Papers

Safety Filters (SF) are leveraged to design certifiably safe controllers, which ensures forward invariance on a defined safe set when the filter is feasible. Predictive Safety Filters (PSF) embed these constraints to a closed-loop model-based optimization method to improve constraint satisfaction, and reduce feasibility loss caused by myopic, one-step filtering. Related viability-based methods emphasize approximating a viability kernel which ensures admissible control for all future time, but requires significant computational expense. This work introduces a Jacobian-based kinematic safety filter leveraging an augmented state variable with task-space velocity and filters task-space acceleration to preserve the feasibility of a low-level filter while enforcing joint position and velocity. The proposed method introduces a nested Quadratic Program (QP) formulation, defines a conservative inner approximation of viability envelope and computes a viable planner online. The method is validated in a simplified 2R planar manipulator simulation environment and shows significant improvement compared to a baseline Control Barrier Function Quadratic Program (CBF-QP) based filter. The experiments highlights the improvements in terms of computation time compared to traditional PSF and Reference Governor approach while also showing significant reduction in feasibility violations. Lastly, a simplified demonstration on a simulated 6-DoF manipulator highlights the potential scalability of the method to higher degree-of-freedom setups.

In Fermi's 1926 note, the expression assigned to the probability that all partial sums remain below a threshold is the complementary crossing probability. We obtain the correct probability from the same diffusion equation and locate the inconsistency in the final integration. We then state the limit for independent increments under the Lindeberg condition. A counterexample with smooth densities shows that small individual variances do not suffice to justify this limit. The probabilistic results are classical; the purpose of this note is to reconcile the stated event with the printed calculation and to make the sufficient hypotheses for the discrete limit explicit.

Motion planning for automated vehicles in interactive traffic has to simultaneously ensure safety, respect traffic rules, and maintain comfortable progress under multi-modal behavior uncertainty. Imposing all these requirements as hard constraints reduces feasibility, whereas treating them all as costs allows safety-critical requirements to be traded against progress. We propose a hybrid hard–soft Signal Temporal Logic (STL) MPC framework that optimizes a single shared ego trajectory against every retained behavior hypothesis: minimum-distance and speed predicates are imposed as explicit hard constraints, while soft STL robustness terms shape clearance, comfort, and interaction quality within the resulting feasible driving corridor. This retains robustness to discrete interaction modes without branch-specific contingent ego policies. We further identify substantial symbolic graph-construction overhead and introduce reachability-certified relevance screening and vectorized symbolic construction to reduce computational cost while preserving the feasible set and objective. Closed-loop Monte Carlo evaluation over six highway and intersection scenarios shows the highest strict success rate among the compared planners with no observed collisions or rule violations, at roughly a quarter of the planning latency of the unoptimized formulation. An ablation study separates the two layers: the hard constraints define the safety envelope, while the soft terms improve clearance and motion quality within it.

Predictive coding networks (PCNs) promise properties not offered by backpropagation-trained networks: learning from purely local information, a single network that both discriminates and generates, and flexible inference by energy minimization. However, their iterative inference is expensive, making hardware acceleration desirable, and a useful, efficient accelerator needs both depth and aggressive quantization. Canonical state-based PC delivers neither: its inference signal decays exponentially with depth, so deep models fail to train, and low precision makes it worse. We show that pairing two recent methods carries the full PCN property set into the deep, 4-bit regime: bidirectional PC (bPC), which unifies discrimination and generation, and the error-based reparameterization (ePC), which optimizes prediction errors rather than states during inference. Error optimization delivers the output signal to every layer in a single backward pass, removing the signal decay; one additional element, global-norm clipping of the error gradients, stabilizes the error dynamics at depth. The resulting ePC+bPC model trains stably up to at least eight layers and retains its full-precision accuracy and clean class-conditional generation under W4A4E4 quantization-aware training, across FP4 and three posit formats. On six-layer networks, where state-based bPC collapses to chance, ePC+bPC classifies more than 50 accuracy points above it after one epoch of training, with class-conditional generations 5-9x better in RMSE. 4-bit quantization is nearly free: full-precision and 4-bit accuracies differ by at most ~5 points, and by under two in the best-performing formats. We characterize the two failure modes the method overcomes, bounded signal decay in state-based PC and error divergence in unregularized error optimization, and discuss implications for a 4-bit-native PCN accelerator.

