Recent multimodal language models can reason directly about robot scenes, but it is unclear whether they need to repeatedly reinterpret raw visual observations at every step of an interaction. We propose shifting routine spatial reasoning from images to text and symbols through a 3D geometric abstraction that is refreshed locally from observations and read directly by the language models. Specifically, our interface represents scene geometry via typed, evidence-aware symbolic references to object parts, grounds them from calibrated RGB-D, and returns compact textual checkpoints with metric residuals after each action. Symbolic task structure can thus be reused across decisions while metric values are rebound to the current scene, with direct visual reasoning invoked only on demand. Across offline policy synthesis and continuous online execution, reasoning over grounded text and symbols improves multi-step manipulation completion while substantially reducing repeated multimodal queries, positioning explicit geometric state as an effective substrate for agentic robot policies.
Spherical-harmonic neural operators provide an efficient representation for global forecasting, but their discretized pointwise nonlinearities can break rotational equivariance through aliasing. Clebsch-Gordan (CG) tensor products provide exactly equivariant interactions between spherical-harmonic representations, but their computational cost grows rapidly with spectral bandwidth and has limited their use at forecasting scale. We introduce LCG-SFNO, which combines low-rank CG interactions within a controlled low-degree band with coefficient-space residual propagation and an exactly projected quadratic nonlinearity, preserving SO(3) equivariance throughout the learned operator. To make the CG interaction practical, we further develop SSHCG, a sparse GPU implementation with a factorized alternative for wider coupled bands. On spherical shallow-water dynamics and the ERA5-based WeatherBench benchmark, LCG-SFNO reduces rotational error to numerical precision (more than three orders of magnitude below SFNO on shallow water and five orders of magnitude below it on WeatherBench), while matching SFNO on shallow-water forecasting and substantially improving forecast skill relative to SFNO on WeatherBench. Matched ablations show that CG coupling accelerates convergence, while SSHCG keeps the coupling to about 10 percent of a training step at the operating bandwidth, making exact equivariant coupling practical at forecasting scale.
Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved mathematical reasoning, yet progress on hard prompts often stalls: a prompt can remain unsolved for many training steps before abruptly transitioning to solved--a discrete "zero-to-one" jump whose underlying dynamics and steerability remain poorly understood. We investigate two questions: what drives this transition, and can it be steered? Through event-based analysis measuring the time-to-first-positive (TTFP), we find that negative rollouts preceding successful transitions consistently retain higher early-stage generation entropy, distinguishing near-solvable failures from dead ends. This signal motivates NAPO (Negative-Augmented Policy Optimization), a method integrated with Group Relative Policy Optimization (GRPO) that ranks negatives in unsolved groups via an early-branching driver and assigns graded advantages, injecting informative gradients precisely where standard group-relative updates vanish. Under fixed rollout budgets, NAPO accelerates early solution discovery and improves Pass@256 by 10.0 points on AIME24 and 6.6 points on AIME2025, demonstrating that zero-to-one transitions are diagnosable and steerable through driver-guided negative learning. Our code is available at https://github.com/jameszhu-pixel-time/Z2O.
Open-vocabulary 3D occupancy prediction represents scene geometry and semantics in a unified voxel grid, enabling recognition beyond predefined categories. One approach reconstructs scenes with 3D Gaussians and converts them into voxel occupancy. However, Gaussian scale inflation and excessive overlap can distort voxel occupancy predictions, while semantic mixing can arise within Gaussians spanning multiple categories and during 3D--2D semantic feature alignment. We propose GCSR-OCC, which combines geometry calibration and multi-mode query-conditioned semantic routing for indoor occupancy prediction from a single RGB image. The Evidence-Conserving Gaussian-to-Occupancy operator (EC-G2O) uses kernel mass normalization, $p$-norm aggregation, and a learnable gain to suppress scale inflation and excessive local evidence accumulation while calibrating occupancy responses. Multi-mode Query-First Gaussian Semantic Routing (MM-QGSR) matches multiple semantic modes per Gaussian to text queries and aggregates query-specific evidence into voxels through a learnable text-conditioned router. Fine-grained subclass queries and smoothed semantic aggregation further refine voxel-level predictions. Without 3D semantic annotations, GCSR-OCC achieves state-of-the-art performance in open-vocabulary occupancy prediction on Occ-ScanNet, with 63.31% geometric IoU and 27.44% semantic mIoU. It also reduces geometric aggregation latency from 19.76 ms to 12.88 ms. Our code will be made publicly available.
Recent advances in reasoning models have demonstrated remarkable capabilities on mathematical and coding tasks. However, their effectiveness in embodied domains, where the agent must continuously interact with environments and process observation-action interleaved trajectories, remains largely unexplored. We present Embodied-Reasoner, a reasoning model for interactive embodied tasks. Unlike mathematical reasoning that relies primarily on logical deduction, embodied scenarios demand spatial understanding, temporal reasoning, and ongoing self-reflection based on interaction history. To address these challenges, we synthesize 9.3k coherent Observation-Thought-Action trajectories containing 64k ego-centric images and 90k diverse reasoning processes (analysis, spatial reasoning, reflection, planning, and verification). We develop a three-stage training recipe that progressively enhances the model’s capabilities through imitation learning, rejection sampling tuning on self-exploration trajectories, and reflection tuning. The evaluation shows that our model significantly outperforms advanced visual reasoning models, e.g., exceeds OpenAI o1, o3-mini, and Claude-3.7 by +9%, 24%, and +13%. Analysis reveals that our model exhibits fewer repeated searches and logical inconsistencies, with particular advantages in complex long-horizon tasks. Real-world testing further validates the effectiveness of our approach.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表