Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally expensive retraining under new physical conditions, parameterized PINNs (P$^2$INNs) commonly adapt pre-trained operators using singular value decomposition (SVD) for out-of-distribution (OOD) regimes. However, SVD-based fine-tuning often suffers from rigid subspace locking and truncation of important high-frequency spectral modes, limiting its ability to capture complex physical transitions. While parameter-efficient fine-tuning (PEFT) methods appear to be promising alternatives, applying conventional adapters such as LoRA to P$^2$INNs introduces a severe Pareto trade-off, as additive updates increase parameter overhead and disrupt the structured physical manifolds inherent in operator representations. To address these limitations, we propose Manifold-Orthogonal Dual-spectrum Extrapolation (MODE), a lightweight micro-architecture designed for physics operator adaptation. MODE decomposes physical evolution into complementary mechanisms including principal-spectrum dense mixing that enables cross-modal energy transfer within frozen orthogonal bases, residual-spectrum awakening that activates high-frequency spectral components through a single trainable scalar, and affine Galilean unlocking that explicitly isolates spatial translation dynamics. Experiments on challenging PDE benchmarks including the 1D Convection--Diffusion--Reaction equation and the 2D Helmholtz equation demonstrate that MODE achieves strong out-of-distribution generalization while preserving the minimal parameter complexity of native SVD and outperforming existing PEFT-based baselines.

Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must also predict beyond the training time range. Existing methods usually cannot handle parameter generalization and temporal extrapolation at the same time. Standard parameterized models treat time as just another input and therefore fail to capture intrinsic dynamics, while recent continuous-time latent methods often rely on expensive test-time auto-decoding for each instance, which is inefficient and can disrupt continuity across the parameterized solution space. To address this, we propose Disentangled Latent Dynamics Manifold Fusion (DLDMF), a physics-informed framework that explicitly separates space, time, and parameters. Instead of unstable auto-decoding, DLDMF maps PDE parameters directly to a continuous latent embedding through a feed-forward network. This embedding initializes and conditions a latent state whose evolution is governed by a parameter-conditioned Neural ODE. We further introduce a dynamic manifold fusion mechanism that uses a shared decoder to combine spatial coordinates, parameter embeddings, and time-evolving latent states to reconstruct the corresponding spatiotemporal solution. By modeling prediction as latent dynamic evolution rather than static coordinate fitting, DLDMF reduces interference between parameter variation and temporal evolution while preserving a smooth and coherent solution manifold. As a result, it performs well on unseen parameter settings and in long-term temporal extrapolation. Experiments on several benchmark problems show that DLDMF consistently outperforms state-of-the-art baselines in accuracy, parameter generalization, and extrapolation robustness.

Structure-aware Prompt Adaptation from Seen to Unseen for Open-Vocabulary Compositional Zero-Shot Learning

The goal of Open-Vocabulary Compositional Zero-Shot Learning (OV-CZSL) is to recognize attribute-object compositions in the open-vocabulary setting, where compositions of both seen and unseen attributes and objects are evaluated. Recently, prompt tuning methods have demonstrated strong generalization capabilities in the closed setting, where only compositions of seen attributes and objects are evaluated, i.e., Compositional Zero-Shot Learning (CZSL). However, directly applying these methods to OV-CZSL may not be sufficient to generalize to unseen attributes, objects and their compositions, as it is limited to seen attributes and objects. Normally, when faced with unseen concepts, humans adopt analogies with seen concepts that have the similar semantics thereby inferring their meaning (e.g., "wet" and "damp", "shirt" and "jacket"). In this paper, we experimentally show that the distribution of semantically related attributes or objects tends to form consistent local structures in the embedding space. Based on the above structures, we propose Structure-aware Prompt Adaptation (SPA) method, which enables models to generalize from seen to unseen attributes and objects. Specifically, in the training stage, we design a Structure-aware Consistency Loss (SCL) that encourages the local structure's consistency of seen attributes and objects in each iteration. In the inference stage, we devise a Structure-guided Adaptation Strategy (SAS) that adaptively aligns the structures of unseen attributes and objects with those of trained seen attributes and objects with similar semantics. Notably, SPA is a plug-and-play method that can be seamlessly integrated into existing CZSL prompt tuning methods. Extensive experiments on OV-CZSL benchmarks demonstrate that SPA achieves competitive closed-set performance while significantly improving open-vocabulary results.

