We study the average-case hardness of establishing that a graph does not have a large clique in both proof and communication complexity. We show exponential lower bounds on the length of cutting planes and bounded-depth resolution over parities refutations of the binary encoding of clique formulas on randomly sampled dense graphs. Moreover, we show that the randomized communication complexity of finding a falsified clause in these formulas is polynomial.

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

Recently, post-training methods based on reinforcement learning, with a particular focus on Group Relative Policy Optimization (GRPO), have emerged as the robust paradigm for further advancement of text-to-image (T2I) models. However, these methods are often prone to reward hacking, wherein models exploit biases in imperfect reward functions rather than yielding genuine performance gains. In this work, we identify that normalization could lead to miscalibration and directly removing the prompt-level standard deviation term yields an optimal policy ascent direction that is linear in the advantage but still limits the separation of genuine signals from noise. To mitigate the above issues, we propose Super-Linear Advantage Shaping (SLAS) by revisiting the functional update from an information geometry perspective. By extending the Fisher-Rao information metric with advantage-dependent weighting, SLAS introduces a non-linear geometric structure that reshapes the local policy space. This design relaxes constraints along high-advantage directions to amplify informative updates, while tightening those in low-advantage regions to suppress illusory gradients. In addition, batch-level normalization is applied to stabilize training under varying reward scales. Extensive evaluations demonstrate that SLAS consistently surpasses the DanceGRPO baseline across multiple backbones and benchmarks. In particular, it yields faster training dynamics, improved out-of-domain performance on GenEval and UniGenBench++, and enhanced robustness to model scaling, while mitigating reward hacking and preserving semantic and compositional fidelity in generations.

As wearable devices like smart glasses integrate Large Multimodal Models (LMMs) into the continuous first-person visual streams of individual users, the evolution of these models into true personal assistants hinges on visual personalization: the ability to reason over visual information unique to the wearer. We formalize this capability as Personal Visual Context Learning (Personal VCL), the prompt-time capability of using user-specific visual context to resolve personalized queries. To systematically evaluate this, we present Personal-VCL-Bench, a comprehensive benchmark capturing the personal visual world across persons, objects, and behaviors. Our analysis of frontier LMMs identifies a profound context utilization gap, revealing that the mechanisms for leveraging visual evidence, as well as aggregating multiple visual observations, remain critically understudied. Motivated by these findings, we propose the Agentic Context Bank, a strong inference-time baseline that structures a user's visual context into a self-refining memory bank and employs query-adaptive evidence selection. Our baseline approach consistently improves over standard context prompting regimes across tasks and evaluated backbones, demonstrating a practical path towards future personalized LMMs.

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While Lévy processes provide a natural mathematical framework for capturing jumps and heavy tails, Bayesian inference for Lévy-driven stochastic differential equations (SDEs) remains intractable with existing methods: Monte Carlo approaches are rigorous but lack scalability, whereas neural variational inference methods are efficient but rely on Gaussian assumptions that fail to capture discontinuities. We address this tension by introducing a neural exponential tilting framework for variational inference in Lévy-driven SDEs. Our approach constructs a flexible variational family by exponentially reweighting the Lévy measure using neural networks. This parametrization preserves the jump structure of the underlying process while remaining computationally tractable. To enable efficient inference, we develop a quadratic neural parametrization that yields closed-form normalization of the tilted measure, a conditional Gaussian representation for stable processes that facilitates simulation, and symmetry-aware Monte Carlo estimators for scalable optimization. Empirically, we demonstrate that the method accurately captures jump dynamics and yields reliable posterior inference in regimes where Gaussian-based variational approaches fail, on both synthetic and real-world datasets.

