Papers

The Green-Kubo (GK) method which is used to obtain the shear viscosity of a model liquid in equilibrium molecular dynamics (MD) often requires long simulation times to obtain acceptable statistics. This work extends the GK approach to include spatial correlations. The total shear stress in the GK expression is split into a grid of its components in contiguous volumes. In doing this, the autocorrelation of the total system stress can be rewritten as the cross-correlation of the subvolume stresses. This provides a novel real-space insight into the liquid structure, something previously only treated in Fourier space by liquid-state theory. A novel travelling wave like structure is exposed that is shown to be well fitted by a leading Gaussian pulse added to a second negative Gaussian for the bounce back. The fitting parameters include the wave position, magnitude and width which show deep insights into the liquid property. The wave moves at the speed of sound over short times before decreasing in speed with the square root of time, while the wave packet spreads out also as the square root of time. The magnitude is decreasing with form $t^{-3/2}$, a result with strong significance in the history of MD simulation. These fitted forms mean the entire spatial temporal response of the liquid can be modelled in closed form by fitting to data, with short term requiring MD and the long time and distances approximated by the Gaussian form. By limiting the correlation to localized interactions the longer range contribution, which essentially only contribute to the noise, can be eliminated. This looks like a promising approach to model viscosity by taking short MD runs and fitting the long time behaviour.

This paper evaluates Nash- and Stackelberg-based decision-making controllers for autonomous intersection crossing using a three-stage evaluation pipeline culminating in physical Quanser QCar 2 experiments with hardware-in-the-loop (HIL) execution. The controllers are implemented in MATLAB/Simulink, deployed through Quanser Real-Time Control (QUARC) software, and executed on the onboard NVIDIA Jetson AGX Orin processor. The evaluation includes MATLAB numerical simulation, qualitative validation in Quanser Interactive Labs (QLabs), and physical QCar 2 experiments. The experiments consider symmetric and asymmetric intersection approaches, leader-follower interactions, conflicting Stackelberg role assignments, and non-cooperative obstacle-vehicle behaviors. The results characterize the effects of hierarchy assignment, obstacle-vehicle behavior, and physical implementation on the considered game-theoretic autonomous driving controllers. Comparison between software simulations and hardware experiments further highlights the importance of accounting for sensing and state-estimation uncertainty when translating game-theoretic controllers from simulation to physical systems. A video demonstration of the QLabs simulations and physical QCar 2 hardware experiments is available at https://youtu.be/gkV6lz0twRk.

For Gaussian location mixtures with identity covariance, we prove that the nonparametric maximum likelihood estimator of the mixing distribution is unique for Lebesgue-almost every dataset, for every sample size and dimension. In particular, uniqueness holds almost surely whenever the joint distribution of the observations is absolutely continuous. The proof uses the finite-support theorem for Gaussian location NPMLEs and almost-everywhere differentiability of the optimal log-likelihood. Wherever this optimal value is differentiable, all NPMLEs have the same density derivatives at the observations. A minimal linear dependence among Gaussian evaluation vectors then rules out distinct solutions. An appendix extends the result to arbitrary fixed, known, observation-specific positive-definite covariances.

Post-Quantum Cryptography (PQC) is being deployed while embedded systems increasingly adopt lightweight virtualization for workload isolation and security. Both trends change performance characteristics, yet their interaction is not well understood. To address this, we present a measurement study of PQC primitives on embedded-class ARM hardware under three execution environments with a shared software stack: native execution, a Docker container, and a Unikraft unikernel running under QEMU. We benchmark five signature and five key encapsulation mechanism families, and, for comparison, two classical algorithms each. We evaluate them using different parameter sets for a total of around 70 configurations, measuring execution time, memory, and energy per operation. To better gauge the impact on applications, we evaluated TLS 1.3 cipher combinations. We find that container overhead is negligible for primitive computation, whereas unikernel overhead depends on the algorithm. For most PQC families the overhead is negligible. A moderate overhead (1.28-1.53) arises in BIKE, HQC, and MAYO, and, above all, in Falcon signing (17.8-19.2). Per-operation energy closely tracks execution time in all environments. For TLS handshakes, container and unikernel clients need more time and energy per handshake, while all three environments converge once expensive post-quantum algorithms dominate the handshake. In these cases algorithm choice affects per-handshake energy by up to three orders of magnitude, far outweighing the environment. Overall, virtualization cost is inversely related to cryptographic cost: environment choice matters most for computationally cheap, standardized algorithms, while for expensive schemes, algorithm choice alone dominates performance.

