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Tree-structured rollouts give critic-free reinforcement learning with verifiable rewards (RLVR) step-level credit: fork a chain at an intermediate point, and sibling outcome differences estimate step value. Each fork adds sampling cost, so realistic budgets typically allow only a few forks per chain. A fork placed where the outcome is already largely settled yields siblings that mostly agree and provide almost no credit signal; hence, for a given tree size, where forks are placed largely determines how much step-level RL can gain. Most existing mainstream methods place forks by structure, such as fixed lengths, midpoints, and delimiters, or by next-token entropy. We formalize fork placement as locating the \emph{pivots} of the chain's value curve, where the expected outcome turns. We propose \emph{belief-shift branching}: read the model's answer belief at candidate boundaries and fork just before the step where consecutive beliefs diverge most. Three instantiations, none needing step-level supervision, span access levels: a black-box probe, a logit-lens depth profile, and a learned activation direction, which is fit offline and therefore used only in the validation before RL training. The signal only \emph{places} forks, and the probe costs about $1\%$ of step compute on mathematics and under $5\%$ on code when it runs inside the rollout engine. In that validation, against Monte-Carlo value curves, a belief-shift signal ranks first in each of the eight model$\times$benchmark panels, ahead of entropy, structural, and LLM-judge baselines. In RL across three model families and two domains, belief-shift forking leads every mathematics aggregate, on OLMo-3-7B by $+2.6$ aggregate and $+2.9$ on AIME 2026 over the strongest baseline, and sweeps every OLMo code column, by $+6.5$ on LiveCodeBench-medium.

When an agent writes code, the development framework becomes the control system for a non-deterministic worker. Spec-first, agent-driven frameworks have gained rapid traction since 2025; the installable ones, GitHub Spec Kit, obra/superpowers, BMAD, and GSD, and our own, all capture intent through a specification or durable planning artifacts. Since they agree on capturing intent up front, what separates them is how each enforces the engineering discipline that keeps agent-written code clean, correct, and maintainable. Every framework enforces that discipline somehow; they differ in how. We characterize three modes: enforcement by persuasion (prompt discipline the model may ignore), by front-loaded structure (strong specs, then a trusted build), and through controls the agent cannot edit (a deterministic orchestrator, human-approved gates, immutable tests, and a green result that must pass against a live, branched database). We introduce Consort, a spec-first, test-driven agent framework built on the third, enforcing that discipline through controls the agent runs inside but cannot bypass, in which a deterministic orchestrator drives separate role agents through a spec-first design lane and a test-driven build lane on a live database branch. We argue that enforcing the tests and gates in code keeps agent-written code honest and verifiable, while its specialized roles, like the human roles before them, are what make it maintainable, claims we frame as a pre-registered, testable hypothesis.

A long-lived KV cache must be compressed before the queries that will read it exist. Selection by observed attention collapses there: on a NoPE-MLA model, H2O and SnapKV retrieve 0.00 and 0.33 of needles at 8x compression, because a token's importance has not yet been observed. VestigeKV instead derives a sparse attention pattern from a signal the cache already carries, occupying the sparse-attention literature's one unoccupied quadrant: training-free and query-independent. In NoPE-MLA the 64-dimensional decoupled branch is a vestige of RoPE that training repurposes into a salience channel; reading 11% of each row, it partitions the cache into an attended tier and a GPU-resident archive that no row ever leaves, reachable each step by a certified, query-adaptive trigger. Nothing is trained and cache rows are never quantized, so every quality effect attributes to selection and scheduling. On Kimi Linear 48B, retrieval holds at 1.00 under 8x and 0.96 under 32x from 8k to 65k context, with zero gap to full-row selection, and the recall tier holds 128x at 1.00 (8k). Both tiers stay on the GPU, so the win is speed, not memory: the per-step scan reads ~26% of the bytes dense attention would, and on a two-node sglang deployment the crossover sits at ~40k context, reaching 1.18x at 256k and 1.39x at 496k. The mechanism is exclusive to NoPE: the identical operator on a RoPE MLA collapses to 0.08, query-independent salience exists only without rotation, and query-universal exact merging is provably impossible under RoPE. All thresholds were frozen before their data; 20 archived verdicts and 8 closed routes accompany the paper.

