled by local references, their local correction histories factor exactly from the proper-time difference between them. Error correction therefore does not erase time dilation: when the memories are compared, the accumulated difference appears as a relational phase rotation. During locally referenced operation this rotation is invisible to every local error syndrome; at discrete phases admitted by a code, the final relational evolution instead returns exactly as a deterministic logical gate, including an $S$-type Clifford gate at a $\pi/2$ excursion. These results connect fault-tolerant quantum information with relativistic clocks and establish protected quantum memories as a platform for preserving proper-time information and for long-coherence tests of quantum evolution involving relativistic proper time.

High-dimensional Gaussian DAG learning faces a statistical-computational gap: methods with sharp sample complexity rely on computationally expensive subset search and a supplied indegree bound, whereas polynomial-time alternatives have less favorable sample complexity. We introduce HOST, an efficient DAG learning algorithm that replaces subset search with nodewise hold-out scoring and convex regression, without requiring a supplied indegree bound. Our key insight is that recovering a correct ordering does not require uniformly small estimation errors in ordering scores but only one-sided control of those errors. In the ordering step, HOST exploits the fact that score estimation using hold-out samples inflates ordering scores in expectation, which is the favorable direction for candidates that should not yet be selected. Given the ordering, HOST recovers parents by recursively removing indirect effects from total effects between two nodes. Under suitable conditions, HOST exactly recovers a $p$-node DAG of maximum indegree $d$ with sample complexity of order $d\log p$ in polynomial time. Experiments show that HOST achieves competitive graph recovery while exhibiting favorable runtime scaling.

Tactile sensing provides essential contact information for robotic manipulation, yet incorporating it into pretrained vision-language-action (VLA) models remains challenging. A common concern is that simply introducing touch during task-specific fine-tuning may fail to bridge the cross-modal gap, yielding limited gains or even reduced success. Consequently, existing methods often rely on large-scale tactile policy pretraining or separate visuotactile alignment, adding data requirements and training stages. We introduce SimpleTouch, a simple VLA extension that augments $\pi_{0.5}$ with a tactile expert, to test whether these additional stages are necessary. Leveraging all tokens from a frozen pretrained tactile encoder, the expert learns from action supervision and multi-horizon prediction of future tactile latents. This single-stage training uses only task demonstrations, without additional tactile policy pretraining or separate alignment. With 50 demonstrations per task, SimpleTouch achieves the highest success rate among evaluated methods on all six UniVTAC tasks. Its average success rate reaches 77.5%, compared with 45.2% for FTP-$\pi_{0.5}$ and 66.7% for FTP-1, corresponding to gains of 32.3 and 10.8 percentage points, respectively. Across four real-world tasks, it averages 71.3%, exceeding FTP-1 by 8.8 percentage points. These results demonstrate that, given pretrained VLA and tactile representations, additional tactile policy pretraining is not a prerequisite for strong performance on these tasks, offering a simpler route to contact-rich manipulation. Project page: https://simpletouch-robot.github.io/

We provide updated mass and orbital constraints on the planetary system around HD 65216, consisting of at least two giant planets on eccentric orbits. We first analyse new RV data to constrain the periods and eccentricities of both planets, before applying the Hipparcos-Gaia proper motion anomaly to constrain the inclination of HD 65216 c. From this joint analysis, we find that HD 65216 c is most likely in an eccentric orbit ($e$ = 0.42$\pm$0.05) with a longer period (7007$^{+192}_{-161}$ days) than previously determined. The proper motion anomaly is consistent with a bimodal distribution of inclinations, with peaks at sin$i\sim$0.5, producing true masses of 2.23$^{+0.96}_{-0.77}$ M$_{\mathrm{J}}$ and 3.32$^{+1.40}_{-1.16}$ M$_{\mathrm{J}}$ for HD 65216 b and c respectively, assuming the planets are co-planar. Finally, we simulate Gaia DR4 epoch astrometry and the DR3-DR4 proper motion anomaly. We find that these methods will be sensitive enough to further constrain orbital parameters and true mass.

