Reinforcement learning with verifiable rewards (RLVR) has become a leading approach for improving large language model (LLM) reasoning capabilities. Most current methods follow variants of Group Relative Policy Optimization, which samples multiple reasoning completions, scores them relative to each other, and adjusts the policy accordingly. However, these approaches invariably sample discrete tokens at each reasoning step, discarding the rich distributional information in the model's probability distribution over candidate tokens. While preserving and utilizing this distributional information has proven beneficial in non-RL settings, current RLVR methods seem to be unnecessarily constraining the reasoning search space by not using this information. To address this limitation, we investigate mixture-of-token generation (MoT-G) in RLVR. We present a unified framework that generalizes existing MoT-G approaches, including existing training-free methods that construct mixture embeddings as weighted sums over token embeddings, and extend RLVR to operate directly in this continuous mixture space for generating chain-of-thought. Evaluating two MoT-G variants on Reasoning-Gym, a suite of reasoning-intensive language tasks, we find that MoT--G methods achieve substantial improvements (5--35 \% gains on 7 out of 10 tasks) compared to standard decoding with the Qwen2.5-1.5B model, while reaching comparable accuracy with half the number of trajectories, suggesting improved training efficiency. Through comprehensive hidden-state and token-level analyses, we provide evidence that MoT--G's benefits may stem from its ability to maintain higher hidden-state entropy throughout the reasoning process and promote exploration in token space.

An image of a room may be conjured given only the description of the underlying objects and their associated relations.

Large language models (LLMs) have demonstrated significant capabilities in natural language processing and reasoning, yet their effectiveness in autonomous planning has been under debate. While existing studies have utilized LLMs with external feedback mechanisms or in controlled environments for planning, these approaches often involve substantial computational and development resources due to the requirement for careful design and iterative backprompting. Moreover, even the most advanced LLMs like GPT-4 struggle to match human performance on standard planning benchmarks, such as the Blocksworld, without additional support. This paper investigates whether LLMs can independently generate long-horizon plans that rival human baselines. Our novel enhancements to Algorithm-of-Thoughts (AoT), which we dub AoT+, help achieve state-of-the-art results in planning benchmarks out-competing prior methods and human baselines all autonomously.

The degree to which neural networks can generalize to new combinations of familiar concepts, and the conditions under which they are able to do so, has long been an open question. In this work, we study the systematicity gap in visual question answering: the performance difference between reasoning on previously seen and unseen combinations of object attributes. To test, we introduce a novel diagnostic dataset, CLEVR-HOPE. We find that while increased quantity of training data does not reduce the systematicity gap, increased training data diversity of the attributes in the unseen combination does. In all, our experiments suggest that the more distinct attribute type combinations are seen during training, the more systematic we can expect the resulting model to be.

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

The visual world around us can be described as a structured set of objects and their associated relations. An image of a room may be conjured given only the description of the underlying objects and their associated relations. While there has been significant work on designing deep neural networks which may compose individual objects together, less work has been done on composing the individual relations between objects. A principal difficulty is that while the placement of objects is mutually independent, their relations are entangled and dependent on each other. To circumvent this issue, existing works primarily compose relations by utilizing a holistic encoder, in the form of text or graphs. In this work, we instead propose to represent each relation as an unnormalized density (an energy-based model), enabling us to compose separate relations in a factorized manner. We show that such a factorized decomposition allows the model to both generate and edit scenes that have multiple sets of relations more faithfully. We further show that decomposition enables our model to effectively understand the underlying relational scene structure.

Kevin Chen, an assistant professor at the Massachusetts Institute of Technology, envisions a time when his insect-sized drone could be used as a search and rescue robot -- to find survivors in disaster debris that bigger drones couldn't reach. Kevin Chen, an assistant professor at the Massachusetts Institute of Technology, envisions a time when his insect-sized drone could be used as a search and rescue robot -- to find survivors in disaster debris that bigger drones couldn't reach. The reason it's so hard to kill a mosquito is that they move really well. Scientists are trying to build a robot with that kind of agility. And these tiny but mighty flying robots could be used in life-and-death situations, such as finding people in a collapsed building.

If you've ever swatted a mosquito away from your face, only to have it return again (and again and again), you know that insects can be remarkably acrobatic and resilient in flight. Those traits help them navigate the aerial world, with all of its wind gusts, obstacles, and general uncertainty. Such traits are also hard to build into flying robots, but MIT Assistant Professor Kevin Yufeng Chen has built a system that approaches insects' agility. Chen, a member of the Department of Electrical Engineering and Computer Science and the Research Laboratory of Electronics, has developed insect-sized drones with unprecedented dexterity and resilience. The aerial robots are powered by a new class of soft actuator, which allows them to withstand the physical travails of real-world flight.