For any positive integer $k$, let $J_{k}$ be Jordan's totient function. We show that $J_{k}$ is not injective when $k=3,4,6$.

Tree speculative decoding for recurrent-hybrid language models requires each accepted path to maintain consistent recurrent state, convolution history, and attention caches. We present LumoTree, a GPU serving design that coordinates verification and commitment through a shared tree descriptor. The verifier processes independent paths in parallel and reuses recurrent state tiles across local updates. Boundary states connect dependent paths. Accepted-path replay publishes the selected continuation into native running state, alongside coordinated convolution gathering and attention-cache remapping. Fused selection, device-resident acceptance, graph replay, and tree-aware attention integrate this organization into the serving cycle. The design separates temporary branch computation from persistent request state while retaining native prefix-cache interfaces. We evaluate numerical behavior, serving performance, and coding-agent outcomes on NVIDIA DGX Spark.

We prove the long-standing conjecture that, for every odd prime $p$, the only integral solutions of $a^2-2=b^p$ are $(a,b)=(\pm 1, -1)$. We also completely solve the analogous equations $y^2-D=x^p$ for $D=3$ and $D=5$ and describe a general approach for other positive squarefree values of $D \not \equiv 1 \pmod 8$. The proof refines the interpolation determinant method for linear forms in two logarithms in special cases, introducing new ideas for both the arithmetic lower bounds and the analytic upper bounds.

Ring All-Reduce is a widely used protocol for aggregating gradients across workers in large-scale distributed training. For a system with $N$ workers, its normalized per-worker communication is $2(N-1)/N$. In this work we present a communication-efficient Ring All-Reduce (CERAR) protocol for “approximate” gradient aggregation. CERAR partitions each local gradient into $c$ components and relies on linear encoding and decoding operations. It performs $L=c+N-2$ communication rounds over an $N$-worker ring, yielding normalized communication rate $1+(N-2)/c$ and normalized storage rate $1+N/c$. We present an explicit Vandermonde matrix based construction whose approximation error can be made arbitrarily small, with communication and storage rates approaching one as $c$ increases. However, this comes at the cost of ill-conditioned encoding matrices. We therefore give an alternate construction whose error is $O(\epsilon)$, while the relevant condition numbers are $O(\epsilon^{-r_\star})$, where $r_\star=\lceil c/N\rceil-1$. This motivates a condition-number-constrained optimization formulation for obtaining numerically stable practical designs. Our experiments show that, compared with the production-standard NCCL on NVIDIA A100 PCIe GPU clusters with low-bandwidth PCIe interconnect, CERAR reduces raw All-Reduce time by up to 47%. For training a 1.4-billion-parameter Pythia model, it reduces training time by about 17% for the same number of iterations while achieving essentially identical validation loss. On GPU clusters with high-bandwidth NVLink interconnects, CERAR performs worse in the All-Reduce phase and slightly worse in overall training time. However, the gap narrows for larger model sizes, suggesting that further gains may be possible with more optimized CERAR implementations.