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at inference time which is described in the large-token limit by a mean-field continuity equation. Leveraging ideas from the convergence analysis of interacting multi-particle systems, with particles corresponding to tokens, we prove that the token distribution rapidly concentrates onto the push-forward of the initial distribution under a projection map induced by the key, query, and value matrices, and remains metastable for moderate times. Specifically, we show that the Wasserstein distance of the two distributions scales like $\sqrt{{\log(β+1)}/β}\exp(Ct)+\exp(-ct)$ in terms of the temperature parameter $β^{-1}\to 0$ and inference time $t\geq 0$. For the proof, we establish Lyapunov-type estimates for the zero-temperature equation, identify its limit as $t\to\infty$, and employ a stability estimate in Wasserstein space together with a quantitative Laplace principle to couple the two equations. Our result implies that for time scales of order $\logβ$ the token distribution concentrates at the identified limiting distribution. Numerical experiments confirm this and, beyond that, complement our theory by showing that for finite $β$ and large $t$ the dynamics enter a different terminal phase, dominated by the spectrum of the value matrix.

Preserving the admissible set of the ideal magnetohydrodynamics (MHD) equations is important not only for producing physically meaningful numerical solutions, but more importantly for achieving robust computations. In this paper, we develop an optimization-based limiter to enforce admissibility while preserving global conservation and accuracy. For an easy and efficient projection, we decompose the admissible set into slices parameterized by the magnetic energy, so that the MHD projection reduces to a one-dimensional minimization, which can be solved efficiently by the Brent method. The splitting method can be used to efficiently solve the global minimization problem of the optimization-based limiter, which can be used to enforce cell average admissibility in discontinuous Galerkin (DG) schemes, and pointwise admissibility can be further enforced by the Zhang-Shu positivity-preserving limiter. We apply the limiter to high-order DG schemes and present numerical results for a few representative MHD problems.

We study deterministic online algorithms for the problem of chasing sets of cardinality at most $k$ in a metric space, also known as metrical service systems and equivalent to width-$k$ layered graph traversal. We resolve the 30-year-old gap of $Ω(2^k)\cap O(k2^k)$ on the competitive ratio of this problem by giving an $O(2^k)$-competitive deterministic algorithm. This bound is optimal even among randomized algorithms against adaptive adversaries. We also (slightly) improve the deterministic lower bound to $D_k$, defined recursively by $D_1=1$ and $D_{k+1}=2D_k+\sqrt{8+8D_k}+3$, which we conjecture to be exactly tight. For $k=3$, we provide a matching upper bound of $D_3$. Our results imply slightly improved upper and lower bounds for distributed asynchronous collective tree exploration and for the $k$-taxi problem, respectively. Our algorithm generalizes the classical doubling strategy, previously known to be optimal for $k=2$. The previous best bound for general $k$ was achieved by the generalized work function algorithm (WFA), and was known to be tight for WFA. Our improved bound therefore implies that WFA is sub-optimal for chasing small sets.

Large-scale pretraining has made Vision-Language-Action (VLA) models promising foundations for generalist robot manipulation, yet adapting them to downstream tasks remains necessary. However, the common practice of full fine-tuning treats pretraining as initialization and can shift broad priors toward narrow training-distribution patterns. We propose PriorVLA, a novel framework that preserves pretrained priors and learns to leverage them for effective adaptation. PriorVLA keeps a frozen Prior Expert as a read-only prior source and trains an Adaptation Expert for downstream specialization. Expert Queries capture scene priors from the pretrained VLM and motor priors from the Prior Expert, integrating both into the Adaptation Expert to guide adaptation. Together, PriorVLA updates only 25% of the parameters updated by full fine-tuning. Across RoboTwin 2.0, LIBERO, and real-world tasks, PriorVLA achieves stronger overall performance than full fine-tuning and state-of-the-art VLA baselines, with the largest gains under out-of-distribution (OOD) and few-shot settings. PriorVLA improves over pi0.5 by 11 points on RoboTwin 2.0-Hard and achieves 99.1% average success on LIBERO. Across eight real-world tasks and two embodiments, PriorVLA reaches 81% in-distribution (ID) and 57% OOD success with standard data. With only 10 demonstrations per task, PriorVLA reaches 48% ID and 32% OOD success, surpassing pi0.5 by 24 and 22 points, respectively.