TIMI: Training-Free Image-to-3D Multi-Instance Generation with Spatial Fidelity

Precise spatial fidelity in Image-to-3D multi-instance generation is critical for downstream real-world applications. Recent work attempts to address this by fine-tuning pre-trained Image-to-3D (I23D) models on multi-instance datasets, which incurs substantial training overhead and struggles to guarantee spatial fidelity. In fact, we observe that pre-trained I23D models already possess meaningful spatial priors, which remain underutilized as evidenced by instance entanglement issues. Motivated by this, we propose TIMI, a novel Training-free framework for Image-to-3D Multi-Instance generation that achieves high spatial fidelity. Specifically, we first introduce an Instance-aware Separation Guidance (ISG) module, which facilitates instance disentanglement during the early denoising stage. Next, to stabilize the guidance introduced by ISG, we devise a Spatial-stabilized Geometry-adaptive Update (SGU) module that promotes the preservation of the geometric characteristics of instances while maintaining their relative relationships. Extensive experiments demonstrate that our method yields better performance in terms of both global layout and distinct local instances compared to existing multi-instance methods, without requiring additional training and with faster inference speed.

Benchmarking Few-shot Transferability of Pre-trained Models with Improved Evaluation Protocols

Few-shot transfer has been revolutionized by stronger pre-trained models and improved adaptation algorithms.However, there lacks a unified, rigorous evaluation protocol that is both challenging and realistic for real-world usage. In this work, we establish FEWTRANS, a comprehensive benchmark containing 10 diverse datasets, and propose the Hyperparameter Ensemble (HPE) protocol to overcome the "validation set illusion" in data-scarce regimes. Our empirical findings demonstrate that the choice of pre-trained model is the dominant factor for performance, while many sophisticated transfer methods offer negligible practical advantages over a simple full-parameter fine-tuning baseline. To explain this surprising effectiveness, we provide an in-depth mechanistic analysis showing that full fine-tuning succeeds via distributed micro-adjustments and more flexible reshaping of high-level semantic presentations without suffering from overfitting. Additionally, we quantify the performance collapse of multimodal models in specialized domains as a result of linguistic rarity using adjusted Zipf frequency scores. By releasing FEWTRANS, we aim to provide a rigorous "ruler" to streamline reproducible advances in few-shot transfer learning research. We make the FEWTRANS benchmark publicly available at https://github.com/Frankluox/FewTrans.

Beyond the Majority: Long-tail Imitation Learning for Robotic Manipulation

While generalist robot policies hold significant promise for learning diverse manipulation skills through imitation, their performance is often hindered by the long-tail distribution of training demonstrations. Policies learned on such data, which is heavily skewed towards a few data-rich head tasks, frequently exhibit poor generalization when confronted with the vast number of data-scarce tail tasks. In this work, we conduct a comprehensive analysis of the pervasive long-tail challenge inherent in policy learning. Our analysis begins by demonstrating the inefficacy of conventional long-tail learning strategies (e.g., re-sampling) for improving the policy's performance on tail tasks. We then uncover the underlying mechanism for this failure, revealing that data scarcity on tail tasks directly impairs the policy's spatial reasoning capability. To overcome this, we introduce Approaching-Phase Augmentation (APA), a simple yet effective scheme that transfers knowledge from data-rich head tasks to data-scarce tail tasks without requiring external demonstrations. Extensive experiments in both simulation and real-world manipulation tasks demonstrate the effectiveness of APA. Our code and demos are publicly available at: https://mldxy.github.io/Project-VLA-long-tail/.

