Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles (2409.10502v1)

Abstract: Causal LLMing using the Transformer architecture has yielded remarkable capabilities in 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 LLMing 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. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves $94.21\%$ of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves $92.04 \%$ of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

• The paper shows that using solver-decomposed reasoning sequences markedly improves performance, with complete Sudoku accuracy reaching 87.18% and beam search boosting results to 94.21%.
• The study employs both fixed and random order training, revealing that structured, iterative search and stepwise reasoning are crucial for effective puzzle solving.
• The research highlights emergent reasoning capabilities in CLMs, with probing accuracies over 93% and performance on par with specialized neural solvers without tailored network designs.

Causal LLMing Can Elicit Search and Reasoning Capabilities on Logic Puzzles

This research paper investigates the proficiency of Causal LLMs (CLMs) employing the Transformer architecture in performing complex reasoning tasks, such as solving Sudoku and Zebra puzzles. The paper's primary focus is understanding whether CLMs can effectively engage in search and reasoning operations by decomposing these tasks into smaller, logically sequential steps.

Key Insights and Methodology

The authors begin by illustrating the inherent reasoning challenges posed by Sudoku and Zebra puzzles, positing that to solve such puzzles, models must:

1. Conduct iterative search across the puzzle grid.
2. Apply sophisticated strategies to infer the correct values at specific cells.

Given these steps, the authors trained Transformer models to handle these puzzles, examining how different ordering of the solution steps impacted the models' performance. They delineate their approach into the following setups:

1. Fixed and Random Order Training: In these schemes, the ordering of cells in the training data was either predetermined or randomized. The fixed order model yielded a cell accuracy of 58.64% and a complete puzzle accuracy of 7.2%, whereas the random order training resulted in significantly lower performance with complete puzzle accuracy around 1%.
2. Solver-Decomposed Reasoning Order: This approach utilized solver-generated sequences, derived via a set of human-like strategies, to train the model. Here, the model achieved substantial improvements with a cell accuracy of 94.23% and a complete puzzle accuracy of 87.18%.

Further enhancements were evident when the authors applied beam search decoding, which bolstered the complete puzzle accuracy to 94.21% for Sudoku puzzles.

Results and Probabilistic Reasoning

The paper also presents a comparative paper with other neural network-based solvers, confirming that their Transformer models, even without network or loss function customization, performed comparably to specialized Recurrent Relational Networks (RRN) but without necessitating handcrafted designs.

The authors further investigated the internal mechanics of these Transformers. They found a near-complete overlap between the candidate sets inferred by the trained models and those computed by traditional solvers. This was evidenced by high probing accuracy—over 93% in most cases—indicating implicit emergent reasoning within the Transformer’s activations.

Application to Zebra Puzzles

While Sudoku puzzles were the primary focus, the researchers extended their analysis to Zebra puzzles, a more general and diverse set of logic problems. They confirmed that models trained with solver-decomposed reasoning orders also excelled in these tasks, achieving a cell accuracy of 95.63% and a complete puzzle accuracy of 91.17%.

Implications and Future Directions

The findings underscore the importance of training data structure in eliciting search and reasoning capabilities from CLMs. Importantly, the authors argue that simple next-token prediction can be remarkably effective when paired with structured, stepwise reasoning data. This demonstrates that pre-trained models can serve as robust reasoning engines, a notion that sidesteps the need for post-training methods like fine-tuning or complex prompt engineering.

However, the paper acknowledges limitations such as the synthetic nature of the tasks and the degree to which such controlled settings translate to real-world, more abstract reasoning. Future directions could involve exploring how models can generate or adapt new strategies autonomously and extend these insights to tasks requiring more nuanced long-term planning.

Overall, this paper provides substantial evidence that causal LLMing, with appropriately structured training data, can facilitate advanced reasoning in CLMs, paving the way for further explorations in AI planning and logical reasoning tasks.