Recent advances in 3D generative models have rapidly improved image-to-3D synthesis quality, enabling higher-resolution geometry and more realistic appearance. Yet fidelity, which measures pixel-level faithfulness of the generated 3D asset to the input image, still remains a central bottleneck. We argue this stems from an implicit 2D-3D correspondence issue: most 3D-native generators synthesize shape in canonical space and inject image cues via attention, leaving pixel-to-3D associations ambiguous. To tackle this issue, we draw inspiration from 3D reconstruction and propose Pixal3D, a pixel-aligned 3D generation paradigm for high-fidelity 3D asset creation from images. Instead of generating in a canonical pose, Pixal3D directly generates 3D in a pixel-aligned way, consistent with the input view. To enable this, we introduce a pixel back-projection conditioning scheme that explicitly lifts multi-scale image features into a 3D feature volume, establishing direct pixel-to-3D correspondence without ambiguity. We show that Pixal3D is not only scalable and capable of producing high-quality 3D assets, but also substantially improves fidelity, approaching the fidelity level of reconstruction. Furthermore, Pixal3D naturally extends to multi-view generation by aggregating back-projected feature volumes across views. Finally, we show pixel-aligned generation benefits scene synthesis, and present a modular pipeline that produces high-fidelity, object-separated 3D scenes from images. Pixal3D for the first time demonstrates 3D-native pixel-aligned generation at scale, and provides a new inspiring way towards high-fidelity 3D generation of object or scene from single or multi-view images. Project page: https://ldyang694.github.io/projects/pixal3d/

Memory is a critical component of robotic intelligence, as robots must rely on past observations and actions to accomplish long-horizon tasks in partially observable environments. However, existing robotic memory benchmarks still lack multimodal annotations for memory formation, provide limited task coverage and structural complexity, and remain restricted to simulation without real-world evaluation. We address this gap with RoboMemArena, a large-scale benchmark of 26 tasks, with average trajectory lengths exceeding 1,000 steps per task and 68.9% of subtasks being memory-dependent. The generation pipeline leverages a vision-language model (VLM) to design and compose subtasks, generates full trajectories through atomic functions, and provides memory-related annotations, including subtask instructions and native keyframe annotations, while paired real-world memory tasks support physical evaluation. We further design PrediMem, a dual-system VLA in which a high-level VLM planner manages a memory bank with recent and keyframe buffers and uses a predictive coding head to improve sensitivity to task dynamics. Extensive experiments on RoboMemArena show that PrediMem outperforms all baselines and provides insights into memory management, model architecture, and scaling laws for complex memory systems.

Software developers use metrics to evaluate code quality and productivity, but these practices are still rare in programming education. This project bridges the gap by collecting real-time learning analytics from individual student and whole-class code development logs. This granular, quantitative data provides educators with qualitative insights into the learning process. It allows them to evaluate student comprehension, identify common challenges, and critically assess whether the allocated time for exercises and algorithms is sufficient for mastery. Unlike traditional Learning Management Systems, we propose a novel approach: a plugin for a widely used code editor that captures granular interactions during programming and documentation. The resulting dataset logs coding behaviors, errors, and progress, enabling evidence-based analysis of learning patterns and educational benchmarking. By structuring this real-time programming trail, we support research on teaching methodologies, learner challenges, and skill acquisition. Quantitative metrics complement qualitative assessment by evaluating code, exercise progress, and timestamp logs. Our goal is to provide an open-access database for educators and researchers, fostering data-driven insights to enhance instruction and personalize learning experiences. This work aligns industrial best practices with pedagogical innovation, advancing measurable, empirical approaches to programming education.

We consider anonymous multi-agent path finding (MAPF) where a set of robots is tasked to travel to a set of targets on a finite, connected graph. We show that MAPF can be cast as a special class of multi-marginal optimal transport (MMOT) problems with an underlying Markovian structure, under which the exponentially large MMOT collapses to a linear program (LP) polynomial in size. Focusing on the anonymous setting, we establish conditions under which the corresponding LP is feasible, totally unimodular, and consequently, yields min-cost, integral $(\{0,1\})$ transports that do not overlap in both space and time. To adapt the approach to large-scale problems, we cast the MAPF-MMOT in a probabilistic framework via Schrödinger bridges. Under standard assumptions, we show that the Schrödinger bridge formulation reduces to an entropic regularization of the corresponding MMOT that admits an iterative Sinkhorn-type solution. The Schrödinger bridge, being a probabilistic framework, provides a shadow (fractional) transport that we use as a template to solve a reduced LP and demonstrate that it results in near-optimal, integral transports at a significant reduction in complexity. Extensive experiments highlight the optimality and scalability of the proposed approaches.

