Papers

Large language models (LLMs) excel at structured, verifiable tasks, but their low-entropy bias can produce homogeneous and predictable outputs, limiting their utility for open-ended scientific ideation. Effective discovery, however, spans a broader creative spectrum: from structured day science to loosely structured, serendipitous night science that reaches ideas beyond those typically considered. We introduce AI Night-Scientist, an agentic framework that uses reinforcement learning to teach models when and how to depart from predictable reasoning. Grounded in cognitive science, we model creativity along three axes: action (what to do and how creatively), process (when to explore versus exploit), and outcome (the novelty and usefulness of the resulting idea). We use these axes to train models with GRPO, exposing them to varying degrees and forms of creativity throughout training. This produces substantially more diverse scientific proposals, expanding the range of research directions by 27.8% and contribution types by 14.9% over the base model. It also improves predicted citation impact by up to 32.0 percentage points and originality by 66.2 points. These gains cannot be reproduced by simply increasing decoding temperature; instead, we find that semantic guidance specifying what kind of creativity to pursue is critical. Overall, our results suggest that creativity is a learnable, multi-level ability that can be shaped to help researchers reach ideas beyond those typically explored by LLMs.

An infalling two-point function of a scalar field in a three-dimensional BTZ black hole, with one operator inserted in the exterior and the other inserted along a timelike geodesic, diverges when the infalling insertion point reaches the black hole singularity. In the boundary description, this divergence is tied to the exchange of double-twist operators rather than to the multi-stress-tensor sector that encodes curvature singularities in higher dimensions. We show that the inclusion of a tower of massive particles with Hagedorn growth gives rise to loop corrections that become important near the singularity, where they trigger a Hagedorn transition that renders the tree-level divergence untrustworthy. In the boundary theory, the corresponding tower of primary operators leads to a breakdown of the generalized free field description of the probe operator in the black hole state. In a large black hole, these corrections become important only near the singularity and remain exponentially suppressed at the horizon. The region where these corrections dominate is therefore parametrically separated from the horizon, as anticipated by the principle of black hole complementarity.

Video generation must account for two sources of motion, one induced by the observer's camera path and the other caused by scene dynamics. An ideal camera-controlled video model should account for both motions: let users move the camera while evolving the scene dynamics. While current models handle camera-induced motion well in static settings, they struggle for dynamic scenes: objects are static, move incorrectly, or degrade in generation quality. We introduce DynaTokens, a lightweight set of learnable scene-specific tokens that teach dynamics to an existing camera-controlled world model. Our method is motivated by a simple asymmetry between the two sources of motion: whereas camera motion affects the generated view globally, object dynamics are spatially localized. Through cross-attention, DynaTokens trains the learnable tokens from a few example trajectories for a scene while keeping the base model frozen, and enables dynamics under new query camera paths. DynaTokens achieves a better simultaneous dynamics-camera tradeoff on VBench2 and WorldScore evaluations than LoRA, block finetuning, and specialized trainable-layer baselines. Analyses of token attention, ablations, and motion temporality suggest that matching the trainable interface to the structure of the learning target is important for effective adaptation. Project website: https://glab-caltech.github.io/dynatokens/

Reliable deployment of graph neural networks requires calibration, out-of-distribution (OOD) detection, and robustness to distribution shift, yet existing methods address these needs with separate models and objectives. We model uncertain node embeddings as random graph signals: graph Fourier filters capture structural variation, and a scalar orthogonal-polynomial chaos coordinate captures latent stochastic variation. The resulting doubly-spectral stochastic (DSS) expansion supplies task-matched readouts from one representation: the mean coefficient encodes class evidence for the energy-based OOD score, the higher-order coefficients encode structured logit variation, and quadrature averaging over the chaos coordinate defines the single predictive distribution used for prediction and calibration. A capacity theorem shows that, under a full-rank feature assumption, a restricted subfamily matches the chaos coefficients of any Gaussian-latent random graph signal, with exponentially decaying truncation error under a growth condition; the task-level claims are established empirically. DSS-GNN has two deployment modes: standalone, or as a residual branch beside a deterministic encoder (DSS-Hybrid). Standalone DSS-GNN achieves the lowest Brier score among the compared uncertainty-aware baselines on all 14 node classification benchmarks without post-hoc correction; DSS-Hybrid achieves the best AUROC on most node-OOD settings, competitive cross-graph OOD detection, and the strongest shifted accuracy on all 7 GOOD concept-shift benchmarks under standard empirical risk minimization (ERM). Cross-evaluating both modes on all three tasks shows that each remains effective on the other's tasks, with documented exceptions, and yields explicit deployment guidance.