Computing equilibria in high-dimensional continuous games requires learning and representing rich, multi-modal strategy distributions, something conventional neural policies struggle to achieve. Diffusion models offer a natural solution, but standard diffusion training requires direct samples from a fixed target distribution, which are generally unavailable under iterative game-solving updates. We propose a diffusion-based framework for equilibrium computation that enables diffusion-based variants of Online Mirror Descent (OMD) and Fictitious Play (FP). Our approach derives a reweighted score-matching objective that trains diffusion policies without requiring direct samples from each updated policy. Our main method, DiffNash, combines the fast convergence of OMD with the sample efficiency of FP by reusing past actions through a replay buffer. To correct the resulting distribution shift from sample reuse, we derive an unbiased estimator of the difference between current and past policies' Evidence Lower Bounds, whose exponential provides a tractable proxy for the corresponding importance weight without evaluating diffusion likelihoods. We evaluate our approach on forest protection games and continuous Colonel Blotto games, reducing the Nash gap over the strongest baseline by 35.6% and 24.7%, respectively, with minimal hyperparameter tuning.

Learning solution operators for partial differential equations (PDEs) requires models that can represent spatial structure across grids and scales. This becomes especially important in time-dependent problems, where the learned operator is often used autoregressively: each predicted state is fed back as input to predict future states. In this setting, small spatial errors can be repeatedly propagated through the learned dynamics, leading to instability and drift, vitiating long-term solution fidelity. We propose Mesh-Free Convolutions (MFCs), filters defined in continuous space and discretized only at evaluation time. This allows the same learned filters to be applied across resolutions. Rather than imposing a grid-dependent stencil or a fixed spectral cutoff, MFCs learn smooth scale-dependent filtering and include directional terms for transport-like behavior. Across fluid-dynamics and weather-forecasting benchmarks, MFC-based models produce stable long-horizon rollouts, transfer reliably across resolutions, and better preserve long-time statistics. These results suggest that continuous, mesh-free filtering is a useful inductive bias for PDE operator learning, especially in autoregressive prediction.

Border crossing points are stochastic service systems in which traffic demand, traveler categories, registration status, inspection requirements, staffing, and lane availability interact on multiple time scales. This paper extends an earlier multimodal queue-management framework by introducing an implementation-oriented, multi-horizon forecasting and decision-support architecture based on Light Gradient Boosting Machine (LightGBM) models. In contrast to a single forecasting block, the proposed approach constructs horizon-specific regressors for 15, 30, 60, and 120 min forecasts and jointly estimates future waiting time and queue lengths. The models operate on temporally lagged traffic, service, density, and queue features, while an operational layer incorporates lane compatibility, officer availability, possibly degraded resources, traveler category, preregistration information, and human-approval constraints. Quantile LightGBM models provide 95% prediction intervals for waiting-time forecasts. Beyond prediction, the framework produces machine-readable recommendations, alerts, aggregate key performance indicators, confidence information, and integration outputs suitable for border resource-management and decision-support systems. The results establish a reproducible synthetic-data baseline and a practical interface for subsequent validation with operational border-crossing data.