Large language and vision-language models increasingly power agents that act on a user's behalf through command-line interface (CLI) harnesses. However, most agent benchmarks still rely on synthetic sandboxes, short-horizon tasks, mock-service APIs, and final-answer checks, leaving open whether agents can complete realistic long-horizon work in the runtimes where they are deployed. This work presents WildClawBench, a native-runtime benchmark of 60 human-authored, bilingual, multimodal tasks spanning six thematic categories. Each task averages roughly 8 minutes of wall-clock time and over 20 tool calls, and runs inside a reproducible Docker container hosting an actual CLI agent harness (OpenClaw, Claude Code, Codex, or Hermes Agent) with access to real tools rather than mock services. Grading is hybrid, combining deterministic rule-based checks, environment-state auditing of side effects, and an LLM/VLM judge for semantic verification. Across 19 frontier models, the best, Claude Opus 4.7, reaches only 62.2% overall under OpenClaw, while every other model stays below 60%, and switching harness alone shifts a single model by up to 18 points. These results show that long-horizon, native-runtime agent evaluation remains a far-from-resolved task for current frontier models. We release the tasks, code, and containerized tooling to support reproducible evaluation.

The overlap gap property (OGP) is a statement about the geometry of near-optimal solutions. Exhibiting OGP implies failure of a class of local algorithms; and has been observed to coincide with conjectured algorithmic limits in problems with statistical computational gap. We consider the Stochastic Block Model (SBM), where the graph has a planted partition with $k$ equal-size blocks which form the `communities', and where, for parameters $p>q$, vertices within the same community connect with probability $p$, while vertices in different communities connect with probability $q$, independently across pairs of vertices. Modularity--based clustering algorithms have become ubiquitous in applications. This article studies theoretical limits of local algorithms based on the modularity score on the SBM. We establish that modularity exhibits OGP on the SBM. This rules out a class of local algorithms based on modularity for recovery in the SBM, and shows slow mixing time for a related Markov Chain. Theoretically this is one of the few instances where OGP has been established for a `planted' model, as most such analyses to date consider the `null' model. As part of our analysis, we extend a result by Bickel and Chen 2009, who established that with high probability, the modularity optimal partition of SBM is $o(n)$ local moves away from the planted partition, where $n$ is the graph size. We show that, with high probability, any partition with modularity score sufficiently near the optimal value is close to the planted partition.

We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.

This work revisits standard policy gradient methods used on restricted policy classes, which are known to get stuck in suboptimal critical points. We identify an important cause for this phenomenon to be that the policy gradient is itself fundamentally myopic, i.e. it only improves the policy based on the one-step $Q$-function. In this work, we propose a generalized $k$-step policy gradient method that couples the randomness within a $k$-step time window and can escape the myopic local optima in MDPs with restricted policy classes. We show this new method is theoretically guaranteed to converge to a solution that is exponentially close in performance to the optimal deterministic policy with respect to $k$. Further, we show projected gradient descent and mirror descent with this $k$-step policy gradient can achieve this exponential guarantee in $O(\frac{1}{T})$ iterations, despite only assuming smoothness and differentiability of the value function. This will provide near optimal solutions to previously elusive applications like state aggregation and partially observable cooperative multi-agent settings. Moreover, our bounds avoid the ubiquitous distribution mismatch factors $||d_μ^{π^*} / d_μ^π||_\infty$ and $||d_μ^{π^*} / μ||_\infty$ enabling the $k$-step policy gradient method to escape suboptimal critical points that emerge from poor exploration in fully observable settings.