Vanadium color centers in silicon carbide (SiC) offer telecom O-band emission, sub-microsecond optical lifetimes, and second-scale spin relaxation times, rendering them promising candidates for quantum network nodes. However, efficient photon extraction from the high-refractive-index SiC host remains challenging. Here, we introduce a silicon-on-SiC heterogeneous photonic platform in which silicon nanocavities evanescently couple to shallow vanadium dopants in commercial 4H-SiC, enabling efficient zero-phonon line (ZPL) collection under resonant excitation. In as-grown ensembles, we observe Purcell-enhanced photoluminescence with transient spectral hole burning linewidths of 50 MHz on microsecond timescales. In dilute implanted samples, we isolate individual vanadium centers with high-purity single photon emission and a Purcell-enhanced lifetime of 109 ns. The entire optical interface operates through a single lensed fiber, including a 905 nm repump laser that recovers the vanadium charge state with 95% efficiency. These results establish Si-on-SiC as a scalable, foundry-compatible platform for telecom-wavelength spin-photon interfaces.

The success of large language models (LLMs) has been accompanied by continued growth in model size and pretraining costs. Muon offers high accuracy and training efficiency in LLM pretraining. Recent work introduces row-wise normalization into Muon to balance update magnitudes and improve pretraining performance. However, row-wise normalization alone cannot accommodate different imbalance patterns in update matrices. In this paper, we propose an improved Muon optimizer, called \underline{m}atrix-\underline{eq}uilibrating Muon~(MeqMuon), for LLM pretraining. MeqMuon balances both row and column magnitudes through normalization that can be automatically tailored to different imbalance patterns without manual intervention. Moreover, MeqMuon eliminates the need to store AdamW's second-moment estimates, reducing optimizer-state memory usage. Empirical results demonstrate that MeqMuon achieves better convergence performance than AdamW, Muon, and other baselines in LLM pretraining.

We propose a hierarchical control framework to address severe dynamic instabilities and navigational drift that arise when a two-wheeled inverted pendulum (TWIP) robot attempts asymmetric object manipulation. While two-wheeled platforms are highly manoeuvrable, their constant balancing adjustments make onboard odometry highly unreliable for precise navigation. Furthermore, the addition of a side-mounted robotic arm introduces unactuated lateral roll moments when a payload is lifted, a challenge heavily compounded on uneven terrain. To solve these coupled problems, our architecture divides the workload. An offboard vision system tracks overhead ArUco markers to provide high-latency global waypoint navigation, bypassing odometry drift. Simultaneously, a low-latency onboard control loop rejects active physical disturbances using inertial and encoder data. In our physical experiments, this dual-loop approach enabled the custom-built robot to navigate accurately, reject transient impacts from speed bumps, adapt to a dynamic seesaw ramp, and carry a payload securely without falling over its narrow wheelbase.

Distillation attacks copy the reasoning capabilities of closed-source large language models, allowing bad actors to replicate state-of-the-art performance at low cost. Attackers systematically collect a large volume of frontier model reasoning traces and then train (i.e., "distill") their own models on these traces. Existing defenses against distillation attacks are typically evaluated immediately after distillation, implicitly assuming attackers do not train their models any further. In this paper, we argue that a more realistic threat model includes further training with reinforcement learning after distillation. A misspecified threat model can give a false sense of security – some defenses that seem effective after distillation can be broken after subsequent reinforcement learning. Practically, reinforcement learning lowers the bar for a distillation attack to be effective. We show that simple attacks can steal reasoning capabilities from existing closed-source language models using data easily obtainable from current APIs, yielding reasoning improvements equivalent to more sophisticated attacks that extract the full hidden traces. Results indicate that any distillation defense that leaks sufficient information to reconstruct approximate reasoning traces is likely ineffective. We conclude by discussing broader implications and batch-level distillation defenses which could be more effective.

