Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell.

Like a true Midwesterner, my dad has been feuding with the squirrels in his backyard for years. Every few months, he comes home with a new "squirrel-proof" bird feeder, each more expensive than the previous, each one promising to finally do the trick. My mom rolls her eyes at the pile of hardware-store receipts and discarded feeders. I shake my head watching this all play out--knowing full well those feeders never stood a chance. Walk down the birdseed aisle in any hardware store and you'll find an entire product category promising "squirrel-proof" solutions.

Algorithmic reasoning is a fundamental cognitive ability that plays a pivotal role in problem-solving and decision-making processes. Reinforcement Learning (RL) has demonstrated remarkable proficiency in tasks such as motor control, handling perceptual input, and managing stochastic environments. These advancements have been enabled in part by the availability of benchmarks. In this work we introduce PUZZLES, a benchmark based on Simon Tatham's Portable Puzzle Collection, aimed at fostering progress in algorithmic and logical reasoning in RL. PUZZLES contains 40 diverse logic puzzles of adjustable sizes and varying levels of complexity, providing detailed information on the strengths and generalization capabilities of RL agents. Furthermore, we evaluate various RL algorithms on PUZZLES, providing baseline comparisons and demonstrating the potential for future research. All the software, including the environment, is available at this https url.

While multi-modal large language models (MLLMs) have shown significant progress across popular visual reasoning benchmarks, whether they possess abstract visual reasoning abilities remains an open question. Similar to the Sudoku puzzles, abstract visual reasoning (AVR) problems require finding high-level patterns (e.g., repetition constraints on numbers) that control the input shapes (e.g., digits) in a specific task configuration (e.g., matrix). However, existing AVR benchmarks only consider a limited set of patterns (addition, conjunction), input shapes (rectangle, square), and task configurations (3 3 matrices). And they fail to capture all abstract reasoning patterns in human cognition necessary for addressing real-world tasks, such as geometric properties and object boundary understanding in real-world navigation. To evaluate MLLMs' AVR abilities systematically, we introduce MARVEL founded on the core knowledge system in human cognition, a multi-dimensional AVR benchmark with 770 puzzles composed of six core knowledge patterns, geometric and abstract shapes, and five different task configurations.

We propose a novel reinforcement learning algorithm, AlphaNPI, that incorporates the strengths of Neural Programmer-Interpreters (NPI) and AlphaZero. NPI contributes structural biases in the form of modularity, hierarchy and recursion, which are helpful to reduce sample complexity, improve generalization and increase interpretability. AlphaZero contributes powerful neural network guided search algorithms, which we augment with recursion. AlphaNPI only assumes a hierarchical program specification with sparse rewards: 1 when the program execution satisfies the specification, and 0 otherwise. This specification enables us to overcome the need for strong supervision in the form of execution traces and consequently train NPI models effectively with reinforcement learning. The experiments show that AlphaNPI can sort as well as previous strongly supervised NPI variants. The AlphaNPI agent is also trained on a Tower of Hanoi puzzle with two disks and is shown to generalize to puzzles with an arbitrary number of disks. The experiments also show that when deploying our neural network policies, it is advantageous to do planning with guided Monte Carlo tree search.

Understanding and reasoning about physics is an important ability of intelligent agents. We develop the PHYRE benchmark for physical reasoning that contains a set of simple classical mechanics puzzles in a 2D physical environment. The benchmark is designed to encourage the development of learning algorithms that are sample-efficient and generalize well across puzzles. We test several modern learning algorithms on PHYRE and find that these algorithms fall short in solving the puzzles efficiently. We expect that PHYRE will encourage the development of novel sample-efficient agents that learn efficient but useful models of physics. For code and to play PHYRE for yourself, please visit https://player.phyre.ai.

This paper proposes the RePAIR dataset that represents a challenging benchmark to test modern computational and data driven methods for puzzle-solving and reassembly tasks. Our dataset has unique properties that are uncommon to current benchmarks for 2D and 3D puzzle solving. The fragments and fractures are realistic, caused by a collapse of a fresco during a World War II bombing at the Pompeii archaeological park. The fragments are also eroded and have missing pieces with irregular shapes and different dimensions, challenging further the reassembly algorithms. The dataset is multi-modal providing high resolution images with characteristic pictorial elements, detailed 3D scans of the fragments and meta-data annotated by the archaeologists. Ground truth has been generated through several years of unceasing fieldwork, including the excavation and cleaning of each fragment, followed by manual puzzle solving by archaeologists of a subset of approx.

Recent years have seen a significant progress in the general-purpose problem solving abilities of large vision and language models (LVLMs), such as ChatGPT, Gemini, etc.; some of these breakthroughs even seem to enable AI models to outperform human abilities in varied tasks that demand higher-order cognitive skills. Are the current large AI models indeed capable of generalized problem solving as humans do? A systematic analysis of AI capabilities for joint vision and text reasoning, however, is missing in the current scientific literature. In this paper, we make an effort towards filling this gap, by evaluating state-of-the-art LVLMs on their mathematical and algorithmic reasoning abilities using visuo-linguistic problems from children's Olympiads. Specifically, we consider problems from the Mathematical Kangaroo (MK) Olympiad, which is a popular international competition targeted at children from grades 1-12, that tests children's deeper mathematical abilities using puzzles that are appropriately gauged to their age and skills. Using the puzzles from MK, we created a dataset, dubbed SMART-840, consisting of 840 problems from years 2020-2024. With our dataset, we analyze LVLMs power on mathematical reasoning; their responses on our puzzles offer a direct way to compare against that of children. Our results show that modern LVLMs do demonstrate increasingly powerful reasoning skills in solving problems for higher grades, but lack the foundations to correctly answer problems designed for younger children. Further analysis shows that there is no significant correlation between the reasoning capabilities of AI models and that of young children, and their capabilities appear to be based on a different type of reasoning than the cumulative knowledge that underlies children's mathematical skills.