Rendezvous and proximity operations (RPO) missions are commonly designed as a sequence of distinct phases each governed by its own sample time, constraint set, and cost structure, with the translation from mission-level requirements to model predictive control (MPC) design parameters typically performed ad hoc. This report takes a first step toward a systematic, traceable mapping between mission requirements and MPC design choices, using the ADRIOS / ClearSpace-1 active debris removal mission as a case study across three sequential operations. Its central hypothesis is that Economic MPC (EMPC), in which the stage cost reflects propellant consumption directly, is structurally better suited to proximity operations than fixed-point regulation or reference tracking, because it can exploit the natural, fuel-free relative-orbital-motion trajectories admitted by the Clohessy-Wiltshire-Hill (CWH) dynamics instead of fighting them. We show that a pure-fuel stage cost is fundamentally degenerate for this class of problem as the closed-loop optimum is not strictly dissipative with respect to any single target state or orbit, and analyse, operation by operation, which terminal ingredient (a terminal region, a terminal cost, a terminal equality, or a stage-cost regularisation) is required to repair this degeneracy, at what fuel and time cost, and under what formal guarantee. Across all three operations the economic controllers cut fuel consumption by roughly 40-99% relative to standard quadratic-tracking MPC, at the cost of longer manoeuvre times, and we synthesise the results into a cross-scenario table of mission requirements, MPC ingredients, and their residual limitations.

Many useful language-model tasks cannot be evaluated by exact outcome verification. Rubric-based reinforcement learning (RL) addresses this issue by scoring open-ended responses against explicit criteria. However, because the reward is assigned after the complete response, the training signal does not directly identify which individual decisions contributed to the final score. We propose a two-stage training framework that uses rubrics first as privileged teacher context for dense token-level supervision, then as rewards for further RL. In the first stage, rubric-privileged on-policy distillation (RP-OPD), a student without access to the rubric matches a rubric-aware teacher's next-token distributions at student-generated prefixes. In the second stage, RL directly optimizes the rubric reward and improves beyond the observed distillation plateau. We evaluate the framework on health and science tasks using open-weight models. Across HealthBench, ResearchQA, and RubricHub Science, we compare post-training methods and vary the amount of SFT or RP-OPD training before RL, finding that our two-stage framework achieves the highest scores among the methods evaluated. RP-OPD + RL shows limited signs of reward hacking on RubricHub Science, whereas the SFT + RL baseline increasingly receives high rewards for claims of rubric compliance without providing the required content. These findings support using rubrics to guide on-policy distillation before applying rubric-based RL.

Diffusion models can reach useful sample quality before copying training examples, but fast optimization can compress this generalization window by accelerating sample-specific fitting. We investigate this effect through update geometry and propose Quality-Gated De-whitening (QGD), a controller that retains a fast polar-update prefix and progressively restores fixed-gain momentum. Our random-feature analysis separates covariance-controlled, curvature-equalized and amplitude-controlled memorization clocks. Under aligned spectral assumptions, it establishes a finite-exposure condition under which a fixed-gain tail recovers a delay proportional to dataset size. QGD implements this principle with a confirmed quality gate, a bounded decay envelope and causal copy feedback. Immediate switching is the conservative limit; gradual control balances delayed copying against continued quality improvement. We pair QGD with Copy-Budgeted Selection (CBS), which applies simultaneous binomial calibration to a frozen checkpoint family, followed by a fresh evaluation of the released checkpoint. On 2,000-image CIFAR-10 subsets, QGD preserves the polar baseline's quality-arrival time while expanding its useful interval by 8.32x and reducing common-checkpoint copying by 75.9%. With identical calibration and independent quality evaluation, QGD achieves FID 75.56 versus 79.37 for SGD with the same selector. Exposure-matched controls, independent detector audits and transfer to flow matching and dance generation support adaptive exposure control as a practical way to improve the quality-copying tradeoff.