At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recovering this missing information is necessary for describing local continuation beyond a single point, but finite observations must separate branchwise second-order effects while allowing error in the estimated center. We address this inverse problem using matched score queries at noise scales $σ$ and $λσ$. For a finite union of $C^{2,α}$ half-branches in $\mathbb{R}^D$, the normalized score has the expansion $F_σ=F_0+σG+O(σ^{1+α})$. Matched subtraction cancels the tangent contribution and exposes $G$, which depends linearly on branchwise curvature and log-density slope. Given tangent directions and weights on distinct rays, $G$ uniquely identifies all $sD$ branch parameters, and $sD$ scalar component observations are necessary. An $O(σ^2)$ center error introduces $D$ translation modes, leading to $(s+1)D$ observations under full-rank calibration, except for a translation-invariant full line. We also establish a perturbation bound and a conditional kernel-density-estimation rate. Experiments reproduce the predicted population and $N^{-1/5}$ trends and remain full rank up to $D=20$ with 16 supplied branches. In end-to-end tests for $D=3$--$5$, a known-count first-order frontend yields full rank in all 135 population systems and a median relative jet error of 0.132. With strong first-order error, matched responses reduce median parameter error by a factor of 49.4 relative to naive tangent subtraction.

Verification of neural networks against relational specifications, such as global robustness, is crucial for safety-critical applications of cyber-physical systems (CPS), given their increasing adoption of AI components. Compared to simple trace properties (e.g., local robustness), verifying relational specifications requires reasoning about the relationship between multiple network inferences, which brings significant technical challenges. Existing research has explored abstraction techniques based on sound and convex over-approximation of neural network outputs; however, since these approaches are inherently incomplete and may raise false alarms, they further underscore the need of effective abstraction refinement. In this paper, we propose a branch-and-bound (BaB) framework to mitigate the issue, which iteratively splits the problem until all sub-problems are verified. Specifically, our BaB framework features splitting of relational neurons rather than individual neurons as prior works do, and as the core of our technique, we devise a relational neuron selection strategy based on the dual formulation of the verification problem, which allows us to efficiently select the (most likely) optimal relational neuron that maximizes the refinement brought by problem splitting. We evaluate SaBRe on 817 verification problems across ACAS Xu, MNIST-F, MNIST-C, CIFAR and GTSRB. The results show that SaBRe outperforms different baseline approaches, in terms of the number of solved instances and verification efficiency, which demonstrates the effectiveness of our proposed techniques.

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Fractional flow reserve derived from CT angiography (FFR-CT) simulates flow through a patient-specific vessel model, so its accuracy depends on the connectedness of the segmented tree, not only on volumetric overlap: a segmentation can reach high Dice yet sever a bifurcation, dropping the downstream subtree and reversing the treatment decision. Topology-aware losses such as clDice and Skeleton Recall act on the global centreline and can miss localised breaks. We study the Bifurcation Connectedness Score (BCS), which scores connectedness at each ground-truth bifurcation, and soft-BCS, its differentiable training surrogate. BCS captures a property of segmentation quality the standard metrics miss: it responds strongly to breaks in connectedness while staying largely unchanged under connectedness-preserving narrowing. Higher BCS accompanies closer agreement between the FFR-CT decisions a solver makes on predicted versus ground-truth geometry, most clearly in severe disease (OR 2.16, CI [1.23, 4.18]). Both decisions come from the same solver, so this reflects geometric, not clinical, fidelity. In training, soft-BCS and Skeleton Recall recover the same branches but build different trees. Recovering branches and keeping them connected are separable properties, so we recommend reporting a measure of each.

Multi-branch architectures and CNN-Transformer fusion have long been regarded as effective ways to improve vehicle re-identification (Re-ID) by combining complementary representations. In this work, we revisit this assumption in the foundation-model era through a comprehensive empirical study. A single DINOv3-pretrained ConvNeXt trained with a tuned recipe achieves 88.19 mAP on VeRi-Wild Small and 77.47 mAP on VeRi-Wild Large using visual cues alone, matching the strongest protocol-verified metadata-dependent multi-branch baseline. Applying training-free re-ranking further improves performance to 92.38 and 83.68 mAP, respectively. Using this strong baseline together with retrieval-level branch diagnostics, we evaluate whether increasing representational diversity still provides measurable gains. Across both benchmarks, concatenating multiple branches built on a shared backbone changes the best single-branch performance by less than one mAP point while increasing the embedding dimension by 4x, and the resulting representation has an effective rank close to the original feature dimension. We further study cross-backbone fusion using an asymmetric frozen-anchor strategy to combine ConvNeXt and Vision Transformer representations. Despite these favorable conditions, Transformer branches consistently remain 13-15 mAP below the ConvNeXt backbone, and paired per-query bootstrap analysis estimates the largest observed fusion gain to be only +0.11 mAP (95% confidence interval). Our results suggest that, under the evaluated setting, improving a single strong foundation-model backbone together with retrieval-stage re-ranking is more effective than increasing architectural complexity through additional branches or heterogeneous backbones. We restrict our conclusions to single-seed training and one family of foundation models and discuss conditions under which these observations may not hold.

