PlatonicNav: Unveiling Semantic Correspondence in Navigation with Platonic Topological Maps

Embodied visual navigation, where an agent perceives a complex environment and acts to reach a goal from raw sensory input, underpins a wide range of applications such as household service robotics, assistive robotics, and large-scale autonomous exploration. However, recent attempts to unify vision-and-language navigation (VLN) and object goal navigation (ObjNav) remain at the level of architectural fusion, mixed-task training, and large vision-language pretraining, without examining whether independently trained vision and language encoders may already share a common semantic structure. Moreover, even object-centric topological maps still ground language goals through explicit cross-modal supervision such as CLIP or large vision-language models, leaving open whether such grounding is possible from a purely vision-built map. To address these challenges, we extend the Platonic Representation Hypothesis to embodied navigation and recast vision-only ObjNav, cross-modal ObjNav, and VLN as three different interfaces to the same object-centric semantic manifold. We further introduce PlatonicNav, a training-free framework whose Platonic Topological Map fuses geometric and semantic node distances from a self-supervised visual encoder, and grounds language goals via blind matching without any paired vision-language data. Extensive experiments on simulation benchmarks including HM3D-IIN, OVON, and R2R-CE on MP3D, together with deployment on Unitree Go2, demonstrate that PlatonicNav generalizes across tasks, modalities, and embodiments without explicit cross-modal training. Code: https://github.com/AIGeeksGroup/PlatonicNav. Website: https://aigeeksgroup.github.io/PlatonicNav.

TriSearch: Learning to Optimize Triangulations via Bistellar Flips

We introduce TriSearch, a reinforcement learning framework for optimizing objectives over triangulations of a polytope via bistellar flips. The key idea is a circuit-supported subtriangulation action representation: feasible flips are encoded by their supporting circuit and realized local subtriangulation, enabling a learned policy to rank them using local geometric and combinatorial features. This yields a dimension-agnostic interface and enables efficient traversal of the flip graph without explicit enumeration of the full triangulation space. Instantiated in 3D and 4D, TriSearch generalizes zero-shot from small training instances to larger polytopes with exponentially larger search spaces. It achieves top performance on metric objectives in 3D and, in 4D, discovers more distinct Fine, Regular, Star triangulations of reflexive polytopes, corresponding to Calabi-Yau threefolds, than existing samplers under a fixed budget.

AtelierEval: Agentic Evaluation of Humans & LLMs as Text-to-Image Prompters

Text-to-image (T2I) systems increasingly rely on upstream prompters, either humans or multimodal large language models (MLLMs), to translate user intent into detailed prompts. Yet current benchmarks fix the prompt and only evaluate T2I models, leaving the prompting proficiency of this upstream component entirely unmeasured. We introduce AtelierEval, the first unified benchmark that quantifies prompting proficiency across 360 expert-crafted tasks. Grounded in a cognitive view, it spans three task categories and instantiates tasks using a taxonomy of real-world challenges, with a dual interface for both humans and MLLMs. To enable scalable and reliable evaluation, we propose AtelierJudge, a skill-based, memory-augmented agentic evaluator. It produces subjective and objective scores for prompt-image pairs, achieving a Spearman correlation of 0.79 with human experts, approaching human performance. Extensive experiments benchmark 8 MLLMs against 48 human users across 4 T2I backends, validate AtelierEval as a robust diagnostic tool, and reveal the superiority of mimicry over planning, advocating for an image-augmented direction for future prompters. Our work is released to support future research.

HyLoVQA: Dynamic Hypernetwork-Generated Low-Rank Adaptation for Continual Visual Question Answering

Continual Visual Question Answering (VQA) requires learning from non-stationary streams of visual inputs and questions while preserving past knowledge. Most prior methods adapt by updating a largely shared parameter set. This often leads to cross-level task interference, hindering accurate adaptation to the current task and object. To address this limitation, we propose HyLoVQA. It maintains a drift-resilient memory bank of anchors. The bank stores the content of visual objects and textual tasks, and they are updated using current input features. Conditioned on retrieved anchors, a hypernetwork generates lightweight Low-Rank Adaptation (LoRA) adapters. This ensures parameter efficiency, allowing the model to adapt to each task and object dynamically. Additionally, we formulate an alignment loss that aligns semantic discrepancies in the feature space with functional changes in the parameter space, thereby constraining LoRA adapters to remain focused on the current task and object. Extensive experiments on VQA v2 and NExT-QA under both standard and compositional settings demonstrate the superiority of HyLoVQA over prior state-of-the-art methods.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models

Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with strong nonlinearity, sharp gradients, or multiscale features. We propose the Curriculum-Guided Gaussian Mixture Physics-Informed Neural Network (CGMPINN), which integrates Gaussian mixture modeling with dynamic curriculum learning. Specifically, a GMM is periodically fitted to the PDE residual distribution to quantify spatially varying learning difficulty. A smooth curriculum schedule progressively shifts training focus from easy to harder regions, while precision-based variance modulation suppresses unreliable clusters during early optimization. This dual curriculum is governed by a shared curriculum parameter and can be combined with self-adaptive loss balancing. We further establish theoretical guarantees, including sublinear convergence of the gradient norm for the induced time-varying loss, uniform equivalence between the curriculum-weighted and standard PDE losses, and a generalization bound with an explicit weighting-induced bias characterization. Experiments on six benchmark PDEs spanning elliptic, parabolic, hyperbolic, advection-dominated, and nonlinear reaction-diffusion types show that CGMPINN consistently achieves the lowest relative $L_2$ and maximum absolute errors among all compared methods, reducing relative $L_2$ error by up to 97.8\% over the standard PINN at comparable cost. Our code is publicly available at https://github.com/Mathematics-Yang/CGMPINN.