Recent trackers built on foundation models such as the Segment Anything Model (SAM) achieve strong performance by propagating object masks through memory. However, this strength is also a key source of failure: under occlusion, reappearance, or distractors, an incorrect prediction can enter the tracking loop and be propagated over time, resulting in persistent identity drift. Existing approaches seek to prevent such failures through improved memory and temporal modeling, but once a failure occurs, the tracker has no explicit mechanism to recognize or correct it. We address this gap with Dual-Agent, a failure-aware tracking framework that complements propagation with explicit verification and recovery. We address this gap with Dual-Agent, a failure-aware tracking framework that complements propagation with explicit verification and recovery. A vision-language verification agent first reasons over spatio-temporal context to determine whether the tracker is still following the target. When a failure is detected, a correction agent uses temporal context to recover the target before tracking continues. The correction agent is trained on real SAM3 failures, augmented with targeted identity-switch and distractor perturbations that expose it to challenging ambiguities during recovery. On LVOS-v2 and SecVOS, Dual-Agent improves SAM3 by 1.2 and 2.7 $J\&F$, respectively. Importantly, the proposed framework transfers without retraining to SAM2.1, SeC, and Cutie, as well as to long-term video object tracking benchmarks including LaSOT-ext, TNL2K, and VOT-LT2022. Our results show that explicitly reasoning about when tracking fails and how to recover provides a complementary path to robust tracking beyond improving propagation alone. Project page: valaybundele.github.io/Dual-Agent.

The $\Lambda p$ invariant-mass spectrum near the two physical $\Sigma N$ thresholds in the $K^-d\to\pi^-\Lambda p$ reaction is studied as a probe of the low-energy $\Sigma N$ interaction. The reaction is formulated up to two-step processes, and the coupled $\Lambda p$, $\Sigma^+n$, and $\Sigma^0p$ channels are described within a constant-$K$-matrix model constrained by spin-triplet scattering lengths. The dependence of the $\Sigma N\to\Lambda p$ conversion amplitude on these scattering lengths is examined, and the relation between its line shape and nearby pole positions is investigated. The resulting invariant-mass spectra are studied at different incident kaon momenta and compared qualitatively with existing experimental data. The effects of the spin-singlet $YN$ amplitude and the deuteron wave function are also examined. The line shape near the $\Sigma N$ thresholds is found to be particularly sensitive to the complex spin-triplet $I=1/2$ $\Sigma N$ scattering length, indicating that measurements of this spectrum can provide useful constraints on the low-energy $\Sigma N$ interaction.

Precision measurements of nuclear $\beta$ decay offer a powerful route to tests of physics beyond the Standard Model, but interpreting measurements spectra and correlation observables requires control of subtle nuclear-structure effects. This chapter develops a framework for calculating higher-order corrections–small contributions that can become important at the precision sought in searches for new interactions. After motivating their role in $\beta$-decay observables (with radiative corrections treated in the accompanying chapter), we introduce the relevant kinematics and multipole expansion of the shape factor, identify the subleading contributions, and present the impulse-approximation multipole operators. We then describe the nuclear many-body methods used to obtain the required states and transition densities, and derive the corresponding operator matrix elements in the harmonic-oscillator basis. Taken together, these ingredients enable systematic calculations of nuclear shape factors beyond the long-wavelength approximation, including higher-order multipoles where needed. By helping distinguish Standard-Model recoil effects from possible signatures of new physics, this framework supports the interpretation of increasingly precise $\beta$-decay experiments.

Given a surface of genus $g \geq 2$, its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that the inf spectrum has exponential growth with coefficients that only depend on g, improving the earlier double exponential upper bound. The proof involves developing a number of tools including the process of "thickening" a surface and the notion of model surfaces. These tools may be of independent interest.

GarageWorks is a lightweight FPGA testing framework that enables the same cocotb testbench to be used for both software RTL simulation and FPGA-accelerated hardware simulation. A shared abstraction hides backend-specific interfaces, while synthesizable Advanced eXtensible Interface (AXI) dispatchers provide design-under-test (DUT)-specific control and test operations on the FPGA. GarageWorks is intended for rapid bare-metal testing of standalone designs and on-chip processing logic for scientific sensors, rather than full SoC-level prototyping. The framework has been validated on AMD Alveo V80 FPGAs with several internal designs and provides initial support for AI-assisted generation of DUT-specific test components.