Test-time scaling improves language-model reasoning, but existing approaches often face a difficult trade-off: long chain-of-thought sampling remains single-threaded, while sentence- or solution-level search can be computationally expensive and hard to train end-to-end. We introduce Local Branch Routing (LBR), a token-level test-time scaling framework that expands a small local lookahead tree, forwards all sampled branches through the language model, and uses a lightweight router to select the depth-1 subtree to commit. By routing over the hidden states of candidate local futures, LBR allows each token decision to use evidence beyond the root next-token distribution while avoiding full solution-level search. The resulting prune-shift-grow decoding process preserves discrete branch identities and defines a tractable tree-trajectory likelihood: newly grown nodes are counted when first sampled, and router decisions are assigned explicit probabilities. This enables end-to-end reinforcement learning with verifiable rewards, jointly optimizing the base model and router under the same likelihood-ratio principle as discrete-token RLVR. On synthetic hierarchical-planning tasks, LBR shows that post-candidate hidden states provide useful routing evidence. On mathematical reasoning benchmarks, LBR improves both Pass@1 and Pass@32 over discrete chain-of-thought, vanilla discrete-token RLVR, and RL-compatible soft-token branching baselines. These results suggest that lightweight local branching offers an efficient, trainable, and discrete form of language-model test-time scaling.

This study presents a method for modeling diverse plant branches by iteratively estimating material parameters to support delicate branch manipulation. Branch manipulation is necessary in agricultural robotics for plant repositioning, stabilizing, and clearing visual obstructions in dense foliage. The proposed method builds a tetrahedral branch model from point-cloud data and simulates its behavior using the finite element method. Using real observed deformation data, it iteratively estimates branch parameters and then computes an optimal path with a deformation-aware motion planner to move and stabilize branches within another robot's field of view. Across 30 trials on branches with varying geometries and material properties, the proposed method reduced the deformation energy by 35.69% while increasing the path length by 8.10% on average.

Multimodal time series forecasting, which pairs numerical sequences with domain-relevant textual reports, promises to inject world knowledge into forecasting pipelines. However, we uncover a critical failure mode in existing frameworks that we term text collapse: the text branch converges to a content-independent transformation, contributing negligible discriminative signal regardless of the input description. We argue that text collapse is a consequence of a fundamental asymmetry in time series forecasting: the numerical input is strongly autocorrelated with the output, making the numerical backbone inherently dominant, while the text branch, despite carrying complementary and often critical information, is insufficiently utilized, leading to its systematic underexploitation. To address this, we propose \textbf{REST-TS} (\textbf{R}esidual-\textbf{E}xclusive \textbf{S}upervision for \textbf{T}ext in \textbf{T}ime \textbf{S}eries), which turns the asymmetry into a design principle: the numerical backbone produces its own independent numerical forecast, and the text branch is exclusively supervised to predict the structured components of the residual, the prediction gap that numbers cannot explain. Because no numerical pathway can reduce these losses, the text branch must extract genuine content from the input description. Evaluated across diverse real-world domains and backbone architectures, REST-TS achieves state-of-the-art performance and consistently demonstrates greater text-branch utilization than existing frameworks, providing strong empirical evidence that supervising the text branch on the residual compels it to extract genuine content from the input.