Vehicle-to-Everything (V2X) communication has emerged as a promising paradigm for autonomous driving, enabling connected agents to share complementary perception information and negotiate with each other to benefit the final planning. Existing V2X benchmarks, however, fall short in two ways: (i) open-loop evaluations fail to capture the inherently closed-loop nature of driving, leading to evaluation gaps, and (ii) current closed-loop evaluations lack behavioral and interactive diversity to reflect real-world driving. Thus, it is still unclear the extent of benefits of multi-agent systems for closed-loop driving. In this paper, we introduce MDrive, a closed-loop cooperative driving benchmark comprising 225 scenarios grounded in both NHTSA pre-crash typologies and real-world V2X datasets. Our benchmark results demonstrate that multi-agent systems are generally better than single-agent counterparts. However, current multi-agent systems still face two important challenges: (i) perception sharing enhances perceptions, but doesn't always translate to better planning; (ii) negotiation improves planning performance but harms it in complex and dense traffic scenarios. MDrive further provides an open-source toolbox for scenario generation, Real2Sim conversion, and human-in-the-loop simulation. Together, MDrive establishes a reproducible foundation for evaluating and improving the generalization and robustness of cooperative driving systems.

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary objectives. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary-objective SFT within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver the goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies, resulting in two finetuned models. The parameters' difference between the two models can then be interpreted as capability vectors provided by auxiliary objectives. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Internal and external experiments demonstrate that our capability vectors (1) are effective and versatile across diverse models, (2) can generalize to novel environments and embodiments out of the box.

Guardrail Classifiers defend production language models against harmful behavior, but although results seem promising in testing, they provide no formal guarantees. Providing formal guarantees for such models is hard because "harmful behavior" has no natural specification in a discrete input space: and the standard epsilon-ball properties used in other domains do not carry semantic meaning. We close this gap by shifting verification from the discrete input space to the classifier's pre-activation space, where we define a harmful region as a convex shape enclosing the representations of known harmful prompts. Because the sigmoid classification head is monotonic, certifying the worst-case point is sufficient to certify the entire region, yielding a closed-form soundness proof without approximation in O(d) time. To formally evaluate these classifiers, we propose two constructions of such regions: SVD-aligned hyper-rectangles, which yield exact SAT/UNSAT certificates, and Gaussian Mixture Models, which yield probabilistic certificates over semantically coherent clusters. Applying this framework to three author-trained Guardrail Classifiers on the toxicity domain, every hyper-rectangle configuration returns SAT, exposing verifiable safety holes across all classifiers, despite seemingly high empirical metrics. Probabilistic GMM certificates also expose a divergent structural stability in how these models represent harm. While GPT-2 and Llama-3.1-8B maintain robust coverage of 90% and 80% across varying boundaries, BERT's safety guarantees prove uniquely volatile. This 'coverage collapse' to 55% at the optimal threshold reveals a sparsely populated safety margin in BERT, which only achieves full coverage by adopting an extremely conservative pessimistic threshold. These approaches combined, provide new insights on how effective Guardrail Classifiers really are, beyond traditional red-teaming.

Information abstraction reduces the computational cost of solving imperfect-information games by clustering information sets into a smaller number of \emph{buckets}. Existing methods either rely on domain-specific features such as rank or equity, which are inapplicable to games with non-standard payoff structures, or require expensive offline neural-network training on billions of samples. We propose \textbf{Warm-up Expected Value-based Abstraction (WEVA)}, a simple yet effective alternative: run a small number of Counterfactual Regret Minimization (CFR) iterations on the full game as a \emph{warm-up} phase, extract per-hand expected value features at every decision node, form a depth-weighted multi-node feature vector, and apply $k$-means++ clustering to obtain the abstraction mapping. WEVA requires no domain knowledge, no pre-training, and incurs only a small overhead on top of the abstract-game solve. Experiments on three structurally diverse games, with different bucket numbers and CFR variants, show that WEVA consistently outperforms equity-based and rank-based abstractions, reducing exploitability by up to over $80\%$. Surprisingly, as few as $W{=}10$ warm-up iterations already produce abstractions that outperform existing information abstraction methods in most settings. These results establish WEVA as an \emph{effective, efficient, and general} approach to information abstraction in imperfect-information extensive-form games.