Autoregressive (AR) video generation enables scalable long-video synthesis by sequentially generating fixed-length chunks, but incurs substantial computational cost from repeated denoising and attention over growing historical contexts. Recent cache reuse methods exploit temporal redundancy to reduce this cost, yet are mainly designed for single-trajectory generation, making them less suitable for sequentially coupled AR trajectories where approximation errors can accumulate and propagate across chunks. To address this challenge, we propose TRAC, a Trajectory-aware Reuse and Adaptive Correction framework for efficient and robust AR video generation. TRAC integrates three complementary components: (1) Robust Cumulative Scheduling (RCS), which selects cache reuse schedules by accounting for cumulative rollout errors and their variation across chunks and prompts; (2) Autoregressive Trajectory-aware Guidance Scheduling (ATGS), which coordinates classifier-free guidance refreshes along the global AR trajectory; and (3) Spectral Structure Correction (SSC), which adaptively restores low-frequency structural information to mitigate long-term error accumulation. By combining these innovations, TRAC substantially improves the efficiency-quality trade-off of AR video generation. For example, on VBench with SkyReels-V2, it achieves a 6.03x speedup over the vanilla model with only ~0.6% VBench score degradation, while consistently outperforming existing AR acceleration methods in both latency and generation quality. The code is publicly available at https://github.com/yolosjxhhhhhh/trac.

Emerging experimental quantum network deployments are based on collaborations between research institutions and rely on telecommunications fiber infrastructure. Currently, such networks consist of mostly Dual Input Repeaters (DIRs) and can be viewed as composed of (mostly) line graphs. In order to evaluate the performance of such networks (e.g., in terms of Entangled Pair Rate, EPR, and average Fidelity) we developed a custom quantum network simulation platform that takes into account both the quantum and classical network components. To support the verification of the simulation results, we develop a novel approach for performance analysis of DIRs. We compare the simulation results to the analytical results for DIRs and to prior results for repeaters with more than two inputs. We observe that although the expected memory utilization cannot be bounded, a small DIR memory size is sufficient and leads to minimal performance degradation. For line networks with a single repeater and $3$ repeaters, we explore the dependency of incoming and outgoing memory size requirements on the number of nodes (network size), their connectivity (fiber length) and various quantum error settings (amplitude damping and phase flip channels). We evaluate the EPR and the average Fidelity for a sub-network of a deployed network with $3$ repeaters, using two alternative paths. We show that as the number of nodes increases or when the fiber lengths between nodes differ significantly, additional node memory is needed to maintain the same EPR (qubits are stored for longer duration to allow completion of entanglement across the network). We also show that the memory size should be above some minimum threshold to allow EP creation (EPR $>0$) as pair selection and swapping completion propagate across the network.

For a given point forecaster, proportional-integral-derivative (PID) calibration configurations can attain similar overall coverage yet produce different interval widths. We introduce PID-Expert, an online aggregation method for improving the efficiency of conformal prediction intervals for time series. PID-Expert combines thresholds from a fixed library of PID calibrators, each evolving under its own coverage feedback. Aggregation weights depend on normalized interval width and miscoverage, while a shared multiplier adapts the miscoverage penalty using feedback from the reported interval. We establish local regret bounds for weighted expert losses under the realized multiplier sequence and, separately, a pathwise upper bound on time-averaged aggregate miscoverage, with control in expectation and almost surely under a stability condition. Across four simulation settings and two real-data applications, PID-Expert produces narrower mean intervals than a prespecified Conformal PID benchmark while keeping overall empirical coverage close to the nominal level. Compared with expert selection and equal averaging, aggregation generally provides a more balanced coverage–width trade-off across forecasting settings. Rolling analyses further reveal local coverage–efficiency trade-offs, particularly following abrupt distributional shifts. Overall, PID-Expert reduces reliance on a single PID configuration while improving interval efficiency.

We develop a method for lossy compression of incompressible (i.e., divergence-free) velocity fields that preserves zero divergence and, on periodic domains, periodicity. We fit the nodal velocities with property-preserving matrix-valued kernels and compress their coefficients using standard lossy compressors. Every decompressed coefficient vector defines a field with the same constraints, independently of the compression tolerance. We present several fitting schemes designed around either low-rank representation of or sparsity in the interpolation matrix. More specifically, we show results for global Matérn interpolation, a two-level Nyström approximation, Nyström–Wendland residual interpolation, multilevel Wendland interpolation and a property-preserving (redundant) kernel frame. We derive nodal error bounds that relate the compressor tolerance to the additional velocity error. Experiments with four compressors on cavity, Taylor–Green, and species-transport flows verify the bounds under their coefficient-error assumptions and compare storage at matched velocity accuracy. The low-rank methods give compact representations when they resolve the velocity field sufficiently accurately; residual, multilevel, and frame interpolation extend the attainable accuracy when they do not. We also measure changes in turbulent velocity statistics. The resulting representations support an accuracy–compression tradeoff while preserving incompressibility and periodicity analytically.