Large language models increasingly serve as execution engines for agentic systems, yet they still consume context through a sequential text interface. This creates a mismatch with modern structured agent workflows, in which independent branches explore subtasks, retrieve evidence, or generate candidate solutions before a final synthesis step. Existing systems typically merge these branches by concatenating their textual outputs, which discards the parallel structure and incurs redundant prefill computation. In this work, we introduce Parallel-Synthesis, a plug-and-play framework that enables a synthesizer to directly consume the KV caches produced by parallel worker agents. Parallel-Synthesis combines a cache mapper that calibrates independently generated branch caches with a fine-tuned synthesizer adapter that enables generation from this non-sequential cache interface. We train Parallel-Synthesis using data that exposes the synthesizer to parallel cache contexts, teaches aggregation across cached branches, and distills reasoning behavior from standard text-concatenation-based synthesis. Across nine downstream datasets spanning math, science QA, code generation, GAIA, and multi-agent database diagnosis, Parallel-Synthesis matches or outperforms text-based synthesis on seven datasets and remains close on the other two. It also reduces time-to-first-token by 2.5x-11x, suggesting that direct cache-based synthesis is a promising interface for more native and efficient synthesis over parallel agent branches.

Quality-diversity reinforcement learning (QD-RL) aims to construct policy repertoires that contain both high-performing and behaviorally diverse policies. Existing QD-RL methods mainly diversify policy instances after rollout evaluation or use learned value information to improve policy quality and behavior targeting, while the learning branches that generate candidate policies remain less explored. This paper proposes SV-QD-RL, a structure-value coupled framework that represents each candidate as a structure-conditioned actor-critic branch. Each branch contains an actor, a structural mask, a branch-specific critic, a replay state, and evaluation attributes including behavior, return, sparsity, and value profile. The structural mask defines the actor subspace in which the branch learns, while the branch-specific critic and replay state shape its value-learning trajectory. A branch-aware QD archive then evaluates and retains branches according to behavioral quality, structural footprint, and value-profile information. Experiments on MuJoCo continuous-control tasks show that SV-QD-RL constructs policy repertoires with strong archive quality and behaviorally useful diversity. Ablation and diagnostic analyses further indicate that structural conditioning, critic differentiation, and memory-consistent refinement make complementary contributions to behavioral specialization. Schedule-aware repertoire evaluation shows that the learned archive provides selectable policy alternatives under changing behavior-level requirements. These results suggest that coupling actor structure with branch-specific value learning is an effective mechanism for generating diverse QD-RL policy repertoires.

LLM-agent workflows chain model calls and tool invocations, and spend most of their wall-clock time waiting on upstream operations before downstream ones can start. Speculative execution can reclaim that idle time by launching a downstream operation with a predicted upstream input, but here each speculation costs real money (per-token billing) and its success probability is hard to estimate and drifts over time. This paper presents a method organized around five design decisions: (D1) start a downstream operation before its upstream completes; (D2) price each speculation in real dollars at separate input and output rates; (D3) expose a single operator dial for latency versus cost; (D4) decide via an expected-value rule with a failure-weighted cost term and a preference-adjusted threshold; and (D5) estimate the success probability with a Bayesian Beta-Binomial posterior whose prior is keyed to a dependency-type taxonomy. Variants of these ideas appear in recent work; the combination, with every decision logged in dollars, is what is new. The rule fires only on edges passing an admissibility precondition (side-effect-free, idempotent, or stageable behind a commit barrier), since a wrong speculation is rolled back by re-execution, which refunds tokens but cannot un-send an irreversible side effect. We specify the runtime mechanics, a closed-form result that the rule self-limits as the upstream branching factor grows, a five-stage calibration pipeline (offline replay, shadow, canary, online calibration, drift-triggered kill-switch), and a workload-fit rubric over eight production archetypes. Contrast tables against the four closest published systems (DSP, Speculative Actions v2, Sherlock, B-PASTE) show differentiators on every dimension, and a synthetic validation suite confirms the predicted decision boundary, probability threshold, posterior recovery, and streaming-cancellation behavior.

Sudoku is a representative constraint satisfaction problem that requires global structural reasoning under strict discrete constraints. The existing works of solving Sudoku mainly focus on two dominant approaches, i.e., traditional heuristic and deep learning solver. However, they suffer from two complementary limitations: learning-based solvers lack hard correctness guarantees, while complete symbolic solvers are still prone to long-tail search. To address these shortcomings, we propose a novel diffusion model-guided approach, termed as DiBS, for the branch selection search process. Specifically, DiBS keeps the symbolic solver complete and uses the diffusion model as a branch-ordering guide. The core method is ranking candidate values under the current partial assignment and lightweight consistency signal. Furthermore, we provide an in-depth theoretical proof to reveal how it works and why it works. Experiments on the challenging Royle 17-clue Sudoku benchmark show that our DiBS substantially reduces search cost relative to strong heuristic baselines, especially in nodes, backtracks, and long-tail percentiles. Besides, these results confirm that learned global guidance is effective on hard instances where branch-order mistakes are most expensive. All codes are available at https://github.com/shanxierdan/DiBS.

