Papers

We extend Burnside's $p^a$-Theorem on conjugacy classes of prime-power size by proving that no non-abelian finite simple group possesses a conjugacy class of size $2p^n$ for any prime $p$ and $n\geq 0$. Based on this, we partially extend a well-known result of L. Kazarin by showing that, given a finite group $G$, the subgroup generated by a conjugacy class $x^G$ of size $2p^n$ where $x$ has odd order, is a solvable normal subgroup of $G$. If instead the subgroup $\langle x^G \rangle$ generated by such a class $x^G$ is non-solvable (which forces $x$ to have even order), then $p= 5$ and $\langle x^G \rangle/S(\langle x^G \rangle)$ is isomorphic to the symmetric group $S_5$, where $S(\langle x^G \rangle)$ denotes the solvable radical of $\langle x^G \rangle$.

Supervised fine tuning (SFT) is commonly monitored through training and evaluation loss, but loss does not fully characterize how model functionality evolves along the same trajectory. We study this gap through dialect adaptation of Qwen3-ASR, MiMo-Audio, and FireRed-LLM across learning rates from $10^{-5}$ to $10^{-3}$. Character error rate (CER) reveals pronounced transient collapse and recovery whose severity and temporal structure are only weakly reflected by loss. Bidirectional layer patching reveals strong cross checkpoint functional incompatibility during recoverable collapse, with model dependent depth profiles that reorganize during recovery. Pairwise gradient similarity alone does not reliably indicate optimization stability, whereas raw gradient spectral analysis provides a clearer structural distinction between stable and unstable optimization: successfully converged runs approach a broad and temporally stable spectral energy distribution, while failed runs remain spectrally concentrated or exhibit persistent fluctuations. Finally, AdamW update transfer bypasses pronounced early collapse, yet substantial Mandarin degradation still emerges later in training. These results motivate three separable SFT dynamics: collapse, repair, and drift, and show that transient collapse is not necessary for persistent source domain degradation.

Chip-scale microresonator-based frequency combs, commonly referred to as microcombs, are promising sources for field-deployable metrology applications. However, intrinsic microresonator noise can make it difficult to generate microcombs with sufficiently low noise for applications. A widely used approach to overcome this limitation is to trap the DKS in the microresonator by phase-modulating the pump laser, although integrating a low-noise modulation reference in a fully on-chip platform remains challenging. Here, we propose an optoelectronic self-trapping scheme in which the impact of intrinsic microresonator noise on microcomb repetition-rate jitter is suppressed through feedback-controlled phase modulation of the driving laser so that the intrinsic noise of the laser sets the ultimate performance limit. This modification eliminates the need for an external low-phase-noise RF source, thereby enabling chip integration. We develop both analytical and numerical models for the proposed system and benchmark its performance against conventional externally referenced bulk implementations, showing that the proposed approach achieves comparable microcomb noise suppression while maintaining chip-scale compatibility.

The writhe of a closed curve measures its coiling, and for a ribbon along it, writhe is the contribution to the linking number not due to twist. In stellarators, large writhe implies large helical excursion and has previously been either an uncontrolled outcome in optimization, or fixed beforehand by the choice of the coordinate system. We present a simple method to target the underlying writhe of the plasma boundary during optimization. Our method calculates writhe and linking number directly from the underlying elliptical boundary of the stellarator. It therefore does not require any properties of the MHD equilibrium solve, such as the true magnetic axis, making it fast to evaluate and smooth to differentiate. Examples for quasi-helically symmetric stellarators show that this target works well in practice.