Agent environments are essential for large language model (LLM) development. They use programmatic verifiers to turn complex outcomes into rewards. Verifiers can be attacked into awarding full credit to cheating agents without completing the intended task, causing inaccurate evaluation and misalignment in training. As agent environments scale in numbers and difficulty, so must the repairing of exploitable verifiers. To this end, we ask whether today's model with scaled compute can automatically harden agent environments to prevent potentially stronger future models from reward hacking. We introduce a scalable, fully automatic approach to weak-to-strong verifier hardening. It first sets up an isolated verifier sandbox that agents cannot directly modify, then uses a hacker-fixer loop to find and repair remaining verifier vulnerabilities. We apply this loop to Terminal Bench, KernelBench, and SETA, substantially reducing attack success across these agent environments. The iterative design scales with the hardening budget, producing progressively stronger defenses as the number of loop iterations increases and outperforming the static, non-iterative baseline. An earlier version of our hacker-fixer loop has been adopted by the official Terminal Bench repository as a way to audit exploits in its environments. Project page: https://verifier-hardening.github.io/.

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra with root system $\Phi$. A subset $S\subseteq\Phi$ is closed if $\alpha,\beta\in S$ and $\alpha+\beta\in\Phi$ imply $\alpha+\beta\in S$. For finite and affine Kac-Moody algebras, this closure property is known to extend from pairs to arbitrary finite sums that are roots. We prove that every closed subset of the root system of any symmetrizable Kac-Moody algebra is closed under arbitrary finite sums that are roots. The proof uses real-root strings and simultaneous separation of positive imaginary roots, together with an addition lemma for fundamental imaginary roots. As an application, we extend a necessary condition for wideness of regular subalgebras from finite and affine types to all symmetrizable Kac-Moody algebras: the symmetric closure of the roots associated to a wide regular subalgebra is the entire root system.

Autoregressive (AR) video generation enables long-horizon synthesis but requires repeated forward passes through large diffusion transformers. Training-free caching reduces this cost by reusing intermediate computation, yet existing controllers often couple two decisions: when to synchronize the cache exactly and how much computation to repair between synchronizations. We introduce Frequency-Step Cache (FSC), which separates these roles. FSC schedules exact full-computation anchors on a dense-to-sparse trajectory, while a lightweight latent-space risk based on frequency-resolved drift and token age controls inter-anchor repair through whole-step replay, selective token recomputation, or full repair. On SkyReels-V2, whole-step reuse provides most of the acceleration, while selective token computation is most effective as fidelity repair. A controlled ablation shows that using one reactive signal for both synchronization and repair reduces fidelity at matched latency, with the same separation advantage observed on FramePack and Matrix-Game. Across multiple autoregressive video backbones, FSC improves speed-quality trade-offs. On SkyReels-V2, FSC-Speed reaches 2.36x speedup versus MotionCache's 2.275x while improving SSIM by 0.019 and PSNR by 0.5 dB. At MotionCache-matched speed, FSC-Quality improves SSIM by 0.031 and PSNR by 1.0 dB and lowers LPIPS by 0.024. Without retuning, FSC-Quality transfers to SkyReels-V2 14B at 2.12x speedup versus 1.79x for MotionCache.

With ever increasing personalized large language model (LLM) services, the next question to answer is how to improve the quality of services/users' experiences, which is indicated by personalized LLM generation accuracy/quality and inference latency. Although state-of-the-art designs, e.g., parameter-efficient fine-tuning (PEFT), retrieval-augmented generation (RAG) or Full PEFT+RAG, can help, they largely ignore the heterogeneous semantic concentrations of users' historical data and cannot fully unleash the potential of personal data for personalized LLM performance enhancement. In this paper, we propose PEFT Union RAG (PUR), a novel “fast and accurate” approach that exploits the semantic concentration of users' personal historical data to split workload between PEFT and RAG, aiming to improve personalized LLM performance in terms of better generation accuracy/quality and lower inference latency. Briefly, PUR partitions user's personal historical data and assigns semantic concentrated “core” information to PEFT for offline parametric fine-tuning, while retaining dispersed information for RAG. During the online LLM inference, PUR directly generates responses for “core” queries covered by the PEFT region and invokes RAG only for sporadic “peripheral” queries. Experimental results show that, by appropriately splitting workload between PEFT and RAG, PUR consistently achieves the best generation accuracy/quality for various users across multiple tasks, while reducing inference latency by 14.4%–46.6% compared with the best performed method.