This study presents a novel hybrid prognostic framework for uncertainty-aware Remaining Useful Life (RUL) estimation in turbofan engines using the NASA C-MAPSS dataset. The framework employs a state-aware strategy that bifurcates the engines operational lifespan into "healthy" and "degraded" regimes. An LSTM-based autoencoder, trained strictly on nominal data (RUL > 150 cycles), monitors reconstruction error to act as a robust state classifier. For the healthy regime, a Conditional Weibull Survival Analysis is used for Mean Residual Life estimation. For the degraded regime, a Probabilistic Neural Network with Monte Carlo Dropout captures both aleatoric and epistemic uncertainties. Rather than using rigid binary labels, a calibrated sigmoid function converts the autoencoders output into continuous state probabilities, dynamically weighting the final ensemble prediction. The primary strength of this framework is its generation of physically consistent uncertainty bands, yielding high-confidence predictions near end-of-life while accurately reflecting the inherent variance of early operation, providing a robust tool for risk-informed maintenance.

Text-to-music generation has advanced rapidly, with modern autoregressive and diffusion-based models producing convincing music from natural-language prompts. However, much of this progress relies on large-scale training data and external pretraining, making it difficult to isolate which design choices remain effective when data and pretraining are controlled. We study this setting using a Diffusion Transformer backbone with lyric and timbre conditioning, adapted to an instrumental-only text-to-music task in which the auxiliary lyric and timbre branches receive only degenerate conditioning signals. Through controlled ablations, we find that models retrained without these branches score lower across AudioBox aesthetics, LLM-as-judge, and human MOS, and that reinvesting the saved parameters as additional DiT depth recovers only marginally. This suggests the auxiliary branches may act as training-time architectural anchors whose contribution goes beyond their explicit conditioning content. We validate the same model through comparisons with external instrumental baselines and through our submission to the ICME 2026 Academic Text-to-Music (ATTM) Grand Challenge, where our Performance submission ranked first under both the objective metrics and the subsequent organizer-administered MOS over 35 raters, attaining the highest overall MOS across all challenge submissions, while our Efficiency submission was a finalist that tied for second under the objective metrics.

Recent progress in large language models has led to the emergence of reasoning models, which have shown strong performance on complex tasks through specialized fine-tuning procedures. While these methods reliably improve pass@1 accuracy, prior works have observed that they show a coverage shrinkage behavior, where pass@k degrades relative to the base model. In this paper, we investigate the cause of reasoning shrinkage under SFT-based post-training. We hypothesize that this behavior is driven by properties of the fine-tuning data, specifically related to decision points or "forks in the road" scenarios where model encounters indecipherable patterns with multiple valid reasoning paths. To test this hypothesis, we design controlled case studies that simulate such decision-point settings, spanning indecipherable nodes in graph branching, and reasoning modes. By tracking post-training dynamics in these settings, we find that the shrinkage phenomenon is tightly correlated with the prevalence of decision-point scenarios in the training data. We also demonstrate that this shrinkage behavior can be partially mitigated through targeted data synthesis design of decision-points and a more systematic diversity-encouraging decoding mechanism. Our findings identify data-centric factors as a key driver of shrinkage in reasoning models and highlight diversity-aware designs as an effective lever for controlling it. (Data and code for reproducing our experiments are available at https://github.com/psunlpgroup/reasoning_forks )