Modern text-to-video (T2V) models generate visually compelling videos, yet meaning-preserving changes in prompt wording can substantially alter semantic realization and overall quality. Existing prompt rewriting modifies the inference input, whereas conventional post-training constructs supervision from one prompt formulation at a time; neither explicitly optimizes reliability across equivalent forms. We introduce VARI (Verified Alignment over Representations of Intent), a group-structured framework that treats automatically verified formulations of the same visual intent as a shared supervision unit. VARI builds matched form-seed rollout pools, cross-scores each video against all forms, and applies a wording-independent structured intent audit to identify valid realizations and hard semantic failures. Group-Consistent Distillation (GCD) aligns every verified form with interchangeable valid realizations, while Form-Contrastive Flow-DPO (FC-DPO) learns group-level preferences from audited positive-negative pairs, prioritizing same-seed, different-form contrasts. On HunyuanVideo-1.5, VARI attains the highest T2V-CompBench, VBench, and StoryEval scores among the evaluated methods. On prompt-form extensions of T2V-CompBench and VBench, it improves weakest-form alignment over the strongest prompt-level baselines by 2.45 and 3.55 points and reduces cross-form drop by 30.5% and 32.2%, respectively, while preserving visual quality. Human evaluation, natural-caption controls, prompt-enhancement experiments, diversity analyses, and transfer to LTX-2.3 further support the robustness and transferability of these gains, while VARI requires no additional inference-time module.

Learning robot policies from demonstrations is often limited by the cost of collecting diverse, high-quality expert data. While an appealing alternative is to expand a single successful demonstration into a diverse set of successful trajectories, existing augmentation methods typically rely on manually designed transformation rules or complex trajectory planning, requiring substantial task-specific engineering and human effort. We introduce OneDemo, a reinforcement learning framework that learns to edit a single successful demonstration for new task configurations. We formulate demonstration editing as a structured reinforcement learning problem, in which an editor learns, from sparse task-success rewards, both when to transition between object-centric trajectory segments and how to geometrically adapt each segment. The learned editor serves both as a task policy and as a reusable demonstration generator. Across 15 Meta-World tasks, OneDemo reaches a 92.7% success rate within 53.7k environment interactions on average. Across 9 DexMimicGen tasks, it generates successful demonstrations with a 98.4% average success rate, and BC-RNN policies trained on the generated data achieve 99.6% average success at matched dataset scale. These results show that learning to edit a single successful demonstration provides a structured and effective basis for both policy learning and scalable demonstration generation.

Mini-publics are an increasingly popular family of democratic innovation to broaden citizen engagement. However, convening a representative sample in person is resource-intensive, and requires significant organizational efforts to coordinate travel, venue logistics, and facilitator training. This chapter outlines the design and development of the Stanford Online Deliberation Platform, initially tailored for Deliberative Polling, building upon insights from in-person moderation in that setting, but supporting a broader range of methods and approaches in the deliberative space. The platform supports structured conversations for small groups (ideally 8-15 people) with automated moderation functionality, enabling the groups to assume ownership of the deliberative conversation rather than relying on a moderator persona. We describe the platform's architecture and key design decisions, including the deliberation flow, room assignment, speaker management, speaking nudges, agenda management, outcome development, and real-time monitoring. Between its inception in 2018 and 2025, the platform has facilitated over 30,000 unique participants engaging in deliberations; we catalog 54 deliberations with at least 100 participants up to December 2025, spanning a diverse range of languages, countries, and topics. Finally, we establish a standardized vocabulary for future analyses by defining the terminology employed in the platform's data and documenting significant software revisions over time.

Large-scale applications of lifelong multi-agent path finding (LMAPF) call for computationally inexpensive movement decisions under changing traffic conditions and across varied layouts. We propose a navigation policy in which a convolutional network computes a shared spatial field over the map once per timestep and a compact goal-conditioned operator derives agents' movement preferences. The complete policy is trained end-to-end using average-reward reinforcement learning with throughput as the reward, without planner demonstrations or a separate online path planner. For structured and unstructured layouts, we train one policy per class on mixtures of small maps and deploy each without retraining on larger, unseen layouts and agent populations. Across six layouts with 10000 agents, our policies achieve throughput comparable to or higher than the strongest evaluated baselines. The proposed method has an average execution time below 10 ms per step, more than an order of magnitude faster than several established planners.