We study adversarial imitation learning (AIL), in which an agent learns to imitate expert demonstrations by optimizing a policy against an adversarial reward that distinguishes expert and learner behavior. Historically, reward regularization and entropy-based policy regularization are key components of empirically successful methods such as GAIL and LS-IQ, yet their finite-sample benefits remain underexplored. We establish fast rates for jointly regularized AIL in finite-horizon Markov decision processes with general function approximation. Our model-free algorithm, Dually Regularized AIL, combines KL policy regularization with a quadratic reward penalty weighted by expert and learner occupancies. With K online episodes and N expert trajectories, we prove a $\widetilde{O}\left(\frac{1}{K}+\frac{1}{N}\right)$ bound on the regularized imitation gap for fixed regularization parameters. Our analysis combines an online mirror descent construction for general convex reward classes to control estimation error from finite expert data and stochastic learner feedback, with a sharp analysis of optimistic KL-regularized policy learning. To the best of our knowledge, Dually Regularized AIL is the first algorithm to simultaneously achieve $\widetilde{O}\left(\frac{1}{\epsilon}\right)$ sample complexity in both expert demonstrations and online interactions for this regularized AIL objective, even with stochastic experts. These results provide a rigorous characterization of the complementary statistical benefits of reward and policy regularization in AIL.

Recent observations have challenged the duration-based classification of gamma-ray bursts (GRBs), making the detection of an associated supernova (SN) or kilonova crucial for conclusively identifying their progenitors. We investigate the origin of GRB 240825A at $z=0.659$, whose prompt emission gave conflicting indications of a merger or collapsar origin and for which no SN was detected in deep ground-based observations. We analyze JWST/NIRSpec observations obtained 66.5 days (40.1 days in the rest frame) after the burst. We identify a SN signal using a pixel-by-pixel decomposition of the 2D spectrum and isolate it by jointly modeling the host and transient emission. We constrain the line of sight extinction from the afterglow spectral energy distribution and characterize the host through broadband photometry and nebular emission lines. Despite a dusty line of sight ($A_V=1.37\pm0.08$ mag), with tentative evidence of a 2175 Å bump, and a bright host galaxy ($M_B=-20.5$ AB mag), we identify a point-like source at the GRB position with broad spectral features similar to those of SN 1998bw. The SN contributes $\sim$10-15% of the NIRSpec flux and would contribute only $\sim$1% of the total flux in a ground-based optical image at the same epoch. Its extinction-corrected luminosity is comparable to SN 1998bw, although it remains sensitive to the host subtraction and template assumptions. The host is an extended, dusty, star-forming galaxy with $\log(M_\star/M_\odot)=10.12\pm0.05$, SFR $=5.88\pm1.60\,{\rm M_\odot\,yr^{-1}}$, and a super-solar metallicity of $12+\log({\rm O/H})=8.87\pm0.04$, above the metallicity typically observed for collapsar GRB hosts. The detection of a dust-obscured SN firmly establishes the massive-star origin of GRB 240825A and shows that JWST can uncover SNe in dusty, chemically enriched environments that were previously largely inaccessible.

A mobile impurity particle immersed in a quantum degenerate gas leads to the formation of a quasiparticle, which can serve as a sensor for its environment. Here, we develop a unified wave function description of an impurity in a two-dimensional Bose-Hubbard model across the Mott-insulator to superfluid transition. Using a multi-mode variational ansatz based on the quantum Gutzwiller approach, we show that the impurity can form several kinds of polaronic and molecular states. In addition to their spectral properties, the wave function provides direct access to the microscopic structure of these states, and we demonstrate that strong correlations in the critical regime of the quantum phase transition give rise to several non-analytic features in the polaron properties. Increasing the impurity-boson interaction leads to transitions between polaron and molecular ground states, and the number of bosons in the impurity dressing cloud grows rapidly at the quantum critical point as the bath modes soften. We furthermore reveal qualitatively distinct non-equilibrium many-body dynamics after the injection of the impurity in the different phases of the Bose-Hubbard model. Our spectral, real space, and dynamical predictions describe complementary properties of polarons in a strongly correlated bosonic bath, which can be observed using current techniques with atoms in optical lattices.

