Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks (2106.04537v2)

Abstract: Deep neural networks are powerful machines for visual pattern recognition, but reasoning tasks that are easy for humans may still be difficult for neural models. Humans possess the ability to extrapolate reasoning strategies learned on simple problems to solve harder examples, often by thinking for longer. For example, a person who has learned to solve small mazes can easily extend the very same search techniques to solve much larger mazes by spending more time. In computers, this behavior is often achieved through the use of algorithms, which scale to arbitrarily hard problem instances at the cost of more computation. In contrast, the sequential computing budget of feed-forward neural networks is limited by their depth, and networks trained on simple problems have no way of extending their reasoning to accommodate harder problems. In this work, we show that recurrent networks trained to solve simple problems with few recurrent steps can indeed solve much more complex problems simply by performing additional recurrences during inference. We demonstrate this algorithmic behavior of recurrent networks on prefix sum computation, mazes, and chess. In all three domains, networks trained on simple problem instances are able to extend their reasoning abilities at test time simply by "thinking for longer."

• The paper reveals that RNNs trained on simple tasks can generalize to more complex problems solely by increasing the number of computation iterations.
• The study uses tasks like prefix sums, maze solving, and chess puzzles to validate the iterative, algorithm-like behavior of RNNs.
• The results suggest that RNNs offer a scalable problem-solving approach that can outperform traditional feed-forward networks in complex reasoning scenarios.

Background

Deep neural networks have established their prowess in visual pattern recognition but translating this success to complex reasoning tasks has been challenging. Recurrent neural networks (RNNs), on the other hand, offer an intriguing capability that mirrors human problem-solving. Humans extend their problem-solving skills learnt on straightforward problems to tackle more complex ones simply by spending more time thinking about the problem. Computers mimic this through algorithms that scale with problem size. This paper explores whether RNNs trained on simple tasks can extrapolate their knowledge to solve more complex tasks by merely increasing their computation at test time.

Generalizing to Complex Problems

RNNs demonstrate an impressive ability to generalize from simple to more complex problems without the addition of new parameters or retraining. Unlike standard feed-forward networks, which fail to extend their reasoning power in this manner, RNNs benefit from iterative processes—analogous to human thinking—wherein they apply transformations to incoming data over multiple steps. Remarkably, when RNNs trained on easy tasks are tested on harder tasks and allowed more iterations—symbolic of 'thinking longer'—they show significantly improved performance. This showcases the potential of RNNs to learn scalable problem-solving methods instead of static mappings from inputs to outputs.

Innovative Experiments

The research hinges on three reasoning tasks historically resolved using algorithms: computation of prefix sums, maze solving, and chess puzzles. These tasks require sequential reasoning, allowing quantifiable problem difficulty modulation—perfect for analyzing logical extrapolation capabilities of RNNs. The core finding is that RNNs trained on easy versions of these tasks generalize to harder variants when allowed more iterations at test time. Intriguingly, the paper shows that simply increasing the number of iterations—the depth of thought, so to speak—enhances RNNs' performance considerably, often surpassing traditional feed-forward networks.

Insights Into the Learning Process

An in-depth analysis of the RNNs offers rich insights. Visualizations of the iterative process in solving mazes illustrate how the networks progressively refine their outputs with each iteration, moving closer to the solution. Similarly, in prefix sum computation, RNNs seem to work progressively along the input, suggestive of an underlying learned algorithmic behavior. For chess puzzles, the iterative outputs underline an increasing model confidence in determining the best next move—a challenge far more complex than the previous tasks.

Forward-Thinking Discussion

The paper invites contemplation on whether learned models can behave like classical algorithms. One of the questions raised is whether networks can be designed to keep improving performance with more computational time. This possibility has profound implications: it suggests the potential for training machines to solve unknown problems of the future—a prospect hardly conceivable with static feed-forward networks.

Conclusive Thoughts

This paper reveals that RNNs possess a remarkable capacity to generalize from simple to complex problems by increasing their computational budget, akin to human incremental reasoning. The ability to learn scalable problem-solving techniques could redefine AI's capability to resolve tasks traditionally handled by algorithm-driven systems. The implications extend beyond academic curiosity and potentially pave the way for creating more advanced, adaptive, and context-aware artificial intelligence systems.