In first-principles calculations of metallic systems, the discrete electronic mesh in the Brillouin zone necessitates a smearing function and its width (e.g., the widely used 0.02 Ry Methfessel-Paxton scheme) to enforce continuity of energy and occupation at the Fermi surface. However, the quantitative impact of such empirical parameters on phonon-mediated superconductivity has long been overlooked, leading to their habitual selection by mere convention. Here, using hexahydride CsH6 as a benchmark, we systematically investigate the magnitude and propagation mechanism of smearing-induced errors against the parameter-free optimized tetrahedron method. Long-tailed smearing delocalizes the occupation window, causing substantial Fermi-level shifts, flattening of the density of states, and hardening phonon modes, thereby weakening electron-phonon coupling. Conversely, short-tailed smearing suffers from insufficient sampling, producing density-of-states oscillations and enhanced Fermi-surface nesting; via amplified electronic screening and Peierls instabilities, this softens acoustic modes and generates imaginary frequencies, causing CsH6 to be dynamically unstable and discarded. However, the optimized tetrahedron method reveals that CsH6 is dynamically stable under ambient pressure with a remarkable superconducting transition temperature of 121 K. To prevent subjective empirical parameters from obscuring theoretically promising high-temperature superconductors, we derive a simple scaling relation for the smearing width, applicable to different smearing functions, from the free-electron-gas model, offering an objective, precise, and efficient protocol for parameter selection in high-throughput screening.

We study the $(K,N,S,M,K_c)$ distributed linearly separable computation (DLSC) setting, where a master employs $N$ workers with a per-worker computation load of $M$ to recover $K_c$ deterministic linear combinations of $K$ messages in the presence of up to $S$ stragglers. We propose a DLSC framework based on nested cyclic codes that achieves $M=\frac{K}{N}(S+K_c)$. For sufficiently large $K$, we establish the matching converse $M\geq\frac{K}{N}(S+K_c)$, proving the asymptotic computation load optimality of the proposed framework. By instantiating cyclic locally recoverable codes (LRCs) as base codes in the framework, the master can recover the desired $K_c$ linear combinations by contacting fewer than $N-S$ workers under many straggler scenarios. This essentially softens the straggler threshold without increasing the computation load or communication cost. Finally, we extend the construction to reduce the per-worker communication load by a factor of $m$, while achieving an asymptotically optimal computation load of $M=\frac{K}{N}(S+mK_c)$.

Augmented reality (AR) changes how users perceive and attend to their surroundings. Prior work suggests AR can reduce attention to the physical world, but it remains unclear whether this holds in environments dense with both virtual and physical objects, and which factors most affect object recall. This study examines recall in a mixed-reality office scene after an object-selection task, testing object-level factors (virtuality, size), context-level factors (semantic congruency, saliency), and user-level factors (cueing, dual tasking). Cueing informed participants of a later recall test, while dual tasking added cognitive load through a secondary audio task. Virtual objects were recalled more accurately than physical ones. Cueing produced a modest improvement in recall of present objects. Using playback software to reconstruct each participant's view throughout the trials, we computed object-level saliency and found a weak positive correlation with recall, slightly stronger than the effects of virtuality, but not reaching statistical significance. These findings have implications for AR interface design and for building mixed-reality environments that better support cognition during real-world tasks.

This work is a step towards a general understanding of fluctuations for systems of particles described at large scale by fractional diffusion. First, we derive formally a Large Deviation Principle for the empirical measure of mean-field interacting particles with a Lévy-type noise. In the case of independent particles, this unveils a generalized gradient flow structure at large scales. Second, we derive and solve numerically a stochastic Partial Differential Equation describing the fluctuating hydrodynamics of this system. The results compare well with direct numerical integration of the particles' dynamics.