Mental health stigma has profoundly harmful impacts but its complexity makes it difficult to evaluate. Stigma may involve explicit derogation, but also subtler forms of blame, fear, paternalistic pity, social distancing, structural exclusion, and discrimination. We introduce a theory-grounded benchmark for automatic evaluation of mental health stigma in online communication, consisting of naturally occurring online news and social media text annotated with a fine-grained taxonomy of stigma across multiple mental health conditions. Our annotation framework comprises a binary stigma-detection task and a multi-level taxonomy covering (i) stigma mode, (ii) domain, and (iii) specific components of certain forms of stigma. We apply this framework to texts mentioning six mental health conditions and evaluate large language models alongside stigma-related classifiers for detecting sentiment, toxicity, and hate speech. Results show that mental health stigma is not well captured by models trained to detect these neighboring constructs, and that LLMs often overpredict stigma unless given explicit operational rules - mirroring the importance of decision rules in human annotation. We release the publicly available part of benchmark, annotations, prototypical exemplars of stigma and code at: https://github.com/jemimakang/mh_stigma.

Long-form generators for music, motion and video produce sequences chunk by chunk, with each chunk generated by iterative denoising while rewards are defined over the full sequence. Existing inference-time steering methods typically act on one axis at a time: best-of-N at the end, Feynman-Kac steering across denoising steps, or streaming pruning across chunks, and are often compared under unmatched compute or different return rules. We introduce budget-matched chunked steering and propose LatticeSMC, a sampler derived from a Feynman-Kac model on the two-dimensional lattice of chunk index and denoising step. Two telescoping results make its design exact: for chunk-additive rewards, the two axes induce identical weights, so resampling should occur where lookahead is cheapest; for terminal rewards, any prefix score defines an exact intermediate potential, making prefix-evaluable rewards twists with no estimation or extra denoiser calls. LatticeSMC resamples on these potentials at chunk boundaries and, when scoring is free, within chunks, returning either a weighted draw or the best particle. Under matched compute, on music-to-dance diffusion and 40-second text-to-music generation, it raises beat alignment from 0.234 to 0.441 (best-of-N: 0.354) and prompt adherence from 0.470 to 0.560 at 32 particles, while preserving held-out quality. It also retains its advantage on long-range rewards and is preferred by human raters in 60-77 percent of pairwise comparisons. Finally, we show that commitment strength should follow the information in the current potential, while the value of lookahead is predicted by the within-set predictability of future reward.

The space of $n\times n$ density matrices is the full state space of an $n$-level quantum system. While it has been asserted in the literature on quantum information theory that decomposing this state space into equirank pieces yields a Whitney stratification, rigorous proofs have remained absent. Using methods from invariant theory, this work provides a proof that the rank decomposition of the matrix algebra constitutes a (b)-regular stratification in the sense of Whitney. Furthermore, we demonstrate how the Uhlmann connection - which describes the adiabatic holonomy of mixed states and reduces to the Berry connection on pure states - can be geometrically treated as a stratified connection on a stratified vector bundle. Finally, our appendix provides a self-contained exposition of stratified fiber bundles and the new concept of stratified connections, which may be of independent interest.

Large language models (LLMs) increasingly serve as general-purpose interfaces to factual knowledge, but their parameters do not automatically reflect information that changes after pretraining. Knowledge editing (KE) provides a targeted alternative to costly retraining by modifying selected knowledge and preserving unrelated knowledge and general capabilities. Conventional KE uses structured factual triples, whereas unstructured KE (UKE) uses free-form passages containing multiple facts. Nonetheless, existing UKE editors exhibit a failure mode known as context reliance: edited LLMs can often reproduce the editing passage but fail to reliably recall its individual facts without the original passage context. We identify context-induced difficulty underestimation under the standard passage-level editing objective: later facts receive increasingly rich ground-truth context and consequently incur lower initial losses, making them appear easier to learn. In response, we propose FOVEATED, a plug-and-play framework that constructs focused views of each sentence by randomly shifting the Rotary Position Embedding (RoPE) positions assigned to the keys of its preceding context. The perturbation is applied during editing and removed afterward, leaving the model's native positional encoding unchanged at inference time. We instantiate FOVEATED for both direct-optimization and locate-then-edit editors. We theoretically analyze how FOVEATED counteracts context-induced difficulty underestimation and empirically demonstrate consistent improvements across five KE editors, two LLM backbones, and three benchmarks.