Randomized perturbations can reveal downstream responses without identifying which causal relationships are direct. Conditioning on intermediate responses may induce associations through unmeasured common causes, even when the source is randomized. We introduce Proxy-Adjusted Balanced Masking (PABM), a nonparametric framework for recovering directed acyclic graphs from targeted interventions, response data, and recorded proxies. PABM uses valid target-specific interventions to identify candidate ancestors. It then compares conditional target distributions with and without a candidate response and, when supported by the design, its intervention variable, adjusting for other ancestors and proxies. Each comparison uses matched observations, adjustment variables, and fitting procedures. Identification requires every included nonparent comparison to have zero conditional gain and each parent to have positive gain in at least one comparison. We establish population identification, finite-sample recovery conditions that accommodate incomplete adjustment and estimation error, and familywise error control under valid held-out p-values. Continuous-response simulations show favorable graph recovery relative to specified comparator pipelines; K562-calibrated count simulations reveal a selection–ranking tradeoff. Proxy ablations assess sensitivity to recorded information. An analysis of K562 Perturb-seq data illustrates descriptive candidate-network construction; proxy adequacy for unmeasured biological variation remains unresolved.

Control barrier functions (CBFs) have become one of the most popular tools for encoding and enforcing state constraints in safety-critical robotics. Standard CBF approaches are inherently myopic in nature as they enforce safety only at the current time step. Consequently, the system can be driven toward the boundary of the safe set where no feasible safe control exists at a future timestep. Model predictive control (MPC) based approaches address this by enforcing state constraints over a receding horizon. However, such approaches generally require the model to be known for solving a constrained optimization problem at every step, which is computationally expensive for real-time deployment. We propose BarrierFormer, a barrier-supervised transformer framework that addresses these limitations by encoding rollout-level CBF constraints in learning a model-free safe policy. A causal transformer encodes observation-action history, autoregressively generates a predictive rollout through the dynamics head to replace the model, and provides a residual correction to a nominal controller through the action head to replace the online computation. A barrier critic operating on local observations evaluates CBF constraint violations along this rollout, and a safety teacher computes barrier-consistent actions satisfying these constraints as direct supervision targets for the learned control policy. During inference, the policy maps observation-action history to control actions without any online optimization or model knowledge, enabling real-time model-free predictive safety enforcement. Evaluations across linear and nonlinear, 2D and 3D dynamical systems for safe goal-directed navigation demonstrate that BarrierFormer outperforms existing reinforcement learning (RL)-based, diffusion-based, MPC-based, and transformer-based approaches in safety rate and inference latency.

We prove the Zygmund conjecture in all parameters: the maximal operator associated with products of cubes with side lengths $(s_1,\ldots,s_{m-1},\phi(s_1,\ldots,s_{m-1}))$, where $\phi$ is any positive coordinatewise nondecreasing function, satisfies the weak $L(\log L)^{m-2}$ estimate for every $m\geq3$. The estimate is new for $m>3$. Our approach is to prove Rey's recent conjecture on the exponential integrability of the overlap function $h_{\mathcal G}=\sum_{I\in\mathcal G}\mathbf{1}_I$, with exponent $1/(m-1)$, for sparse incomparable families $\mathcal G$ of $m$-parameter dyadic rectangles, $m\geq2$. The Zygmund conjecture, even in the continuous form above, follows by strengthening a reduction given by Rey.

Agentic AI extends LLM security beyond generated content to persistent state, autonomous actions, tool use, and interactions with humans and other agents. Existing threat classifications often emphasize individual dimensions, obscuring connections among entry points, affected components, and security consequences. The known threat landscape also differs from the coverage demonstrated by empirical research. Through a structured review of 66 studies published from 2022 to 2026, we introduce T={S, B, P, A}, a cross-dimensional representation linking affected functional or system surfaces {S}, interaction or trust boundaries {B}, violated security properties {P}, and empirically examined architectures {A}. We analyze 22 artifact-backed red-teaming studies and 11 representative security benchmarks to characterize empirical coverage and evaluation maturity. Within the selected studies, evidence concentrates on prompt/reasoning, memory, and tool-mediated attacks, predominantly in single-agent settings. Persistent, Human–Agent, complex multi-agent, systemic, and long-horizon threats receive less coverage. These findings describe the selected corpus rather than establish gaps across all empirical research. Heterogeneous metrics, limited adaptive defense evaluation, architectural imbalance, and incomplete execution-state capture further constrain comparison and reproducibility. We derive 13 open research questions to guide more systematic, architecture-aware, and reproducible security evaluation of agentic AI.