Training deep research agents, namely systems that plan, search, evaluate evidence, and synthesize long-form reports, pushes reinforcement learning beyond the regime of verifiable rewards. Their outputs lack ground-truth answers, their trajectories span many tool-augmented decisions, and standard post-training offers little mechanism for turning past attempts into reusable experience. In this work, we argue that rubrics should serve not merely as final-answer evaluators, but as the shared interface that structures policy execution, judge feedback, and agent memory. Based on this view, we introduce RubricEM, a rubric-guided reinforcement learning framework that combines stagewise policy decomposition with reflection-based meta-policy evolution. RubricEM first makes research trajectories stage-aware by conditioning planning, evidence gathering, review, and synthesis on self-generated rubrics. It then assigns credit with Stage-Structured GRPO, which uses stagewise rubric judgments to provide denser semantic feedback for long-horizon optimization. In parallel, RubricEM trains a shared-backbone reflection meta-policy that distills judged trajectories into reusable rubric-grounded guidance for future attempts. The resulting RubricEM-8B achieves strong performance across four long-form research benchmarks, outperforming comparable open models and approaching proprietary deep-research systems. Beyond final performance, we perform thorough analyses to understand the key ingredients of RubricEM.

As generative AI tools increasingly influence creative practice, they raise longstanding HCI questions about how creatives learn complex software and how they can be better supported. We conducted an interview study with artists and hobbyists (n=8) and a follow-up survey (n=159) to understand how this population approaches and seeks guidance for GenAI image tools. We found that creatives commonly use either self-experimentation or tutorials to explore GenAI tools, yet many struggle with confusing AI terminology. To gain further insight into creatives' learning experiences, we developed a research probe to elicit creatives' perceptions of structured guidance. Our user study with 17 creatives revealed that, even when creatives described the guidance as helpful for understanding AI, many still preferred self-experimentation, feeling that guidance could limit their creativity. Our findings highlight a central tension in supporting AI literacy for creatives: balancing guidance and promoting literacy while preserving creative freedom.

In the classical Min-Sum Radii problem (MSR) we are given a set $X$ of $n$ points in a metric space and a positive integer $k\in [n]$. Our goal is to partition $X$ into $k$ subsets (the clusters) so as to minimize the sum of the radii of these clusters. The Min-Sum Diameters problem (MSD) is defined analogously, where instead of the radii of the clusters we consider their diameters. For both problems we present FPT approximation schemes for the natural parameter $k$. Specifically, given $ε>0$, we show how to compute $(1+ε)$-approximations for both MSD and MSR in time $(1/ε)^kn^{O(1)}$ and $(1/ε)^{O(k/ε\log 1/ε)}n^{poly(1/ε)}$ respectively. The previous best FPT approximation algorithms for these problems have approximation factors $4+ε$ and $2+ε$, respectively, and finding an FPT approximation scheme for both these problems had been outstanding open problems.

Deep learning models in medical imaging often fail when deployed in new clinical environments due to distribution shifts in demographics, scanner hardware, or acquisition protocols. A central challenge is underspecification, where models with similar validation performance exhibit divergent real-world failure modes. Although stress testing has emerged as a tool to assess this, current methods typically rely on simple, uninformed perturbations (e.g., brightness or contrast changes), which fail to capture clinically realistic variation and can overestimate robustness. In this work, we introduce a counterfactual stress testing framework based on causal generative models that create realistic "what if" images by intervening on attributes such as scanner type and patient sex while preserving anatomical identity, enabling controlled and semantically meaningful evaluation under targeted distribution shifts. Across two imaging modalities (chest X-ray and mammography), three model architectures, and multiple shift scenarios, we show that counterfactual stress tests provide a substantially more accurate proxy for real out-of-distribution performance than classical perturbations, capturing the direction and relative magnitude of performance changes as well as model ranking. These results suggest that causal generative models can serve as practical simulators for robustness assessment, offering a more reliable basis for evaluating medical AI systems prior to deployment.