Aligning large language models (LLMs) to diverse user preferences is fundamentally hindered by standard alignment paradigms that optimize for monolithic users. In this work, empirical studies are first used to reveal the existence of a massive, untapped performance headroom for personalized generation through test-time alignment. We demonstrate that personalized generation is uniquely suited for test-time scaling methods like Best-of-N (BoN) because it can be viewed primarily as a candidate matching problem rather than a generator capability bottleneck. While reward models could in principle exploit this headroom, they are poorly calibrated for personalization, and their billion-parameter scale makes scoring large candidate pools prohibitively expensive. To overcome this limitation, we propose a parameter-efficient framework utilizing million-parameter scale multi-layer perceptron (MLP) ranking models. Our personalized ranking model directly reuses the internal embeddings of the base generator with minimal overhead. By scaling train-time data to provide fine-grained personalized preferences, this million-parameter ranking model accurately scores large candidate pools and can seamlessly guide generation to reduce the cost of materializing N candidates. Extensive experiments on nine datasets spanning three personalized generation settings show that our personalized ranking model effectively exploits the discovered headroom, outperforming billion-parameter generalist reward models on every dataset, with under 0.4% of their parameters and four orders of magnitude lower scoring latency.

We introduce the Continuous Embedding Diffusion Reasoner (CEDR), a training and inference pipeline for continuous latent diffusion models that achieves strong performance on mathematical reasoning and code generation. We learn compact answer representations from three hidden layers of the autoregressive Qwen3-4B model. A staged curriculum first trains the ELF-based diffusion backbone with teacher prompt conditioning, then initializes a compact prompt encoder through imitation and jointly adapts both networks. This replaces the large teacher contextual prompt encoder at inference with a compact learned Transformer. The multilayer answer representation also enables asynchronous inference, with different components denoised under separate clocks. We further adapt DiffusionNFT to learned self-conditioning guidance, enabling reinforcement learning with verifiable rewards. Controlled ablations evaluate the effects of representation design, prompt training, and denoising schedules. CEDR outperforms recent continuous-diffusion baselines at comparable backbone scales, including before reinforcement learning. With a 638M-parameter denoising backbone and DMD2-style stochastic sampling, post-NFT CEDR-L achieves {pass@1, pass@8} accuracies of {68.97%, 80.82%} on GSM8K and {32.40%, 53.80%} on MATH500 at 64 denoising steps per sample, and {37.56%, 51.00%} on HumanEval+ and {26.96%, 39.92%} on MBPP+ at 128 steps per sample. Code and model weights are available at https://github.com/chengxiang/CEDR and https://huggingface.co/xc91/CEDR, respectively.

This paper gives two parallel algorithms for $\Delta+1$ edge coloring, where $\Delta$ denotes the maximum degree of any vertex. The first is a deterministic parallel algorithm with $\tilde{O}(\Delta^3)$ span and $\tilde{O}(m \Delta^3)$ work. Our second algorithm and our main result is a more efficient randomized algorithm, achieving $\tilde{O}(\Delta^2)$ span and $\tilde{O}(m \Delta^2 )$ work both with high probability. These bounds substantially improve over the recent deterministic parallel algorithm of Elkin and Khuzman, which has $\tilde{O}(\Delta^4)$ span and $\tilde{O}(m \Delta^5)$ work. Our deterministic algorithm thus represents a $\tilde{O}(\Delta)$ improvement on span and $\tilde{O}(\Delta^2)$ on work compared to their algorithm, and our randomized algorithm improves the span and work by $\tilde{O}(\Delta^2)$ and $\tilde{O}(\Delta^3)$ factors, respectively. Moreover, our improvements do not come at the expense of larger logarithmic factors.

Users of Workday's deployed LLM-based agents often request features which can be addressed by defining named procedures, also known as skills, in the LLM context, effectively augmenting agents' capabilities. However, as an agent's skills library grows in size, so does the agent's operational cost. Progressive disclosure (lazy-loading) of skills as needed may reduce operational costs, but its impact on overall latency and skill-retrieval quality remains unclear. In this report, we investigate the impact empirically and find that progressive disclosure improves skill-retrieval quality but marginally degrades overall latency.