We introduce and study $\mathcal{FG}$-order continuous operators between Riesz spaces, based on Tantrawan's generalized (unbounded) order convergence. This framework includes several familiar classes of operators and allows their properties to be studied in a unified setting. We establish order boundedness and lattice-theoretic results; in particular, we show that strongly order continuous operators are automatically order bounded and prove that the modulus of an order bounded $\mathcal{FG}$-order continuous operator remains $\mathcal{FG}$-order continuous under suitable assumptions. The latter result gives an affirmative answer to a previously posed problem for strongly order continuous operators. We also establish a general result ensuring classical order continuity, from which order continuity results for several familiar classes of operators follow. Furthermore, we characterize, under suitable hypotheses, when the space of order bounded $\mathcal{FG}$-order continuous operators is a band. Finally, we prove an extension theorem for positive $\mathcal{FG}$-order continuous operators, providing a counterpart of Veksler's extension theorem in this framework.

Mechanistic interpretability defines features as the fundamental units of a neural network and circuits as the weighted subgraphs that carry out its computation. Because individual neurons are polysemantic, Cross-Layer Transcoders (CLTs) were introduced as a way to approximate a model's circuits by generating an attribution graph. The nodes of that graph, however, are unlabeled features: reading a graph means pruning it and then working out by hand what each surviving node means. To make CLTs easier to use for circuit discovery, we introduce Circuit-Diff, which intervenes on the model itself with a low-rank factual edit and takes the features whose role in the attribution graph changes under that edit as related to the edited knowledge. On the edits we examine, the flagged nodes are not only detectors of the object token: read off the CLT's released feature dashboards, they include features for the history, geography and associations surrounding the old and new objects. We formalize the method, measure how reliable a frozen CLT remains after a factual edit, test the selected nodes causally by patching them on up to 24 CounterFact edits, give a case study, and release an open-source implementation built on the circuit-tracer package, together with two further tools (multi-prompt aggregation and rule-based supernode labeling).

A set pair system $\{(A_i,B_i)\}_{i=1}^m$ is $1$-cross intersecting if $|A_i \cap B_i|=0$ for all $i$ and $|A_i \cap B_j| = 1$ whenever $i \neq j$. Let $m(a,b,1)$ denote the maximum size $m$ of a $1$-cross intersecting set pair system $\{(A_i,B_i)\}_{i=1}^m$ where $|A_i| \leq a$ and $|B_i| \leq b$ for all $i$. We prove a conjecture of Füredi, Gyárfás, and Király [Combin. Probab. Comput. 32 (2023)] that asserts $m(n,n,1)/\binom{2n}{n} \to 0$ as $n \to \infty$.

In 1936, the protostar FU Orionis began to brighten. Two years later, it was 100 times brighter and has not dimmed since. This object defined the class of FUor-type accretion bursts in protostars. Previous attempts to model FUors simulate isolated protostellar discs, thereby limiting the mass available to drive the burst and shortening its duration. However, these protostars are embedded within the interstellar medium, from which they actively accrete via accretion streamers. This work seeks the origin of FUors starting at interstellar medium scales. An unbiased search of star particles from a 25AU resolution star cluster formation simulation was performed to find FUor candidates. Most candidates were low-mass secondary stars in highly eccentric binaries, like FU Orionis. Zoom-in simulations down to 0.79AU resolution found candidates experience dramatic accretion suppression and bursts at the closest binary separation at periastron. Approaching periastron, the candidate's orbital speed becomes supersonic striping away nearby gas. After periastron, the orbital speed decreases allowing gas to accrete onto the candidate rapidly via Bondi-Hoyle-Lyttleton (BHL) accretion. BHL accretion tails form behind the candidate and appear as accretion streamers. This dramatic suppression and burst near periastron is a physical mechanism for strong variable accretion in embedded young eccentric binaries. This mechanism also implies that FU Orionis returned to its former accretion rate.