Ti-15Mo (wt%) is a well-established $\beta$-stabilized alloy whose mechanical response is strongly governed by phase stability and deformation mechanisms that operate at the single-grain scale. Because these intragranular mechanisms are intrinsically anisotropic, understanding the orientation dependence of the elastic and plastic response is critical to the texture-engineered processing of wrought components. Here, we quantify the nanomechanical anisotropy of single-crystal Ti-15Mo by combining EBSD with nanoindentation to correlate hardness, indentation modulus, strain rate sensitivity, and indentation yield response with the crystallographic surface normal near $\langle111\rangle,\langle124\rangle,\langle011\rangle,\langle023\rangle$, and $\langle013\rangle$ directions. While the modulus anisotropy is small (~10%), contrary to the prediction for a cubic crystal with A>1, orientations near $\langle111\rangle$ exhibit the lowest moduli. Yield onset is likewise softest near $\langle111\rangle$ and spans 41%, while hardness spans only 6.6% and follows neither the modulus nor the yield ordering. The alloy also exhibits yield behavior not captured by the simple CRSS/Schmid-factor models evaluated here. Strain-rate-jump tests yield V*=18-31b$^3$, consistent with kink-pair-nucleation-controlled plasticity; based on V*, the orientations separate into two groups suggestive of glide-dominated versus twin/transformation-participating response. We reveal an inversion of the elastic anisotropy expected for a homogeneous cubic $\beta$-phase and an orientation-dependent yield-onset response that is not reproduced by the simple Schmid-factor models examined here. Retained athermal $\omega$ is proposed as the contributor because $\beta\rightarrow\omega$ collapse occurs on {111}$_\beta$ planes and may provide anelastic compliance through the reversible $\omega\rightarrow\beta$ transformation.

We investigate the effect of initially enlarging a Brownian filtration by its terminal value on backward stochastic differential equations (BSDEs) and reflected BSDEs (RBSDEs). We establish the Brownian innovation representation and the predictable representation property in the enlarged filtration, highlighting the singular information drift arising from the semimartingale decomposition of the original Brownian motion. We derive transfer identities under suitable integrability conditions and provide explicit counterexamples showing that the resulting singular equations may fail to admit unique square-integrable solutions, including in the reflected case. We further develop a conditional parametrization of regular BSDEs and establish a conditional comparison principle for Snell envelopes, illustrating both the strict value of additional information and the failure of general pathwise domination. An exact projection identity is also obtained for zero-driver terminal payoffs. Finally, we discuss possible extensions to irregular obstacles and more general information structures.

Thermoelectrics turn waste heat into electricity, but finding new ones requires transport calculations too costly for whole databases. Searches therefore choose what to calculate from the electronic density of states (DOS), increasingly predicted by machine learning, yet such choices are rarely tested. We test them on all 106,235 Heusler structures in the DXMag database, screening 51,257 on density-functional spectra and 54,978 on neural-network predictions, and judging both by 3,625 band-structure and transport calculations. A DOS-derived Seebeck indicator ranks most compounds passing every transport and stability test within the top 1% of their population, and ten of the eleven established half-Heusler thermoelectrics calculated pass. Predicted spectra lose most band gaps, unnoticed by spectral-similarity metrics, yet still rank passing compounds near the top. The screen certifies 80 computational candidates, 61 without reported measurements. Computed or predicted, the DOS can choose what to calculate; only a band structure shows whether a gap exists.

We prove the uniqueness of global solutions to the two dimensional barotropic compressible Navier–Stokes equations within the regularity class introduced by Danchin and Mucha [14], for general $C^1$ pressure laws. A crucial assumption is that both solutions have bounded divergence, locally integrable in time, which ensures that their densities remain bounded without excluding vacuum or requiring spatial regularity of the density.