Lax extensions (also called relators or relation liftings) are a categorical notion to reason about functors acting on functions and relations in a compatible way. They play a central role to develop sound proof principles for behavioral equivalence of state-based systems and are also important for establishing contextual equivalence for effectful programs. In this paper, we develop the theory of lax extensions for parametrized functors and monads and consider notions of behavioral preorders, equivalence relations or metrics which can now be modulated by additional parameters. From an operational viewpoint, we replace standard contextual equivalence where we quantify over all possible contexts by a refined notion of equivalence where the user can regulate the allowed contexts via chosen parameters.

Robots that learn from a few demonstrations often require two forms of generalization. Compositional generalization recombines skills to solve new tasks, and skill generalization lets the learned policy behind each skill work in new situations. The two depend on each other, yet information is lost between composition and the skills it calls. Where a skill works is determined by the structure its policy is trained with, while composition sees the skill only through a separate description, such as a name, an instruction, or a symbolic operator, that omits this structure. Our key idea is to use each policy's structural prior as part of the interface between composition and the skill. A structural prior states what a behavior depends on, for example that a grasp depends only on the gripper's pose relative to the object. Built into training, it shapes where the policy generalizes; stated in language, it tells composition where the policy applies. We instantiate this idea in Agent Priors-guided Policy Learning (APPL). A construction agent segments complete demonstrations into reusable skills, proposes several structural priors for each skill, and trains and verifies one policy per prior. A runtime agent then selects among these prior-specific policies and composes them toward new task goals using their interfaces. Across MetaWorld and long-horizon ManiSkill tasks, APPL improves out-of-distribution skill generalization and enables previously unseen skill compositions; ablating the interface information substantially reduces performance. These results support the use of training-time structural assumptions as a bridge between skill learning and skill composition.

For $n\ge5$, let $F\colon\mathbb{F}_2^n\to \mathbb{F}_2^n$ be almost perfect nonlinear and write $N=2^n$. It is proven that the linearity $\mathcal{L}(F)$ of $F$, i.e., the largest absolute Walsh coefficient of a nonzero component, is at most $N-6$. If $n$ is even, it is further proven that $\mathcal{L}(F)\le N-\sqrt N/4-2$. These bounds improve the general upper bound of $N-4$ in odd dimension and $N-6$ in even dimensions $n \geq 10$. It is further proven that, for each fixed $k$, the $k$-th largest absolute Walsh coefficient among nonzero components, counted with multiplicity, is at most $(1+O_k(2^{-n}))N/\sqrt{k}$ as $n\to\infty$. The second and fourth largest coefficients are at most $2\lfloor N/3\rfloor$ and $N/2$, respectively. Finally, a bound on the linearity in terms of the number $q$ of nonplateaued nonzero components is derived. In odd dimension, for $q>0$, we have $\mathcal{L}(F)^2\le N(1+\sqrt{q(N-1)})$, so that $\mathcal{L}(F)/N\to1$ implies $q/N\to1$. In even dimension, for every $1/2\le C<1$, the condition $q\le(4C-C^2-1)N/4+1$ implies $\mathcal{L}(F)\le CN$. In particular, $q\le3N/16+2$ implies $\mathcal{L}(F)\le N/2$.

We study BPS states in the D1–D5 CFT through their fortuity, cycle structure, and probe response. Explicit fortuitous states with both long- and short-string geometries show that the cycle partition does not determine fortuity state by state. At large $N$, fixed-charge counting nevertheless selects a long string. In the open uncondensed region, an entropy-carrying exact non-graviton subspace concentrates on one cycle of winding $N-O(1)$. Assuming subexponential monotone dimension, the same holds for the harmonic fortuitous complement. Beyond the critical line, the free ensemble develops a short-string condensate. To test how this cycle structure appears in observables, we study finite-winding probes. The long-cycle scalar correlator approaches the extremal-BTZ response at fixed time, while finite winding is resolved at \(t=O(\sqrt N)\), the exact circle recurs at \(t=O(N)\), and states with the same cycle geometry remain distinguishable by their spectral weights.