Automated kernel vulnerability reproduction is essential for bug triage, patch validation, and regression testing, but still lacks an effective and efficient solution. The core challenge is twofold: a reproducer must first recover the trigger scaffold needed to reach the vulnerable state and determine the precise concrete values that actually trigger the bug. Existing directed fuzzing approaches are ineffective at recovering the necessary trigger scaffold, while LLM-only generation is brittle because it struggles with concrete-value discovery and runtime nondeterminism. We design SyzHarness, a framework that combines LLM reasoning with coverage-guided fuzzing for patch-based Linux kernel vulnerability reproduction. Given a patch, SyzHarness uses an LLM agent grounded by code navigation tools to synthesize a parameterized fuzzing harness that fixes the prerequisite setup logic while exposing only uncertain, bug-critical input parameters to be mutated by Syzkaller. SyzHarness then translates this harness into a Syzkaller compatible interface and iteratively refines it using hierarchical reachability feedback. We evaluate SyzHarness on multiple datasets of triggerable real-world Linux kernel vulnerabilities. On 100 KernelCTF cases, SyzHarness achieves a 78% bug reproduction success rate. On the SyzDirect benchmark, SyzHarness achieves a 73% bug reproduction success rate, substantially outperforming prior directed greybox fuzzing. On 50 recent, known-triggerable syzbot bugs fixed after March 2026, SyzHarness reproduces 40/50 (80%) using only the fix commits as input.

Contact-rich manipulation requires estimating forces, slip and contact geometry that can remain ambiguous in scene images. Optical tactile sensors provide both visual observations of the contact surface and mechanical measurements, yet learning from these signals raises two challenges: representing contact beyond appearance and transferring its benefits to a policy that does not require fingertip observations at deployment. We introduce HapticWAM, a world-action model that combines heterogeneous tactile encoding, structured contact prediction and teacher-student distillation. Its teacher encodes gel images together with deformation, shear, distributed forces, resultant wrench and derived contact state into a frozen video backbone. Rather than predicting tactile pixels alone, the model jointly generates actions and a contact package describing future events and mechanics. Anticipatory Contact Coupling uses the previously imagined package to condition attention, preserving a contact-related input when direct tactile observations are unavailable. Haptic-Imagination Distillation transfers both contact futures and action predictions to a student that retains the generative contact head but removes its fingertip input branches. On a real-world setup, across three contact-rich pick-and-place tasks, HapticWAM Student achieves a 77% per-task mean success rate (41 of 50 starts, 82% pooled), reaching 95% on one of the tasks, outperforming the evaluated teacher and baseline configurations.

Generative AI tools are being widely taken up by students in their physics courses and beyond, often before instructors and institutions can develop policies and effective approaches for the use of these tools. Building on a framework for change in the era of AI, we developed and implemented a faculty learning community to help a university physics department address these challenges collectively. Over six biweekly sessions, faculty worked through course policies, classroom conversations about AI, AI-integrated coursework tasks, and assessment. Each session shared a common structure: we presented local data and department-sourced materials, tested them in small groups, and discussed them together, emphasizing durable pedagogical approaches over specific tools and platforms, and leading with evidence of students' own AI use. The series produced a shared, evolving repository of resources for faculty to draw on. This workshop provides an adaptable, theoretically informed model for a faculty learning community that departments can build on.