Spiking neural networks (SNNs) hold promise for demonstrating superior learning and representation capabilities in deep models. Given the tremendous success of ResNet in deep learning, it would naturally follow to train deep SNNs with residual learning. However, existing residual structures for constructing deep SNNs still present challenges of spike redundancy or information loss, as well as redundant learning. In the present study, we first aim to address issues of relative spike redundancy in identity mapping and information loss in non-identity mapping. To this end, we propose an OR-ADD (OA) shortcut connection to merge output spikes/currents from two branches in the residual structure. Furthermore, to mitigate redundant learning in the backbone branch of the residual structure, we introduce the concept of XOR meta-residuals, i.e., selecting pre-learning residuals using the Exclusive-OR (XOR) operation for the backbone branch. Finally, by integrating the OA shortcut and XOR meta-residuals, we devise the XOR residual block and further construct XOResNet with varying depths based on this block. Extensive experiments on four datasets, Fashion-MNIST, CIFAR-10, CIFAR-100, and miniImageNet, show that the proposed XOResNet outperforms existing state-of-the-art deep SNNs optimized via gradient descent. These results validate the effectiveness of our OA shortcut and XOR meta-residual components in overcoming fundamental limitations of residual learning in SNNs, providing new architectural insights for building high-performance neuromorphic systems.

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

Contact-implicit trajectory optimization (CITO) has attracted growing attention as a unified framework for planning and control in contact-rich robotic tasks. Recent approaches have demonstrated promising results in manipulation and locomotion without requiring a prescribed contact-mode schedule. It is well known that the underlying mathematical programs with complementarity constraints (MPCCs) remain numerically ill-conditioned, and systematic, scalable solution strategies for CITO remain an active area of research. More efficient and principled solvers that can handle contact constraints are therefore essential to broaden the applicability of CITO. In this work, we develop an augmented-Lagrangian approach to CITO for solving MPCC-based CITO with stationarity guarantees. The method can be interpreted as identifying the implicit contact-mode branches on the fly during the trajectory optimization (TO) iterations; we call this approach IMPACT (IMPlicit contact ACtive-set Trajectory optimization). We provide an efficient C++ implementation tailored to trajectory-optimization workloads and evaluate it on the open-source CITO and contact-implicit model predictive control (CI-MPC) benchmarks. On CITO, IMPACT achieves 2.9x-70x speedups over strong baselines (geometric mean 13.8x). On CI-MPC, we show improved control quality for contact-rich trajectories on dexterous manipulation tasks in simulation. Finally, we demonstrate the proposed method on real robotic hardware on a T-shaped object pushing task.

Speculative decoding accelerates Large Language Models via draft-then-verify, where verification can be framed as an Optimal Transport (OT) problem. Existing approaches typically handle multi-draft and multi-step aspects in isolation, applying either flat OT to single-step drafts or per-token rejection sampling to tree-structured candidates. This separation leaves the joint regime (where multi-step dependencies meet multi-draft branching) poorly optimized, as local verification rules fail to exploit the coupling between horizontal and vertical dimensions of candidate trees. In this paper, we propose a unified perspective that casts tree-based verification as a conditional OT problem. Our key insight is that vertical dependencies can be abstracted through prefix acceptance probabilities, which act as dynamic scaling factors to actively guide horizontal draft selection. Based on this principle, we introduce UniVer, a verification algorithm that jointly optimizes across tree levels by composing local optimal transport plans under prefix constraints. We prove that UniVer remains lossless and achieves the optimal acceptance rate under the proposed conditional framework. Extensive experiments across different tasks and models demonstrate that UniVer improves acceptance length by 4.2% to 8.5% over standard recursive rejection sampling without replacement, while maintaining exact distributional alignment with the target model.

Unlike macro-expression, micro-expression does not follow a strictly consistent mapping rule between emotions and Action Units (AUs). As a result, some micro-expressions share identical AUs yet represent completely opposite emotional categories, making them highly visually similar. Existing microexpression recognition (MER) methods mostly rely on explicit facial motion cues (e.g., optical flow, frame differences, AU features) while ignoring implicit emotion information. To tackle this issue, this paper presents a Motion Emotion Feature Decoupling Network (MEDN) for MER. We design a dual-branch framework to separately extract motion and emotion features. In the motion branch, an AU-detection task restricts features to the explicit motion domain, and orthogonal loss is adopted to reduce motion emotion feature coupling. For implicit emotion modeling, we propose a Sparse Emotion Vision Transformer (SEVit) that sparsifies spatial tokens to highlight local temporal variations with multi-scale sparsity rates. A Collaborative Fusion Module (CoFM) is further developed to fuse disentangled motion and emotion features adaptively. Extensive experiments on three benchmark datasets validate that MEDN effectively decouples motion and emotion features and achieves superior recognition performance, offering a new perspective for enhancing recognition accuracy and generalization.