Recent progress in automated repair of performance bugs demands realistic, executable benchmarks. However, existing C++ performance benchmarks are largely built from competitive programming submissions, and recent real-world benchmarks predominantly target Python and .NET. To fill this gap, we present CppPerf-Mine, a configurable pipeline that mines execution-time-improving patches from open-source C++ repositories on GitHub by combining structural commit filtering, an LLM-based commit classifier, and a containerized build & test stage that produces fully reproducible Docker images for each patch. Using CppPerf-Mine, we build CppPerf-DB, a benchmark comprising 347 manually verified patches from 42 mature C++ repositories, 39% of which are multi-file, enabling the evaluation of repository-level repair tools. In our preliminary study, OpenHands correctly fixes only 13.5% of the patches in CppPerf-DB, confirming that real-world C++ performance repair remains an open challenge. CppPerf-Mine and CppPerf-DB are open-source and publicly available at: https://doi.org/10.5281/zenodo.20097425. In addition, a demonstration video is available at: https://www.youtube.com/watch?v=nixlupIgSdM.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

Open-world object counting remains brittle: despite rapid advances in vision-language models (VLMs), reliably counting the objects a user intends is far from solved. We argue that a central reason is that counting granularity is left implicit; users may refer to a specific identity, an attribute, an instance type, a category, or an abstract concept, yet most methods treat "what to count" as a single, category-level matching problem. In this work, we redefine open-world counting as multi-grained counting, where visual exemplars specify target appearance and fine-grained text, with optional negative prompts, specifies the intended semantic granularity across five explicit levels. Making granularity explicit, however, exposes a critical data bottleneck: existing counting datasets lack the multi-category scenes, controlled distractors, and instance-level annotations needed to verify fine-grained prompt semantics. To address this, we propose the first fully automatic data-scaling pipeline that integrates controllable 3D synthesis with consistent image editing and VLM-based filtering, and use it to construct KubriCount, the largest and most comprehensively annotated counting dataset to date, supporting both training and multi-grained evaluation. Systematic benchmarking reveals that both multimodal large language models and specialist counting models exhibit severe prompt-following failures under fine-grained distinctions. Motivated by these findings, we train HieraCount, a multi-grained counting model that jointly leverages text and visual exemplars as complementary target specifications. HieraCount substantially improves multi-grained counting accuracy and generalizes robustly to challenging real-world scenarios. The project page is available here: https://verg-avesta.github.io/KubriCount/.

Cross-domain few-shot medical image segmentation (CD-FSMIS) requires a model to generalise simultaneously to novel anatomical categories and unseen imaging domains from only a handful of annotated examples. Existing prototypical approaches inevitably entangle anatomical structure with domain-specific appearance variations, and thus lack a stable reference for reliable matching under domain shift. We observe that the geometric structure of human anatomy constitutes a reliable, domain-transferable prior that has been overlooked. Building on this insight, we propose GeoProto, a geometry-aware CD-FSMIS framework that enriches prototypical matching with explicit structural priors. The core component, Geometry-Aware Prototype Enrichment (GAPE), augments each local appearance prototype with a learned geometric offset encoding its ordinal position within the organ's interior topology. This offset is derived from an auxiliary Ordinal Shape Branch (OSB) trained under an ordinally consistent objective that enforces monotonic variation of geometric embeddings across interior strata, requiring no annotation beyond standard segmentation masks. Extensive experiments across seven datasets spanning three evaluation settings (cross-modality, cross-sequence, and cross-context) demonstrate that GeoProto achieves state-of-the-art performance.

Safe autonomous Uncrewed Aerial Vehicle (UAV) navigation in urban environments requires real-time path planning that avoids obstacles. MaxConvNet is a potential-field planner that leverages properties of Maxwell's equations to generate a path to the goal without local minima. We extend the 2D MaxConvNet magnetic field planner to 3D, using a convolutional autoencoder to predict obstacle-aware potential fields from LiDAR-derived 101^3 voxel grids. Evaluation across 100 randomized closed-loop trials in two distinct Cosys-AirSim urban environments, a dense night-time cityscape and a suburban district shows a 100% path planning success rate on both maps without retraining. In offline path planning, 3DMaxConvNet produces path lengths comparable to A* on unseen maps while reducing runtime from 0.155--0.17s to 0.087--0.089s, or about 1.7--1.95 times faster than A*. Against RRT*(3k), 3DMaxConvNet achieves similar path quality while reducing planning runtime from 17.2--17.5s to about 0.09s, which is roughly 193--201 times faster than RRT*(3k).