We consider the two-dimensional isentropic compressible Euler equations for a polytropic gas, $p(\rho)=k\rho^{\gamma}$. The $R$–vacuum state–$R$ configuration—two rarefaction waves bounding a vacuum—occurs when the two constant states move apart with sufficiently large relative velocity and is essentially the only vacuum-forming Riemann pattern in the absence of external forces. Local-in-time rarefaction fronts have been constructed only away from vacuum, where the sound speed is bounded away from zero; their construction through the vacuum edge, and hence the structural stability of the $R$–vacuum state–$R$ configuration, has remained open. We establish this stability for $\gamma\in(1,1.3]\cup\{\frac{5}{3},\frac{7}{5}\}$: for sufficiently small perturbations, the Riemann problem admits a continuous entropy solution on a fixed time interval, with the domain partitioned by four characteristic surfaces and the solution in the three central regions belonging to $W^{2,\infty}$ in the self-similar coordinates $(t,x_{1}/t,x_{2})$, even though it may contain logarithmic singularities of the form $c^{\alpha}(\ln c)^{\beta}$ at the vacuum edge. The proof develops a geometric formulation directly on the first-order system, together with a direct analysis of the initial slice at the vacuum edge, where the formal high-order expansion fails.

Proactive human-robot collaboration requires autonomous systems to infer not only immediate actions but also the underlying hierarchical intentions governing human behavior. Current deep learning approaches predominantly focus on flat action classification, failing to capture the structural dependencies connecting kinematic motion to high-level goals. A Neuro-Symbolic Graph Transformer (NSGT) is proposed within this multimodal framework, a Human Reasoning Graph (HR-G) is integrated into the self-attention mechanism via learnable topological biases. Furthermore, the architecture is augmented with a differentiable First-Order Logic (FOL) loss, acting as a structural regularizer by which ontological consistency is enforced across four levels: atomic actions, composite activities, Low-Level Intentions, and High-Level Intentions. Evaluation is performed on the synthesized NTU-Hierarchy dataset, a four-level ontological extension of NTU RGB+D 120, wherein existing sequences were mapped into 119,383 complex hierarchical episodes (85 actions, 16 activities, 8 LLIs, 4 HLIs). To prevent circular supervision, strict isolation between label generation and FOL constraints was maintained. In the base configuration, 91.65% top-1 action accuracy is achieved by the NSGT. When the FOL loss is incorporated into the baseline, logic consistency is improved by 3.26 percentage points to 96.67%. Through the HR-G biases, a tunable trade-off between accuracy and structural coherence is established. In the primary consistency-maximizing configuration ($\lambda$ = 0.5), a logic consistency of 94.59% is reached and ontological contradictions are reduced by 33%, while a robust 89.90% top-1 action accuracy is retained. Finally, interpretable reasoning evidence is provided by the learned HR-G weights, wherein transition edges are strongly exploited ($\beta$ trans $\approx$ +2.6) without explicit supervision.

Particle exchange in two dimensions gives rise to quantum statistics beyond the boson-fermion dichotomy, with central roles in fractional quantum Hall physics, topological quantum computation, and strongly correlated quantum matter. In conventional topological phases, microscopic exchange geometry is compressed into rigid braid and fusion data. We develop a theory of non-Hermitian statistical geometry in which relaxing Hermiticity softens these exchange data into a larger complex space of spectral and relative-geometric degrees of freedom. For two adjacent braid generators, a single projective exchange spectrum is insufficient: their relative eigenline geometry supplies an additional gauge-invariant modulus. On the generic irreducible two-channel branch, braid consistency locks these coordinates through an exact spectrum-geometry relation. Using Riesz projectors and Kato transport, we realize this geometry in a five-arm Kitaev-Majorana network and test spectral and relative-geometric responses in an independent two-dimensional four-vortex Kitaev model. Finite-time dynamics tests the exchange operation, microscopic fusion sewing tests its composition across fusion descriptions, and matched-spectrum controls isolate the role of relative geometry. Nonzero projective Kato curvature shows that braid-consistent, fusion-coherent exchange can depend on the control path. Non-Hermiticity thus exposes exchange geometry, braid consistency re-locks it, fusion coherence further constrains it, and projective flatness determines when geometric exchange becomes intrinsically topological.