We prove sharp residual stability estimates for the critical Poincaré-Sobolev equation near sums of one positive hyperbolic solution and one projected Euclidean bubble in dimensions at least four. The estimates are uniform in the relative positions of the centers. The sharp rate is linear except in dimension six, where it contains a square root of a logarithm. For nonnegative functions, the same estimates hold under an energy constraint near the sum of the two profile energies for \(\lambda\) outside a finite set, and an additional mass constraint removes this restriction. For arbitrary finite numbers of profiles, we identify and realize all nonnegative Palais-Smale levels. We characterize the parameters at which different pairs of profile numbers have the same energy and show that the limiting energy and mass determine both profile numbers.

Supervised machine learning in high-energy physics (HEP) requires training on labeled simulations of particle collisions, which are known to be unfaithful to the underlying physics. This leads to significant inaccuracies and biases in the transfer of trained models to real data, limiting the power of deep learning methods. Self-supervised learning (SSL) is a promising alternative for pretraining directly on real, unlabeled data. However, existing techniques largely operate with inductive biases inspired by domains such as images and natural language. We propose RINO (Renormalization Group DIstillation with NO Labels), which, for the first time, exploits the fundamentally multi-scale renormalization group structure of high-energy jet formation as a physically grounded source of SSL views. We define teacher-student representations across energy scales using different levels of hierarchical clustering, aligned via DINO-style self-distillation. To mirror the background-dominated nature of real collider data, RINO pretrains exclusively on jets from quantum chromodynamics (QCD) processes and is evaluated on out-of-distribution (OOD) transfer to rare signal classes. In our controlled data-efficiency study, RINO matches fully supervised training on JetNet after finetuning on only 1% of the labeled data. With the full labeled dataset, RINO improves OOD classification accuracy on top-quark jets by 5.9% and, without retraining, improves AUC on the unseen Higgs boson decay channel $H \to 4q$ by 4.1% over the strongest SSL baseline. Scale-structure diagnostics reveal that DINO-style self-distillation permits our backbone to retain scale-dependent structure. Ablation studies show that this accounts for an 8.6% OOD accuracy gap with respect to alternative SSL paradigms such as SimCLR. Code is available at https://github.com/zichunhao/RINO.

We study the role of momentum fractionation in the development of chaos on smooth 3-charge supergravity solutions of D1-D5 theory, specifically momentum-fractionated superstrata. We probe the chaos through the dynamics of null geodesics and waves. On fractionated backgrounds, both geodesics and waves show uniformly strong chaos (large chaotic sea and near-perfect agreement with the Berry random wave hypothesis). In contrast, geodesics and waves on single-mode (non-fractionated) superstrata are closer to separability (although still chaotic). We discuss a possibility that such dichotomy can be related to the expectation that monotone BPS states are less chaotic than fortuitous ones. Finally, we explain why our chaos probes are meaningful for microstate geometries even though they become trivial in the black hole limit.

We give a microscopic derivation of the semi-classical entropy of the black holes of 3d Lovelock gravity with an infinite tower of regularized Lovelock corrections, which include the regular BTZ black holes found recently. Working in the mini-superspace formalism, we show that the reduced action and its boundary term can be obtained in closed form at all orders in terms of the generating function of the couplings. Assuming the ground state is described by the soliton obtained from the static black hole by a double Wick rotation, we compute the soliton mass and reproduce the semi-classical entropy from the Cardy formula without central charges for arbitrary couplings. We then extend the mini-superspace to stationary configurations, compute the mass and the angular momentum of the rotating black holes obtained by a boost, and verify the Cardy formula in the presence of rotation.