Software delegates more of its branches to models every year: which queue a ticket enters, whether a command is safe to run, whether a claim clears without a person. What the program needs back is not prose. It is one of n declared options and a number it can threshold. Today that costs a round trip to a frontier model – hundreds of milliseconds, a per-token bill, and a parser – for a question that is usually a conjunction of three clauses. this-that-model-1.0 is a 2B-parameter typed decision model. Its answer is read directly from the hidden state at a designated position and restricted to the option set the caller declared, so no text is generated, nothing can be malformed, and every question in a request is answered in the same forward pass. It decides in 30.9 ms on one laptop GPU and generates zero output tokens doing it, where a frontier API call costs 8758 ms and the hosted systems that answer these questions well spend between 21 and 212 generated tokens per question thinking first, billed for every one. It sustains 32 decisions per second on one consumer GPU and never lets the state leave the machine. On a third party's recorded cohort of 68 decision questions, on their inputs and their wording, it scores 0.941 with a Brier score of 0.042, against 0.765 and 0.133 for the hosted service Jev on the same items. One pass of our 42-family internal suite takes 32 seconds and 0.000217 USD of electricity; the most accurate hosted model we measured needs 155.2 minutes and 10.636 USD. We also report where it loses. On multi-step arithmetic, which a single forward pass cannot carry intermediate results through, it scores 0.560 against their 0.98 to 1.00, and a targeted second training round improved the five task families it was written for and transferred to none of the other 13. The model is open-sourced in https://huggingface.co/flock-io/this-that-model-1.0

Robot foundation models learn manipulation from large demonstration corpora, but surgery is missing from those corpora: across the 780-hour Open-H surgical collection, one dataset carries synchronized force and none covers an aesthetic procedure. Liposuction is the hard case, because the instrument works under the skin and the surgeon operates by feel and by judgment. Humynex Robotics builds curated expert datasets for this kind of procedure. HumynexSurg-1 is the first release: a master liposuction surgeon performing on porcine abdominal tissue while narrating every decision, recorded with synchronized suction pressure, six-axis hand force/torque, top-down RGB-D video, side video and a lavalier microphone – 14 episodes, 42,738 frames, 35.6 minutes, 356 utterances of which 95% compile into a liposuction-specific label schema. The capture follows a patent-pending sensing plan organized around the quantities a policy needs, so a channel captured today by a model can be upgraded to a sensor tomorrow without changing the data format. This release captures the instrument motion as a tool-hand track in the side video and provides the force channel as state; the funded capture adds a measured 6-DoF handle pose, a validated force channel, ultrasound imaging of the fat layer, and palpation sensing. As a proof of concept, NVIDIA Isaac GR00T N1.7 fine-tunes on the dataset with no custom code in under an hour per run and learns the recorded sessions; scaling probes on the same episodes show where further gains come from: every new session lowers the error on an unseen session. The dataset, its label schema, its quality-assurance reports and its evaluation protocol are the product; the next capture, many short sessions across fat regions with the sensors named here, is what the probes point to.

Let $F$ be a singular fibre of a relatively minimal complex elliptic fibration with smooth total space, and let $\Omega$ be a nonvanishing holomorphic two-form near $F$. We show that a small neighbourhood of $F$ is a Weinstein domain for $\mathrm{Re}\,\Omega$ whose completion is a Legendrian surgery, with cocores obtained by completing holomorphic disks transverse to the components of $F$. For every coefficient field and every multiplicative bulk class, we compute the wrapped Floer cohomology of these cocores and prove that it is concentrated in degree zero. The cocores generate, so the bulk-deformed wrapped Fukaya category is equivalent to the category of perfect modules over an explicit algebra: a multiplicative preprojective algebra of affine type for the normal crossing fibres, and a quiver algebra with relations for types $II$, $III$ and $IV$. Applications include formality of the affine plumbing dg algebras; mirrors given by resolved affine surfaces at every classical bulk class for affine D, E and types II, III, IV; and mirrors given by quotient stacks of algebraic tori at root-of-unity bulk classes for the four affine stars.