Looped reasoning with dynamic depth can be viewed as relaxation toward solution attractors in a learned dynamical landscape. In practice, however, latent trajectories often oscillate, cycle, or drift rather than cleanly converge to stable fixed points. How these non-stationary dynamics contribute to reasoning and constrain convergence remains unclear. We show that slowly decaying oscillatory modes can impose their convergence rate on coupled latent dynamics, creating a bottleneck. Yet damping these modes indiscriminately can disrupt the reasoning computation they support. This tension motivates an architectural approach: introducing rotational degrees of freedom along which symmetry-generated rotational motion leaves the reasoning-relevant quotient dynamics unchanged by construction. We propose QRR (Quotient Recurrent Reasoner), a gauge-equivariant recurrent architecture with an exact per-token phase-rotation symmetry. Motion along these symmetry directions leaves the quotient representation unchanged and is dynamically decoupled from reasoning-relevant dynamics. Empirically, QRR achieves stable and faster convergence to solution roots in quotient space, without forming a dominant slow oscillatory bottleneck, while matching or surpassing recent recurrent reasoning models on Sudoku, Maze, and Mini-ARC.

Diffusion large language models (dLLMs) have emerged as a promising alternative to autoregressive LLMs, yet remain susceptible to hallucination. Activation steering offers a promising mitigation approach by guiding parallel token predictions through internal representations. However, existing steering methods largely overlook two characteristics of dLLMs: dynamic denoising states and temporal hallucination risks, which challenge predefined steering vectors and uniform intervention strengths. We propose TRACESTEER, a trace-driven activation steering framework that uses preceding denoising predictions as feedback to jointly adapt steering direction and strength. Specifically, Denoising Feedback Steering (DF-Steering) constructs step-specific steering vectors from preceding predictions and current hidden states. Trajectory-Guided Steering Gate (TS-Gate) regulates their strength using prediction uncertainty and the denoising timestep. With the backbone frozen, factual supervision and magnitude regularization jointly guide the learning of adaptive steering interventions, promoting factual reliability and stability throughout denoising. Experiments on two dLLMs show improved factual reliability on TruthfulQA and generalization across five downstream benchmarks.

In this work we introduce a numerical framework for the simulation of biological capsules based on meshes that adapt iteration-wise to the shape of the membrane. The discretization leverages a Hybrid High Order method (HHO) to solve a Stokes problem with a source term distributed on the interface between the internal and the external phases. The HHO discretization supports meshes composed of general polygons, permitting to use fitted meshes that can be easily generated by cutting the elements intersected by the interface. Moreover, polygonal meshes allow arbitrarily accurate interface discretizations without introducing bulk degrees of freedom. The presentation of the simulation algorithm is completed with a proof-of-concept numerical test on a well-established benchmark: the deformation of an elastic capsule immersed in a shear flow.

The recent experimental synthesis of covalent cage superconductors has ignited hopes for ambient-pressure high-temperature superconductivity, while the computational strategy for discovering new materials poses challenges for accurately estimating superconducting properties. Here, we quantified the response of electron-phonon coupling (EPC) properties in M(BN)5 superconductors to different exchange-correlation (XC) effects using high-throughput first-principles calculations. We found that the metallic covalent bonds responsible for superconductivity exhibit anomalously high sensitivity to functional selection uncertainty, distinguishing them from conventional superconductors mediated by metallic bonding. The widely used PBE functional systematically overestimates lattice volumes, inducing phonon softening, enhanced EPC, and consequent Peierls instability. In contrast, PBEsol, which is more accurate through enhanced treatment of short-range interactions, eliminates imaginary frequencies in Rb(BN)5 that appear at the PBE level, yielding an outstanding superconducting critical temperature (Tc) of 113 K at ambient pressure and 138 K at 2 GPa. Enhanced electron localization and short-range correlation in covalent bonds manifest through dual mechanisms: phonon hardening at the lattice scale and band widening at the electronic scale, which collectively suppress Peierls distortion and delocalize antibonding states. Pressure-dependent analysis reveals that compression attenuates phonon discrepancies between XC functionals, whereas electronic properties remain notably sensitive to XC-induced perturbations of fine electronic bands near the Fermi level.