In multi-group learning, a single predictor must perform nearly as well as the best hypothesis in a class on every group in a rich, possibly infinite and overlapping, collection of subpopulations. The known algorithms with the optimal sample complexity keep track of every pair of a group and a hypothesis, which is impossible for the large classes of interest, and the known oracle-based algorithms have a worse rate. We ask whether the optimal rate can be attained by a learner that accesses the classes only through an empirical risk minimization (ERM) oracle. We give an algorithm that uses $\tilde{O}((d_G+d_H)/\varepsilon^2)$ samples and polynomially many calls to a weighted ERM oracle over pairs of a group and a hypothesis, where $d_G$ and $d_H$ are the VC dimensions of the group and hypothesis classes and $\varepsilon$ bounds the excess risk on every group, weighted by its probability. We also show a matching lower bound of $\Omega((d_G+d_H)/\varepsilon^2)$ samples for every learner even with unlimited computation, so oracle efficiency costs no additional samples. We also consider a natural special case in which every input belongs to at most $k$ groups and these groups can be listed. In this case, an ERM oracle for the hypothesis class alone suffices, with $\tilde{O}((d_H+\log k)/\varepsilon^2)$ samples in the agnostic setting and $\tilde{O}((d_H+\log k)/\varepsilon)$ samples when every group has a hypothesis that is correct on it.

Reusable skills improve multimodal agents without updating model weights, but their effectiveness depends on both the evidence presented and the procedure used to read it. We introduce ViewCraft, which jointly evolves an executable evidence interface and its reading procedure. The interface selects, transforms, and organizes observations; the reader interprets the resulting views. Failure traces guide revisions, replay and paired evaluation retain useful changes, and interface projection recovers visual edits from eligible rejected joint proposals. Across eight benchmarks, ViewCraft improves over direct execution by an average of $6.1$ points in task score, with gains on every benchmark. The advantage persists at a matched input-token budget. On all five multi-source tasks, the learned interface uses 8%-15% fewer input tokens than Initial skill. The learned skills also transfer across executors and outperform direct execution in every evaluated transfer, supporting evidence construction and reading as a coupled, reusable skill.

The set \(P_{n}\) consists of the characteristic vectors of pedigrees, which are combinatorial encodings in one-to-one correspondence with Hamiltonian cycles. For \(n \geq 4\) and \(\tau_{n} = \binom{n}{3}-1\), the Membership Problem for the Pedigree Polytope (M3P) asks whether a given vector \(X \in \mathbb{Q}^{\tau_{n}}\) belongs to \(\mathrm{conv}(P_n)\). This paper gives a complete account, with the full proof statements and machine-verified Lean~4 certificates, of the necessary and sufficient (\NS) condition established in Chapter~5 of Pedigree Polytopes: New Insights on Computational Complexity of Combinatorial Optimisation Problems (Arthanari, 2023): membership of $X$ in $\mathrm{conv}(P_n)$ is characterised by the feasibility, at every stage $k=4,\dots,n-1$, of a recursively constructed layered network, together with, when needed, a multicommodity flow problem $\mathrm{MCF}(k-1)$ achieving its maximum possible flow $z_{\max}$. We present the construction, the \NS{} condition itself, and the proofs of this characterisation, together with the resulting polynomial-time algorithm for M3P. Both directions of the \NS{} condition — sufficiency and necessity (the multicommodity-flow feasibility argument of the book's Chapter~5) — are machine-verified in Lean~4/Mathlib4 with zero unresolved sorrys in either dependency chain. The \NS{} characterisation therefore follows directly from the two machine-checked implications. The complete Lean~4 project is publicly available. A companion introductory article (arXiv:2507.09069) presents the same material for a broader readership, without the Lean~4 verification; the present paper adds full statements, proof sketches, and the complete machine-checked certificates.