Large Language Model as Token Compressor and Decompressor

In this paper, we establish the novel insight that an off-the-shelf LLM can function as an excellent token compressor and decompressor. To demonstrate, we design a self-expressive autoencoding learning framework fine-tunes a pretrained LLM to translate long texts into a compact internal language of discrete, variable-length latent codes, termed Z-tokens, and to reconstruct the original text exactly from them. The resulting representation is content-adaptive: semantically dense segments receive more Z-tokens, while redundant or predictable regions are aggressively compressed, via lightweight LoRA-based adapter heads. Empirically, our method achieves up to 18 times token reduction on Wikipedia, CNN/DailyMail, HotpotQA, and Qulac-style long-query datasets, while preserving reconstruction fidelity and downstream performance. This simple yet effective design supports applications including prompt compression and autoregressive generation directly in the Z-token space, offering a potential pathway toward token-efficient long-context reasoning.

Spectral-Geometric Neural Fields for Pose-Free LiDAR View Synthesis

Neural Radiance Fields (NeRF) have shown remarkable success in image novel view synthesis (NVS), inspiring extensions to LiDAR NVS. However, most methods heavily rely on accurate camera poses for scene reconstruction. The sparsity and textureless nature of LiDAR data also present distinct challenges, leading to geometric holes and discontinuous surfaces. To address these issues, we propose SG-NLF, a pose-free LiDAR NeRF framework that integrates spectral information with geometric consistency. Specifically, we design a hybrid representation based on spectral priors to reconstruct smooth geometry. For pose optimization, we construct a confidence-aware graph based on feature compatibility to achieve global alignment. In addition, an adversarial learning strategy is introduced to enforce cross-frame consistency, thereby enhancing reconstruction quality. Comprehensive experiments demonstrate the effectiveness of our framework, especially in challenging low-frequency scenarios. Compared to previous state-of-the-art methods, SG-NLF improves reconstruction quality and pose accuracy by over 35.8% and 68.8%. Our work can provide a novel perspective for LiDAR view synthesis.

StereoAdapter-2: Globally Structure-Consistent Underwater Stereo Depth Estimation

Stereo depth estimation is fundamental to underwater robotic perception, yet suffers from severe domain shifts caused by wavelength-dependent light attenuation, scattering, and refraction. Recent approaches leverage monocular foundation models with GRU-based iterative refinement for underwater adaptation; however, the sequential gating and local convolutional kernels in GRUs necessitate multiple iterations for long-range disparity propagation, limiting performance in large-disparity and textureless underwater regions. In this paper, we propose StereoAdapter-2, which replaces the conventional ConvGRU updater with a novel ConvSS2D operator based on selective state space models. The proposed operator employs a four-directional scanning strategy that naturally aligns with epipolar geometry while capturing vertical structural consistency, enabling efficient long-range spatial propagation within a single update step at linear computational complexity. Furthermore, we construct UW-StereoDepth-80K, a large-scale synthetic underwater stereo dataset featuring diverse baselines, attenuation coefficients, and scattering parameters through a two-stage generative pipeline combining semantic-aware style transfer and geometry-consistent novel view synthesis. Combined with dynamic LoRA adaptation inherited from StereoAdapter, our framework achieves state-of-the-art zero-shot performance on underwater benchmarks with 17% improvement on TartanAir-UW and 7.2% improvment on SQUID, with real-world validation on the BlueROV2 platform demonstrates the robustness of our approach. Code: https://github.com/AIGeeksGroup/StereoAdapter-2. Website: https://aigeeksgroup.github.io/StereoAdapter-2.

MarsRetrieval: Benchmarking Vision-Language Models for Planetary-Scale Geospatial Retrieval on Mars

Data-driven approaches like deep learning are rapidly advancing planetary science, particularly in Mars exploration. Despite recent progress, most existing benchmarks remain confined to closed-set supervised visual tasks and do not support text-guided retrieval for geospatial discovery. We introduce MarsRetrieval, a retrieval benchmark for evaluating vision-language models for Martian geospatial discovery. MarsRetrieval includes three tasks: (1) paired image-text retrieval, (2) landform retrieval, and (3) global geo-localization, covering multiple spatial scales and diverse geomorphic origins. We propose a unified retrieval-centric protocol to benchmark multimodal embedding architectures, including contrastive dual-tower encoders and generative vision-language models. Our evaluation shows MarsRetrieval is challenging: even strong foundation models often fail to capture domain-specific geomorphic distinctions. We further show that domain-specific fine-tuning is critical for generalizable geospatial discovery in planetary settings. Our code is available at https://github.com/ml-stat-Sustech/MarsRetrieval

Natural Language-Driven Global Mapping of Martian Landforms

Planetary surfaces are typically analyzed using high-level semantic concepts in natural language, yet vast orbital image archives remain organized at the pixel level. This mismatch limits scalable, open-ended exploration of planetary surfaces. Here we present MarScope, a planetary-scale vision-language framework enabling natural language-driven, label-free mapping of Martian landforms. MarScope aligns planetary images and text in a shared semantic space, trained on over 200,000 curated image-text pairs. This framework transforms global geomorphic mapping on Mars by replacing pre-defined classifications with flexible semantic retrieval, enabling arbitrary user queries across the entire planet in 5 seconds with F1 scores up to 0.978. Applications further show that it extends beyond morphological classification to facilitate process-oriented analysis and similarity-based geomorphological mapping at a planetary scale. MarScope establishes a new paradigm where natural language serves as a direct interface for scientific discovery over massive geospatial datasets.