We propose a unified perspective on classical and quantum chaos based on the sensitivity of a system's stationary states to slow driving. We probe this sensitivity via the system's susceptibility to the average protocol speed, which we call the “speed-Fisher information," and relate it to irreversible entropy production in the system. We show that chaotic dynamics manifests as a divergence of the speed-Fisher information with the protocol time, and that this response is controlled by the perturbation's low-frequency spectral weight. This approach to chaos applies to both classical and quantum Hamiltonian systems, and naturally extends to non-Hamiltonian classical flows. Additionally, we identify a quantum regime at times shorter than the Planckian timescale, in which the speed-Fisher information exhibits a uniquely quantum scaling. We illustrate this framework with simple classical and quantum examples

Mechanistic interpretability (MI) aims to explain a model's behaviour through analyzing its internal computations; circuit-based explanations aim to isolate these computations with compact subnetworks validated by ablating the rest of the model. We show that circuits validated this way may fail to recover the underlying mechanism of the model's behaviour by closely reproducing its successful decisions while failing to account for most of its errors. Such explanations should account for the model's particular errors as well as its successes. We evaluate this requirement by measuring exact answer agreement separately on model successes and failures, across circuit sizes and ablation settings, on IOI, Docstring, and six model-task settings from the Mechanistic Interpretability Benchmark. We discover that many tested circuits closely replicate correct behaviour while missing most of the model's errors. On indirect object identification (IOI) for GPT-2 small, under mean ablation, the manual circuit and tested automated circuits, including one trained against the model's full output distribution, agree with the model on 97.3-99.5% of prompts it answers correctly but only 11.4-41.7% of errors. An IOI case study shows that lost errors are recoverable by restoring omitted attention-heads which raise error reproduction from 14.2% to 75.1% on a separate held-out set with 0.41 percentage point decrease on correct agreement, exceeding matched random extensions and scalar-biased control. Intervention traces show how omitted computations produce specific wrong answers for a reproducible subset of errors. In all, these findings show circuits can preserve task success without adequately explaining model's failures, and support exact error reproduction as a necessary, but not sufficient, test of circuit-based explanations of model behaviour.

Structured span annotations, such as quantities with their units, uncertainty modifiers, and event classes, are expensive to create and hard to keep trustworthy once language models enter the loop. We present QuanReview, an open-source system for auditing and correcting such annotation layers. QuanReview aligns two annotation streams over the same documents at character level, resolves unambiguous cases by an explicit and logged policy, and routes candidate conflicts to a browser-based adjudication interface where reviewers accept either side, build field-level hybrids, or flag items for re-annotation. A campaign manager assigns documents to multiple annotators with configurable redundancy, computes agreement at document and span level, auto-merges unanimous documents, and exports the corrected layer in the original file format, so that it can replace the original annotation files directly. Applied to a 4,457-record humanitarian benchmark and an LLM extraction stream, the system fully auto-merged 8% of documents, applied automatic policy decisions to a further 1,513 records, and concentrated human attention on 3,131 candidate conflicts, a mean of 5.4 per reviewed document.

With the recent advancements of neural compressors, explicitly incorporating perception constraints into the design of compression schemes has gained significant attention. Traditionally, these perception constraints ensure that the distribution of the reconstruction does not significantly deviate from the distribution of the source, thus attesting to the perceptual quality of the reconstruction. In this work, we uncover several perception constraints that are naturally present in task-aware compression. In particular, we consider a problem where the primary task is reconstruction and the secondary task is classification (i.e., a statistical test). We study this problem at varying levels of domain information available to us and discuss how to utilize the naturally emerging perception constraints to design rate-minimal compression schemes that also maximize the utility of our secondary task. We show that in this setting, if the decision boundaries of the classifier are ill-defined (mismatch) for our source distribution, then matching onto a target distribution enhances our classification accuracy.

In this paper we study the orbits of the automorphism group on a toroidal spherical variety. In the affine case, we prove that two points lie in the same orbit of the identity component if and only if the kernels of the homomorphisms from the divisor class group to their local divisor class groups coincide. These kernels are described in terms of $B$-stable prime divisors. For a smooth complete toroidal spherical variety, we obtain a similar criterion using the monoids generated by the classes of $B$-stable prime divisors that do not contain a given $G$-orbit.