We present a collaborative streaming anomaly detection system for high-speed data streams that explicitly integrates human analysts into the decision loop. The system combines heterogeneous detectors and aggregates their outputs through a normalization-based weighted consensus, complemented by artifact-aware rules to stabilize anomaly scoring under deployment. To improve interpretability, it derives surrogate models that approximate the ensemble consensus and expose human-readable sensor conditions associated with anomalous behavior. Analysts can actively intervene by reviewing anomaly episodes, adjusting consensus behavior, and refining surrogate rules used for anomaly prediction, producing a human-adjusted ensemble. We evaluate the approach on an industrial stream with 260\,000 events and 3 anomalous episodes, showing robust detection and actionable human-AI interaction.

We classify, up to quasi-isometry, the large-scale geometry of Galton–Watson trees for every finitely supported offspring distribution. Apart from the trivial finite diameter regimes, we condition on infinite diameter. We find that the remaining classes are the ray class, the full tree class (which includes the binary tree), one chain class $(\mathrm{C}_\Lambda)$ for every possible branching semigroup $\Lambda$, and the bushy class. Two independent trees almost surely admit a root-preserving quasi-isometry when their offspring distributions belong to the same class and are almost surely not quasi-isometric when they belong to different classes. Any two survival-conditioned supercritical realisations with finitely supported offspring laws nevertheless a.s.~admit quasi-isometric embeddings in both directions. We prove that the class of a realisation depends only on the support of the offspring distribution, not its specific distribution. For offspring distributions supported on $\{1,2\}$, we additionally obtain an explicit exponential tail bound for the probability of non-existence of a root-preserving $D$-quasi-isometry. The classification also implies that the corresponding random Cantor boundaries are almost surely quasisymmetrically equivalent. Conditioned on nonextinction, this applies to strongly separated fractal percolation, even when the underlying self-similar iterated function systems and retention parameters differ. We also classify two families of trees with continuous random branching times. Our proofs use new automorphism-matching theorems for random graph labellings of trees, based on contraction estimates for mismatch potentials. These matching results for Markov labellings on the binary tree may be of independent interest. The quasi-isometry classification, embeddability, and matching theorems are formally verified in Lean.

Joint Embedding Predictive Architectures (JEPAs) are a promising paradigm for learning task-agnostic latent world models without visual reconstruction. However, standard JEPA training exhibits a strong inductive bias towards slow features, causing feature suppression and the collapse of latent representation. While inverse dynamics provides temporal anti-collapse, it relies on action labels and offers little incentive to embed general, unlabeled dynamics. We introduce Difference Image and Single image embedding Regularization (DISReg), a novel regularizer that builds on an inverse-dynamics-style module that predicts temporal difference image embeddings without any pixel reconstruction loss, encouraging balanced static and dynamic feature learning. DISReg consists of a static term that shapes the distribution of the image embedding and encourages slow features, and a dynamic term, which, unlike direct regularization on the embedding, imposes no constraint on the image embedding's shape or distribution and instead only incentivizes that dynamic features be present. By integrating this regularizer into a standard JEPA, we establish our new architecture, MotionJEPA. Latent probing demonstrates that MotionJEPA produces more complete representations than other methods, and our trajectory analysis shows it maintains geometrically simple latent embeddings with low curvature. We further show that MotionJEPA improves downstream planning success under static-background distractors across four environments.

Temporal Information Retrieval (TIR) has been increasingly critical given the rise of Retrieval-Augmented Generation (RAG). Since temporally mismatched evidence can be highly misleading, TIR aims to retrieve documents that are both semantically and temporally relevant to a query. Two TIR paradigms have emerged - temporal retrievers and temporal re-rankers - differing in how temporal relevance is modeled. While these paradigms provide complementary strengths, our analysis reveals that each alone falls short of robust TIR: temporal retrievers provide flexible query understanding via learned representations, but often fail to explicitly account for temporal constraints; temporal re-rankers can enforce such constraints more explicitly, but often rely on predefined re-ranking rules. To address this, we propose Q-TIE, a re-ranking framework based on learned Temporal Intent Extraction (TIE). By introducing a TIE model that maps each query's temporal constraint into a unified interval representation (i.e., $\langle t_{start}, t_{end} \rangle$), Q-TIE generalizes beyond predefined rules via model-based learning while explicitly modeling temporal constraints as a separate signal - jointly achieving what each paradigm typically trades off. Experiments demonstrate that Q-TIE consistently outperforms existing TIR methods with stronger generalizability across temporal query types, and provides a lightweight yet effective add-on for temporally-aware RAG pipelines. Code: https://github.com/ssoy0701/Q-TIE.