We study automorphisms of Hausel's medium algebras by identifying them with equivariant cohomology algebras of affine Schubert varieties of a complex reductive group $G$. The automorphisms in question are then given by the action of either complex automorphisms or real structures of $G$ on affine Schubert varieties. We focus on describing the fixed points of those automorphisms on the spectra of medium algebras, and prove that the torsion-free quotients of the corresponding coinvariant algebras are isomorphic to equivariant cohomology rings of fixed loci in affine Schubert varieties. In the case of real structures, this naturally leads to and involves the study of affine Grassmannians for quasi-anisotropic (also called quasi-compact) real reductive groups, closely related to recent work of O'Brien. We also discuss relations to automorphisms of Higgs bundle moduli and to symmetric pair variants of medium algebras.

A scenario-based development approach has become state of the art for automated driving systems. Once a set of scenario classes covering the operational design domain is available, concrete scenarios are generated from these scenario classes, e.g., to be used for hazard analysis and risk assessment or for the system's verification and validation. For such applications, a high diversity among the generated concrete scenarios is paramount. The question arises how the quality of collections of concrete scenarios can be assessed in such a setting. In this work, we aggregate scenario distance measures into so-called quality functions that quantify the diversity of concrete scenario collections in the context of automated driving. In particular, we consider the case where scenario classes are formalized as constraint systems and the associated concrete scenario space is not explicitly known. Based on a set of desired properties we construct candidates for such quality functions and give proofs for their property fulfillment. To show the practical relevance of quality functions, we perform a variety of experiments in the context of an abstract scenario-based virtual verification toolchain for automated driving systems. More specifically, we use quality functions to compare the effectiveness of variation methods for sampling, examine the choice of different scenario distance measures, and investigate the effects of temporal aspects on concrete scenario collection quality.

Accurate prediction of object trajectories is fundamental to mechanical understanding and robotic control. However, autoregressive models inherently suffer from cumulative errors, leading to severe drift in long-horizon rollouts. Observing that in many physical systems with dissipative or convergence-to-rest behavior, the final states are often more predictable than transient dynamics (e.g., a sliding object resting under friction or a pendulum stabilizing at equilibrium), we propose ReStep, a cascaded approach that reverses the conventional forward-prediction paradigm. ReStep first employs a stochastic model to directly predict the final state, then leverages Anchored Diffusion to generate goal-conditioned intermediate trajectories. By conditioning on both ”boundary states”, it effectively constrains dynamics and reduces uncertainty, producing physically plausible and temporally coherent transitions. We further integrate ReStep dynamics as the physical engine within a 3D Gaussian Splatting pipeline, enabling a unified physical-visual framework for intuitive inference from images. Extensive experiments on diverse rigid and non-rigid collision datasets show that ReStep achieves superior long-term accuracy, substantially mitigating error accumulation via reverse-consequence modeling.

End-to-end autonomous driving has achieved remarkable progress by planning trajectories directly from raw sensor data. Yet the step from planning to control still relies on hand-tuned tracking controllers that block the gradient path from vehicle motion back to the network. This gap stems from non-differentiable vehicle dynamics, aliased supervision from coarsely sampled expert labels, rate mismatch between high-rate control and low-rate re-planning, and vehicle model discrepancies between training and deployment. This paper proposes DIVA (Differentiable Identified Vehicle dynamics for end-to-end Autonomous driving) to close this gap. An identified actuator-level vehicle model is embedded in the training loop of the end-to-end driving network, forming a differentiable chain from perception to vehicle states. A learning-based control decoder replaces the external controller and is supervised on the rolled-out vehicle states, bypassing the aliased control-input labels. A rate-consistent control-input parameterization reconciles the heterogeneous sampling rates and enables asynchronous execution with a 3.8 ms control-only cycle. On-policy re-identification and an online disturbance observer address training-time distribution shift and deployment-time model mismatch respectively. On the closed-loop Bench2Drive benchmark, DIVA achieves a driving score of 86.7, surpassing the widely adopted state-of-the-art approach by 3.3 points while nearly halving mean jerk and reducing brake switching by 64%, and maintains superior path tracking accuracy under significant vehicle model mismatch at deployment.