We present a far-field beam calibration of the Simons Observatory (SO) Small Aperture Telescopes (SATs) using scanned single-frequency measurements of a drone-mounted source emitting in the 90 GHz band, where the SATs have an angular resolution of $\sim$30$'$. We then compare the results from two campaigns in April and December 2025 to the band-averaged beams from planet observations by the SATs. Measuring the telescope beam response at different frequencies across the observing bands enables modeling the system's frequency-dependent behavior. This helps track optical non-idealities. The comparison with planet beams informs the frequency resolution necessary to accurately reconstruct the band-averaged beams in this way; it uses only the average drone and planet products, as it is intended to demonstrate the feasibility of the frequency-resolved calibration scheme rather than to set the precise beam covariance and instrument requirements. We find that the beams of the two SATs near 90 GHz follow the frequency scaling expected for diffraction-limited optics, with only modest deviations observed in the nearest lobes of one telescope. We establish consistency between the real band-averaged planet beams and the synthesized drone band-averaged beams for the center wafers of both telescopes, with an average deviation smaller than 4% for multipoles $\ell < 500$.

Large language models (LLMs) have shown considerable promise in clinical decision support. However, existing approaches often rely on multi-step reasoning or multi-agent collaboration to execute clinical guidelines, introducing substantial computational overhead without reliably preventing decision errors. To address these limitations, we propose a framework for Medical Decision Execution (MedDEx) that integrates structured patient states with deterministic rule execution to support guideline-based treatment planning. MedDEx separates clinical record interpretation from guideline execution, leveraging LLMs to extract patient information and generate treatment plans while assigning guideline-defined decision logic to a rule executor. Experiments across multiple clinical guideline benchmarks demonstrate that MedDEx improves decision accuracy while reducing inference costs. Further analyses highlight the critical roles of structured patient representations and deterministic rule execution, suggesting that additional LLM reasoning does not necessarily translate into better guideline adherence.

We study a portal of a $Z_2$-odd singlet scalar and a vector like down quark, in which a right handed flavor breaking spurion extends the portal coupling from $b_R$ to $d_R$ and $s_R$. This single coupling vector links the $b\to s$, $b\to d$, and $s\to d$ transitions. We compute the one loop dipole and $\Delta F=2$ Wilson coefficients, and show that a real scalar generates no $\Delta F=2$ amplitude at one loop. Using a seven observable profile likelihood of $B$ meson mixing, $\epsilon_K$, and radiative decays, with the CKM, lattice, and short distance inputs treated as nuisance parameters, we compare a generic spurion, minimal $U(2)^3$ with a free size of the light quark couplings, and a CKM-aligned ansatz. We have found that the present data cannot yet test the flavor structure: the Standard Model is compatible with the data, with a pseudo experiment $p$-value of $0.20$, and no direction of the light quark couplings can be excluded at 95% CL. For $M_D\simeq m_{\mathcal{S}}=1$ TeV and $|\lambda_b|=1$, the relative light quark coupling $\epsilon_R$ is bounded at 95% CL by $0.227$ for a generic spurion and by $0.211$ for minimal $U(2)^3$. More precise measurements of the $B_s$ mixing phase at the LHC and of $\sin2\beta$ at LHCb and Belle-II, together with improved lattice and CKM inputs, can make the minimality of the flavor structure testable if a deviation from the Standard Model is observed.

Deep Research agents rely on long-horizon reasoning and iterative tool use to solve complex information-seeking tasks. However, adaptive decision-making over these trajectories remains challenging, as agents may stop prematurely when further evidence is needed, continue unnecessarily after sufficient evidence has been gathered, or fail to redirect unproductive trajectories. Existing solutions either require costly model retraining and dense turn-level supervision, or rely on heuristic control rules that are not directly optimized for downstream research utility. This motivates a lightweight, utility-aware alternative for Deep Research control. We formulate adaptive rerouting in long-horizon Deep Research as a state-conditioned trajectory correction problem. Based on this view, we introduce RIVO, a lightweight plug-in framework for adaptive trajectory correction. The agent estimates its research state from lightweight signals and determines whether trajectory redirection is needed. Once triggered, the plug-in modifies the Host token logits to steer generation toward a more promising research direction. Theoretical analysis shows that, under a value-alignment condition and bounded local curvature, a sufficiently small logit intervention can locally improve expected downstream research utility. We further construct BrowseCore, a curated dataset with a paired local corpus, for efficient and controlled Deep Research experimentation. Building on this resource, the plug-in is trained from downstream outcomes, enabling it to learn corrections that improve subsequent research and final task performance. Extensive experiments across multiple Deep Research benchmarks and control settings demonstrate the effectiveness of our method, showing that lightweight logit intervention can improve long-horizon research without retraining the underlying Host model.

