Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

Intelligent vision control systems for surgical robots should adapt to unknown and diverse objects while being robust to system disturbances. Previous methods did not meet these requirements due to mainly relying on pose estimation and feature tracking. We propose a world-model-based deep reinforcement learning framework "Grasp Anything for Surgery" (GAS), that learns a pixel-level visuomotor policy for surgical grasping, enhancing both generality and robustness. In particular, a novel method is proposed to estimate the values and uncertainties of depth pixels for a rigid-link object's inaccurate region based on the empirical prior of the object's size; both depth and mask images of task objects are encoded to a single compact 3-channel image (size: 64x64x3) by dynamically zooming in the mask regions, minimizing the information loss. The learned controller's effectiveness is extensively evaluated in simulation and in a real robot. Our learned visuomotor policy handles: i) unseen objects, including 5 types of target grasping objects and a robot gripper, in unstructured real-world surgery environments, and ii) disturbances in perception and control. Note that we are the first work to achieve a unified surgical control system that grasps diverse surgical objects using different robot grippers on real robots in complex surgery scenes (average success rate: 69%). Our system also demonstrates significant robustness across 6 conditions including background variation, target disturbance, camera pose variation, kinematic control error, image noise, and re-grasping after the gripped target object drops from the gripper. Videos and codes can be found on our project page: https://linhongbin.github.io/gas/.

A Mitsubishi Electric machine has cracked the notoriously challenging Rubik's Cube puzzle in less than a third of a second. In the blink of an eye, computer-controlled components moved the squares of the 3 x 3 x 3 cube until each side of the block was a single color, thus completing the game. Humans present applauded the feat. Guinness World Records recognized the 0.305-second time achieved by the TOKUI Fast Accurate Synchronized Motion Testing Robot as a new world best, with it beating the previous record of 0.38 seconds. Mitsubishi Electric received a certificate from the records body on May 21. The fastest time by a human is 3.13 seconds, achieved in June 2023 by Max Park at an event in California.

Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL learning involves directly acquiring data from downstream tasks, which is not feasible for federated learning (FL). To address this limitation, we shift the focus from such a one-to-one interactive neuro-symbolic paradigm to one-to-many Federated Neuro-Symbolic Learning framework (FedNSL) with latent variables as the FL communication medium. Built on the basis of our novel reformulation of the NSL theory, FedNSL is capable of identifying and addressing rule distribution heterogeneity through a simple and effective Kullback-Leibler (KL) divergence constraint on rule distribution applicable under the FL setting. It further theoretically adjusts variational expectation maximization (V-EM) to reduce the rule search space across domains. This is the first incorporation of distribution-coupled bilevel optimization into FL. Extensive experiments based on both synthetic and real-world data demonstrate significant advantages of FedNSL compared to five state-of-the-art methods. It outperforms the best baseline by 17% and 29% in terms of unbalanced average training accuracy and unseen average testing accuracy, respectively.

We give a model-based agent that builds a Python program representing its knowledge of the world based on its interactions with the environment. The world model tries to explain its interactions, while also being optimistic about what reward it can achieve. We define this optimism as a logical constraint between a program and a planner. We study our agent on gridworlds, and on task planning, finding our approach is more sample-efficient compared to deep RL, more compute-efficient compared to ReAct-style agents, and that it can transfer its knowledge across environments by editing its code.

It's a puzzle that can keep most people entertained for hours. But the Rubik's Cube is light work for one robot, which has officially broken the Guinness World Record for the fastest robot to solve a rotating puzzle cube. The bot can complete the puzzle in just 0.305 seconds - so it's safe to say that if you blink, you'll miss it! That's around 10 times faster than the quickest human, who is able to solve the puzzle in an impressive 3.13 seconds. It's a puzzle that can keep most people entertained for hours. But the Rubik's Cube is light work for one robot, which has officially broken the Guinness World Record for the fastest robot to solve a rotating puzzle cube The'fastest robot to solve a rotating puzzle cube' record has been popular for years.

In this work we consider Code World Models, world models generated by a Large Language Model (LLM) in the form of Python code for model-based Reinforcement Learning (RL). Calling code instead of LLMs for planning has the advantages of being precise, reliable, interpretable, and extremely efficient. However, writing appropriate Code World Models requires the ability to understand complex instructions, to generate exact code with non-trivial logic and to self-debug a long program with feedback from unit tests and environment trajectories. To address these challenges, we propose Generate, Improve and Fix with Monte Carlo Tree Search (GIF-MCTS), a new code generation strategy for LLMs. To test our approach, we introduce the Code World Models Benchmark (CWMB), a suite of program synthesis and planning tasks comprised of 18 diverse RL environments paired with corresponding textual descriptions and curated trajectories. GIF-MCTS surpasses all baselines on the CWMB and two other benchmarks, and we show that the Code World Models synthesized with it can be successfully used for planning, resulting in model-based RL agents with greatly improved sample efficiency and inference speed.

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capabilities. In this study, we examine the matching mechanism employed by Transformer for multi-step reasoning on a constructed dataset. We investigate factors that influence the model's matching mechanism and discover that small initialization and post-LayerNorm can facilitate the formation of the matching mechanism, thereby enhancing the model's reasoning ability. Moreover, we propose a method to improve the model's reasoning capability by adding orthogonal noise. Finally, we investigate the parallel reasoning mechanism of Transformers and propose a conjecture on the upper bound of the model's reasoning ability based on this phenomenon. These insights contribute to a deeper understanding of the reasoning processes in large language models and guide designing more effective reasoning architectures and training strategies.

The DreamerV3 agent recently demonstrated state-of-the-art performance in diverse domains, learning powerful world models in latent space using a pixel reconstruction loss. However, while the reconstruction loss is essential to Dreamer's performance, it also necessitates modeling unnecessary information. Consequently, Dreamer sometimes fails to perceive crucial elements which are necessary for task-solving when visual distractions are present in the observation, significantly limiting its potential. In this paper, we present MuDreamer, a robust reinforcement learning agent that builds upon the DreamerV3 algorithm by learning a predictive world model without the need for reconstructing input signals. Rather than relying on pixel reconstruction, hidden representations are instead learned by predicting the environment value function and previously selected actions. Similar to predictive self-supervised methods for images, we find that the use of batch normalization is crucial to prevent learning collapse. We also study the effect of KL balancing between model posterior and prior losses on convergence speed and learning stability. We evaluate MuDreamer on the commonly used DeepMind Visual Control Suite and demonstrate stronger robustness to visual distractions compared to DreamerV3 and other reconstruction-free approaches, replacing the environment background with task-irrelevant real-world videos. Our method also achieves comparable performance on the Atari100k benchmark while benefiting from faster training.

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.