We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set, and receives only a single bit indicating whether the sampled reward belongs to that set. We consider a distribution-free finite-variance setting with arm-wise localization, where direct empirical mean estimation is no longer available and clipping becomes unavoidable. We first formulate a time-uniform 1-bit mean-estimation primitive based on randomized threshold queries and a clipped tail-integral identity. We then embed this primitive into candidate-challenger best-arm identification algorithms. A fixed-clipping algorithm gives a simple anytime $(\epsilon,\delta)$-PAC guarantee, while a phased adaptive-clipping algorithm matches the clipping level to the current resolution and yields a gap-adaptive sample complexity. We also prove a $K$-arm worst-case information-theoretic lower bound showing that the logarithmic penalty caused by finite-variance 1-bit feedback is intrinsic. This bound matches the leading dependence of the phased algorithm up to lower-order $\log\log$ factors.

Document databases such as MongoDB are core infrastructure for modern applications, and natural-language interfaces to them—text-to-MQL—would let non-experts query complex, semi-structured data without mastering the query language. Progress on this task depends on high-quality benchmarks, which are most practically obtained by converting an existing text-to-SQL benchmark to the document setting. Unfortunately, existing efforts rely on heuristics for mechanical conversion: the document schema mirrors the relational foreign-key graph, and each query mirrors its source SQL. As a result in our experiments, these approaches fail to migrate 6 of 21 BIRD databases outright, silently drop up to 25.9% of rows on others, and yield schemas whose ground-truth queries run over an order of magnitude slower as the data scales. We instead propose a conversion pipeline, driven by coding agents with human-in-the-loop verification, that designs each document schema from expected access patterns and rewrites queries to be MongoDB-native. Applying it to BIRD, we build an access-pattern-based text-to-MQL benchmark (AptMQL-Bench). It includes 21 document-oriented databases, 3,186 natural-language requests, and their associated MQL queries—whose databases are migrated from SQLite without data loss and scale efficiently. The strongest model, Claude Opus 4.5, achieves only 57.38% accuracy without external knowledge evidence and 70.34% with it. This indicates that realistic text-to-MQL generation remains challenging.

Language agents should draw on prior attempts and environmental feedback to improve subsequent decisions within the same task. However, providing additional interaction history can sometimes reduce task success, suggesting that agents do not consistently use this information effectively. To investigate this limitation, we examine how agents use history. We find that history improves task completion overall, yet much of this benefit persists even when past actions are shuffled. Disrupting the correspondence between actions and observations causes only a modest decline in task success. We therefore hypothesize that agents do not reliably connect past actions with their outcomes when deciding how to proceed. To test this hypothesis, we explicitly label each returned observation as the outcome of the preceding action. This simple annotation improves task success and reduces next-action repetition without introducing new environmental information. Building on this insight, we introduce a learned calibrator that explicitly reassesses past actions and selectively records experience to guide subsequent decisions, improving task success beyond outcome labeling alone.

Multimodal graph learning has recently emerged as an effective paradigm for in corporating inter-entity relationships into multimodal representations. Existing studies have made substantial progress on how to construct and optimize graphs, but rarely consider a more fundamental question: whether additional relational structures should be introduced for a given dataset and task. Through empirical studies across diverse datasets, tasks, and graph constructors, we reveal that graphification is not consistently beneficial: introducing relational structures can provide substantial improvements in some cases, while offering limited or even negative gains. This observation motivates a new perspective that graph construction should be treated as a selective decision based on its expected utility rather than a default preprocessing step. To address this issue, we propose MAG-SCOUT, a pre-construction graph assessment framework that estimates whether introducing graph structures is beneficial before generating the complete topology. MAG-SCOUT collects limited relational evidence, analyzes its potential taskspecific contribution, and estimates the expected utility of graphification together with construction cost to make a build-or-skip decision. Extensive experiments across six multimodal datasets, three downstream tasks, and diverse graph constructors demonstrate that MAG-SCOUT effectively identifies when graph structures should be introduced, saving 33.1% of task-macro graph work while retaining 96.7% of held-out positive-gain mass under the pre-registered floor.