In this paper we contribute to the study of compactness properties for algebraic structures. We prove two compactness theorems in the context of almost projective modules from $\lambda$-strongly compact and weakly compact, respectively.

We introduce power variations of critical Gaussian multiplicative chaos (GMC) along refining partitions in arbitrary dimension. Under suitable renormalisation, we prove uniform fractional moment bounds via Laplace transform estimates as well as stable convergence to supercritical GMCs. Together, these results provide a unified approach to regularity and spectral questions for critical chaos, yielding: (i) the sharp exponent for the logarithmic modulus of continuity, (ii) the existence of non-empty essential spectrum for critical Liouville quantum gravity surfaces; and (iii) an almost-sure quantitative Fourier decay.

Objectives: There has been increased appreciation of the differences between marginal and conditional estimates and different types of effect measures regarding their applicability to different target populations. This issue of transportability is of concern in model-based cost-effectiveness analysis (CEA) when treatment effects from (international) trials are applied to (country-specific) baseline risk estimates. The objective of this paper is to create awareness regarding the issues that arise when using different types of treatment effect and baseline risk estimates in a model-based CEA to inform health technology assessment (HTA). Methods: We clarify collapsibility, marginal versus conditional estimation, and transportability; derive the ideal modeling approach implied by a marginal cost-effectiveness estimand; and characterize the issues of common modeling approaches, illustrated with a fictitious state-transition model. Results: An individual-level simulation that predicts outcomes from conditional inputs and averages them over the target population targets the marginal cost-effectiveness estimand. Cohort-model approaches that marginalize inputs early, use conditional inputs at mean covariate values, or combine a conditional effect with a marginal baseline (or vice versa) can misstate cost-effectiveness results even with correct-population inputs; inputs from the wrong population add further error. Conclusions: The most rigorous approach is an individual-level simulation that carries conditional inputs (baseline risk, treatment effect, prognostic effects and effect modifiers) and marginalizes late. Cohort approaches instead marginalize early, relying on aggregated inputs, and do not necessarily target the marginal cost-effectiveness estimand of interest for HTA. Model developers should document, for each input, whether it is marginal or conditional and its population.

We study numerical time integration for the motion of a charged particle in a strong magnetic field, focusing on the regime in which the fast gyration is not resolved by the time step. Standard Boris-type methods are structure preserving and accurate when the gyration is resolved, but their error constants deteriorate with increasing field strength; filtered Boris methods improve this behavior but may suffer from singularities and resonance-induced error blow-up. In this work we consider the case of a constant strong magnetic field and derive a broad family of one-step exponential integrators from the variation-of-constants formula, formulated in terms of matrix-valued filter functions. This framework includes existing filtered Boris variants and permits the construction of schemes with uniformly bounded filters. Using a discrete variation-of-constants representation together with summation-by-parts arguments, we establish error bounds whose constants are independent of the magnetic field strength and characterize the filter conditions required for first- and second-order accuracy. In particular, we show that bounded filters avoid resonance blow-up and allow arbitrary time steps, at the cost of a controlled order reduction near resonant frequencies. Numerical experiments confirm the predicted convergence behavior, the different accuracy of position and velocity components, and the role of the leading error terms across a wide range of step-size-field-strength products.

In this paper, we complete the computation of the global log canonical thresholds of Burniat surfaces. Additionally, we determine the global log canonical thresholds for certain infinite families of surfaces of general type, constructed as $ \mathbb{Z}_2^n $-covers of $\mathbb{P}^2$ or $\mathbb{P}^1 \times \mathbb{P}^1$.

In reinforcement learning with verifiable rewards (RLVR), imperfect verifiers can reward incorrect responses, creating opportunities for reward hacking. Using gradient flow with a fixed verifier, we characterize the conditions under which reward rises while correctness falls. We then show that the observations available during RLVR are, in general, insufficient to detect or identify accepted errors, or to guarantee their reduction without sacrificing correct responses. To address this limit, we construct a correction using additional feedback about correctness from audits. This correction achieves selective control: at the current policy, it lowers the probability of accepted errors and raises that of correct responses, provided it outweighs the pressure toward errors from verifier reward. Experiments with log linear and neural contextual bandits and with a language model support the analysis and show that selective control under partial auditing reduces accepted errors while increasing correctness.