Learning More from Less: Unlocking Internal Representations for Benchmark Compression

The prohibitive cost of evaluating Large Language Models (LLMs) necessitates efficient alternatives to full-scale benchmarking. Prevalent approaches address this by identifying a small coreset of items to approximate full-benchmark performance. However, existing methods must estimate a reliable item profile from response patterns across many source models, which becomes statistically unstable when the source pool is small. This dependency is particularly limiting for newly released benchmarks with minimal historical evaluation data. We argue that discrete correctness labels are a lossy view of the model's decision process and fail to capture information encoded in hidden states. To address this, we introduce REPCORE, which aligns heterogeneous hidden states into a unified latent space to construct representative coresets. Using these subsets for performance extrapolation, REPCORE achieves precise estimation accuracy with as few as ten source models. Experiments on five benchmarks and over 200 models show consistent gains over output-based baselines in ranking correlation and estimation accuracy. Spectral analysis further indicates that the aligned representations contain separable components reflecting broad response tendencies and task-specific reasoning patterns.

Do Not Waste Your Rollouts: Recycling Search Experience for Efficient Test-Time Scaling

Test-Time Scaling enhances the reasoning capabilities of Large Language Models by allocating additional inference compute to broaden the exploration of the solution space. However, existing search strategies typically treat rollouts as disposable samples, where valuable intermediate insights are effectively discarded after each trial. This systemic memorylessness leads to massive computational redundancy, as models repeatedly re-derive discovered conclusions and revisit known dead ends across extensive attempts. To bridge this gap, we propose \textbf{Recycling Search Experience (RSE)}, a self-guided, training-free strategy that turns test-time search from a series of isolated trials into a cumulative process. By actively distilling raw trajectories into a shared experience bank, RSE enables positive recycling of intermediate conclusions to shortcut redundant derivations and negative recycling of failure patterns to prune encountered dead ends. Theoretically, we provide an analysis that formalizes the efficiency gains of RSE, validating its advantage over independent sampling in solving complex reasoning tasks. Empirically, extensive experiments on HMMT24, HMMT25, IMO-Bench, and HLE show that RSE consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art scaling efficiency.

Sim-and-Human Co-training for Data-Efficient and Generalizable Robotic Manipulation

Synthetic simulation data and real-world human data provide scalable alternatives to circumvent the prohibitive costs of robot data collection. However, these sources suffer from the sim-to-real visual gap and the human-to-robot embodiment gap, respectively, which limits the policy's generalization to real-world scenarios. In this work, we identify a natural yet underexplored complementarity between these sources: simulation offers the robot action that human data lacks, while human data provides the real-world observation that simulation struggles to render. Motivated by this insight, we present SimHum, a co-training framework to simultaneously extract kinematic prior from simulated robot actions and visual prior from real-world human observations. Based on the two complementary priors, we achieve data-efficient and generalizable robotic manipulation in real-world tasks. Empirically, SimHum outperforms the baseline by up to $\mathbf{40\%}$ under the same data collection budget, and achieves a $\mathbf{62.5\%}$ OOD success with only 80 real data, outperforming the real only baseline by $7.1\times$. Videos and additional information can be found at \href{https://kaipengfang.github.io/sim-and-human}{project website}.

RPT*: Global Planning with Probabilistic Terminals for Target Search in Complex Environments

Routing problems such as Hamiltonian Path Problem (HPP), seeks a path to visit all the vertices in a graph while minimizing the path cost. This paper studies a variant, HPP with Probabilistic Terminals (HPP-PT), where each vertex has a probability representing the likelihood that the robot's path terminates there, and the objective is to minimize the expected path cost. HPP-PT arises in target object search, where a mobile robot must visit all candidate locations to find an object, and prior knowledge of the object's location is expressed as vertex probabilities. While routing problems have been studied for decades, few of them consider uncertainty as required in this work. The challenge lies not only in optimally ordering the vertices, as in standard HPP, but also in handling history dependency: the expected path cost depends on the order in which vertices were previously visited. This makes many existing methods inefficient or inapplicable. To address the challenge, we propose a search-based approach RPT* with solution optimality guarantees, which leverages dynamic programming in a new state space to bypass the history dependency and novel heuristics to speed up the computation. Building on RPT*, we design a Hierarchical Autonomous Target Search (HATS) system that combines RPT* with either Bayesian filtering for lifelong target search with noisy sensors, or autonomous exploration to find targets in unknown environments. Experiments in both simulation and real robot show that our approach can naturally balance between exploitation and exploration, thereby finding targets more quickly on average than baseline methods.