The extension complexity $\operatorname{xc}(P)$ of a polytope $P$ is the minimum number of facets of a polytope that projects onto it. Motivated by the complexity of neural networks, Hertrich and Loho introduced the virtual extension complexity $\operatorname{vxc}(P)$ of a polytope $P$, which is the minimum of $\operatorname{xc}(Q) + \operatorname{xc}(R)$ among all polytopes $Q$ and $R$ such that $P+Q=R$. We show the following results pertaining to virtual extension complexity. First, we resolve the core open problem on the topic by showing the virtual extension complexity can be exponentially smaller than extension complexity. Second, we show there are matroid base polytopes with exponential virtual extension complexity by adapting a semi-algebraic counting argument by Hrubeš that extends the counting arguments of Rothvoss. Finally, we show that the maximum virtual extension complexity of a polygon with $n$ vertices is $\Theta(\sqrt{n})$. This resolves an analogue of a question on extension complexity of Fiorini, Rothvoss, and Tiwary in 2011 in the case of virtual extension complexity.

Phase-annotated conversational data is essential for studying the progression of online grooming of minors and for developing early warning tools. However, the only publicly available source (i.e., Perverted-Justice archive, which contains a subset coded using ChatCoder) is small, outdated, and frozen. We present a synthetic corpus of groomer-victim exchanges, generated using a retrieval-augmented pipeline running on institutional hardware. This pipeline uses an openly available, eight-billion-parameter, refusal-ablated language model. The corpus was created using the five stages of the responsible-generation protocol for synthetic datasets: ontology-driven design based on the ChatCoder luring-communication scheme (eight communicative tags mapped onto four grooming phases); multi-model prompt testing; human-in-the-loop supervision; semantic and feature-level validation; and modality-aware documentation. The released corpus contains 2,121 unique exchanges across seven tags and four phases, each accompanied by a Plutchik emotion field. Validation quantifies the integrity and lexical profile of the corpus, as well as the reproduction of real seed lines, in-domain label recoverability (tag accuracy: 0.85; phase accuracy: 0.93) and its transfer to real ChatCoder offender lines, which were coded automatically at the eight-tag level (31,640 lines) and by human coders at the three-construct level (10,876 posts). Accuracy was measured for lexical and sentence-embedding features, while a real-versus-synthetic discriminator was able to separate the two domains with 91% accuracy. The scope of the corpus includes controlled, phase-conditioned experimentation, pipeline development and augmentation alongside real data and awareness material. The corpus, its datasheet and the audit code are released with vetted access.

Multi-Agent Systems (MAS) have shown strong capability in solving complex tasks by assigning different agents specialized roles and corresponding subtasks. However, agents may overstep their assigned responsibilities and perform subtasks belonging to other roles, which can disrupt workflow, reduce system efficiency, and degrade task performance. To address this issue, we investigate role-related patterns in the model's internal activation space and uncover two key observations: (i) role instructions induce consistent directional shifts in activation space, and (ii) role-adherent and role-overstepping trajectories exhibit distinct activation patterns. Based on these observations, we propose Dynamic Role Activation Steering (DRAS), a lightweight and effective inference-time activation intervention approach to reduce role overstepping in multi-agent collaboration. Specifically, DRAS constructs a role steering vector and a lightweight role-overstepping detector for each role. During LLM generation, the detector estimates the probability of role overstepping from the current activation state, and DRAS dynamically adjusts the steering strength accordingly to guide the agent toward its assigned responsibilities. Experimental results show that DRAS effectively reduces the number of role-overstepping trajectories by up to 86.6% compared with Vanilla MAS, thereby improving task quality score by 10.0%–11.1%, achieving a 1.50$\times$–1.61$\times$ task-completion speedup, and reducing token consumption by 26.8%–38.7%.