Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we analyze how reinforcement learning agents handle problems of varying hardness. We also address many mathematical questions as a part of our study. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.

Constrained reinforcement learning (RL) seeks high-performance policies under safety constraints. We focus on an offline setting where the agent learns from a fixed dataset--a common requirement in realistic tasks to prevent unsafe exploration. To address this, we propose Diffusion-Regularized Constrained Offline Reinforcement Learning (DRCORL), which first uses a diffusion model to capture the behavioral policy from offline data and then extracts a simplified policy to enable efficient inference. We further apply gradient manipulation for safety adaptation, balancing the reward objective and constraint satisfaction.

Large language models are typically adapted to downstream tasks through supervised fine-tuning on domain-specific data. While standard fine-tuning focuses on minimizing generation loss to optimize model parameters, we take a deeper step by retaining and leveraging the model's own learning signals, analogous to how human learners reflect on past mistakes to improve future performance. We first introduce the concept of Mistake Log to systematically track the model's learning behavior and recurring errors throughout fine-tuning. Treating the original transformer-based model as the Pilot, we correspondingly design a Copilot model to refine the Pilot's inference performance via logits rectification. We name the overall Pilot-Copilot framework the Transformer Copilot, which introduces (i) a novel Copilot model design, (ii) a joint training paradigm where the Copilot continuously learns from the evolving Mistake Log alongside the Pilot, and (iii) a fused inference paradigm where the Copilot rectifies the Pilot's logits for enhanced generation. We provide both theoretical and empirical analyses on our new learning framework. Experiments on 12 benchmarks spanning commonsense, arithmetic, and recommendation tasks demonstrate that Transformer Copilot consistently improves performance by up to 34.5%, while introducing marginal computational overhead to Pilot models and exhibiting strong scalability and transferability.

This paper proposes a novel scene understanding task called Visual Jenga. Drawing inspiration from the game Jenga, the proposed task involves progressively removing objects from a single image until only the background remains. Just as Jenga players must understand structural dependencies to maintain tower stability, our task reveals the intrinsic relationships between scene elements by systematically exploring which objects can be removed while preserving scene coherence in both physical and geometric sense. As a starting point for tackling the Visual Jenga task, we propose a simple, data-driven, training-free approach that is surprisingly effective on a range of real-world images. The principle behind our approach is to utilize the asymmetry in the pairwise relationships between objects within a scene and employ a large inpainting model to generate a set of counterfactuals to quantify the asymmetry.

This paper investigates the dynamical properties of tokens in pre-trained Transformer models and explores their application to improving Transformers. To this end, we analyze the dynamical system governing the continuous-time limit of the pre-trained model and characterize the asymptotic behavior of its solutions. Specifically, we characterize when tokens move closer to or farther from one another over time, depending on the model parameters. We provide sufficient conditions, based on these parameters, to identify scenarios where tokens either converge to zero or diverge to infinity. Unlike prior works, our conditions are broader in scope and more applicable to real-world models. Furthermore, we investigate how different forms of positional encoding - specifically absolute and rotary - affect these dynamical regimes. Empirical evidence reveals that the convergence scenario adversely impacts model performance. Motivated by these insights, we propose simple refinements to Transformer architectures that mitigate convergence behavior in models with absolute or rotary positional encoding. These findings support theoretical foundations and design principles for improving Transformer models.

A major distinction between video and image understanding is that the former requires reasoning over time. Existing Video Large Language Models (VLLMs) demonstrate promising performance in general video understanding, such as brief captioning or object recognition within individual frames. However, they often struggle with temporal reasoning such as understanding continuous actions or tracking object transformations over time--which typically demands the integration of multiple frames in a temporally coherent manner. We first explore and explain such failures in Video LLMs from the perspective of language and "image" priors. While existing research has attempted to enhance the temporal understanding of VLLMs through various training strategies, the demand for expensive computational resources and training data often presents significant barriers.

The remarkable progress of Large Language Models (LLMs) presents promising opportunities for Verilog code generation which is significantly important for automated circuit design. The lacking of meaningful functional rewards hinders the preference optimization based on Reinforcement Learning (RL) for producing functionally correct Verilog code. In this paper, we propose Signal-Aware Learning for Verilog code generation (QiMeng-SALV) by leveraging code segments of functionally correct output signal to optimize RL training. Considering Verilog code specifies the structural interconnection of hardware gates and wires so that different output signals are independent, the key insight of QiMeng-SALV is to extract verified signal-aware implementations in partially incorrect modules, so as to enhance the extraction of meaningful functional rewards. Roughly, we verify the functional correctness of signals in generated module by comparing with that of reference module in the training data. Then abstract syntax tree (AST) is employed to identify signal-aware code segments which can provide meaningful functional rewards from erroneous modules. Finally, we introduce signal-aware DPO which is optimized on the correct signal-level code segments, thereby preventing noise and interference from incorrect signals. The proposed QiMeng-SALV underscores the paradigm shift from conventional module-level to fine-grained signal-level optimization in Verilog code generation, addressing the issue of insufficient functional rewards. Experiments demonstrate that our method achieves state-of-the-art performance on VerilogEval and RTLLM, with a 7B parameter model matching the performance of the DeepSeek v3 671B model and significantly outperforming the leading open-source model CodeV trained on the same dataset.

Spiking Transformers have recently emerged as promising architectures for combining the efficiency of spiking neural networks with the representational power of self-attention. However, the lack of standardized implementations, evaluation pipelines, and consistent design choices has hindered fair comparison and principled analysis. In this paper, we introduce STEP, a unified benchmark framework for Spiking Transformers that supports a wide range of tasks, including classification, segmentation, and detection across static, event-based, and sequential datasets. STEP provides modular support for diverse components such as spiking neurons, input encodings, surrogate gradients, and multiple backends (e.g., SpikingJelly, BrainCog). Using STEP, we reproduce and evaluate several representative models, and conduct systematic ablation studies on attention design, neuron types, encoding schemes, and temporal modeling capabilities. We also propose a unified analytical model for energy estimation, accounting for spike sparsity, bitwidth, and memory access, and show that quantized ANNs may offer comparable or better energy efficiency. Our results suggest that current Spiking Transformers rely heavily on convolutional frontends and lack strong temporal modeling, underscoring the need for spike-native architectural innovations. The full code is available at: https://github.com/Fancyssc/STEP.

People stand near humanoid robots on display at the Nvidia booth during the China International Supply Chain Expo (CISCE) in Beijing, China June 22, 2026. Nvidia Corp. is working to make humanoid robots safer around people, arguing that they'll need to handle split-second decisions before they can be trusted to work closely with humans. The chipmaker is offering software and semiconductors that will allow humanoids to enter the workplace and truly interact with people -- even making physical contact if necessary. Nvidia's Halos software, developed from systems used for self-driving vehicles, will be the basis of computers that give robots a much better awareness of what's happening around them, the company said in a statement Monday. Nvidia and its Silicon Valley peers are racing to develop technology for robotics, billing it as the next big market for artificial intelligence. The machines will evolve into a market with billions of devices, tech executives predict.

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.