Every nondegenerate bimatrix game has a Nash equilibrium of Shapley index +1, since all equilibria are isolated, have index +1 or -1, and their indices sum to +1. We prove that the following promise search problem is PPADS-complete: given a rational bimatrix game promised to be nondegenerate, find an exact Nash equilibrium of index +1. The nondegeneracy promise can be removed if nonregular equilibria are also accepted: finding either a regular Nash equilibrium of index +1 or a nonregular Nash equilibrium in an arbitrary rational bimatrix game is also PPADS-complete. To our knowledge, this is the first PPADS-complete equilibrium search problem whose instances are explicit rational normal form payoff matrices, rather than succinct circuits or Turing machines, and thereby addresses an open question posed by Daskalakis [2019].

This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in \(\mathbb{R}^3\). The objective is to stabilize a one-dimensional path on the manifold without imposing a temporal parameterization, thereby distinguishing the problem from trajectory tracking. Working in a geometric framework, we propose two feedback laws: a static controller for prescribed nonzero translational speed and a dynamic controller based on a dynamic extension of the translational speed. By lifting the path to the unit tangent bundle of the surface, we characterize the corresponding path-following manifold and establish its control invariance. We then show that the proposed controllers render the path-following manifold locally exponentially stable under suitable regularity conditions. A numerical simulation illustrates the proposed controller. Code and animations are publicly available at https://gradslab.github.io/UnicycleOnManifolds/.

Modern music streaming platforms face a persistent tradeoff: exploiting familiar content versus driving the exploration of novel items. While users frequently desire discovery, they hesitate to select unknown artists over proven favorites. Providing transparent, natural language rationales that explain why an unexplored item is recommended lowers this barrier. However, while Large Language Models (LLMs) excel at this nuanced explainability, their real-time deployment is severely bottlenecked by prohibitive inference costs and computational overhead. In this paper, we present an industry case study of a decoupled recommendation architecture that successfully scales exploration without compromising latency. Our system isolates LLM inference asynchronously offline, pre-computing personalized candidate pools of undiscovered artists alongside tailored rationales. Large-scale online A/B experiments validate our design. We demonstrate that combining LLM-backed recommendations with these explanatory rationales significantly reduces the trust barrier for new content, yielding statistically significant improvements in both user exploration and overall engagement on the discovery surfaces.

Clinical multimodal models must often predict before all chest X-ray (CXR) and electronic health record (EHR) inputs are available. Existing approaches align observed representations, model missingness, or reconstruct across modalities, but do not jointly exploit within-patient and clinically similar inter-patient evidence. We propose GLR-MM, a Graph-Based Global-Local Reconstruction framework for early ICU mortality prediction. It maps five CXR-EHR modalities to a shared space, reconstructs missing embeddings through complementary local cross-modal and global graph-attention branches, adaptively fuses their estimates, and optimizes class-balanced prediction, reconstruction, and contrastive objectives. On 9,620 MIMIC-derived ICU stays, we evaluate 10%, 30%, and 50% random modality missingness with shared deterministic masks. MUSE performs better under mild and moderate missingness, whereas GLR-MM achieves higher AUROC and AUPRC at 50% by 0.0088 and 0.0249, respectively. These results indicate that graph-guided reconstruction is most useful when inputs are severely incomplete.