Randomly initialised neural networks of width $m$ converge to Gaussian processes as $m \to \infty$, with two types of quantitative bounds characterising this convergence. Finite-sample bounds compare the network with its Gaussian limit at a fixed finite sample set, on an arbitrary domain, in the quadratic Wasserstein distance $\mathcal W_2$, achieving a convergence rate of $m^{-1/2}$ with explicit constants. However, these constants grow with the number of samples, so the bound becomes uninformative as the sample set is refined. Functional bounds remove that dependence by comparing the two as random functions, at the price of spherical input, metrics weaker than $\mathcal W_2$, or slower rates. In this paper, we therefore lift a finite-sample bound to a functional one. The lifting refines the sample set until it is dense in the domain, so the bound must first be made independent of the number of samples. We achieve this by measuring the error per sample, which makes the constant uniform. For a polynomial activation and any compact input set, this gives a rate of $m^{-1/2}$ in the supremum norm, with an explicit constant.

Smart contracts compiled to the Ethereum Virtual Machine (EVM) can manage high-value assets and are difficult to patch after deployment. Compiler miscompilations are therefore especially dangerous: compilation succeeds, but the generated bytecode does not preserve the semantics of the source program. Existing smart-contract compiler fuzzers either focus on robustness failures or rely on differential oracles that compare compiler configurations. We present Soliduzz, an approach for finding miscompilations in EVM smart-contract compilers using assertion-driven equivalence oracles. Soliduzz uses product programs to encode semantic equivalence as executable assertions. The key shift is to compile these self-checking programs and let off-the-shelf fuzzers and symbolic execution engines explore the resulting bytecode for assertion violations, without requiring compiler-specific support from the analyzer. Soliduzz instantiates this idea with two complementary families of metamorphic transformations. The first starts from equivalent expressions and lifts them into smart-contract code that deliberately exercises EVM-specific features such as storage, data locations, control flow, contract interactions, and inline assembly. The second generalizes Equivalence Modulo Inputs (EMI) from fixed concrete inputs to symbolic input spaces. Our symbolic EMI records coverage in the original computation and uses it to guard mutations in the transformed computation. Together, these transformations produce product programs that assert that paired computations yield the same outputs. We evaluate Soliduzz on three EVM smart-contract compilers (solc, solx, and vyper) using several analysis tools. Overall, Soliduzz exposes 29 bugs. Of these, 24 are compiler bugs: 6 miscompilations, 17 internal compiler errors, and 1 hang. The remaining 5 are bugs in the analysis tools.

Graph Neural Networks (GNNs) fundamentally lack the ability to capture structural properties defined by node self-interactions, such as cycle counts, subgraph centrality, and heat kernel signatures. Existing solutions often rely on computationally expensive higher-order architectures or hand-crafted features. In this work, we introduce DIAL, a message-passing layer that gives nodes access to graph structure through the diagonal of graph-derived operators. Our approach uses randomized probing to provide nodes with learnable, permutation equivariant access to diagonal entries. We prove that our approach can express important structural features, including cycle counts, subgraph centrality, and heat kernel signatures. The proposed method can be integrated directly into message passing layers. Experiments on molecular property prediction, cycle counting, and pattern detection demonstrate the effectiveness of DIAL across a range of graph learning tasks.