I review the purported opposition between computational and dynamical approaches in cognitive science, i argue that both computational and dynamical notions will be necessary for a full explanatory account of cognition, and give a perspective on how recent research in complex systems can lead to a much needed rapprochement between computational and dynamical styles of explanation.

Large language models (LLMs) have performed well on several reasoning benchmarks, including ones that test analogical reasoning abilities. However, it has been debated whether they are actually performing humanlike abstract reasoning or instead employing less general processes that rely on similarity to what has been seen in their training data. Here we investigate the generality of analogy-making abilities previously claimed for LLMs (Webb, Holyoak, & Lu, 2023). We take one set of analogy problems used to evaluate LLMs and create a set of “counterfactual” variants—versions that test the same abstract reasoning abilities but that are likely dissimilar from any pre-training data. We test humans and three GPT models on both the original and counterfactual problems, and show that, while the performance of humans remains high for all the problems, the GPT models' performance declines sharply on the counterfactual set. This work provides evidence that, despite previously reported successes of LLMs on analogical reasoning, these models lack the robustness and generality of human analogy-making.

We discuss the role of computational temperature in Copycat, a computer model of the mental mechanisms underlying human concepts and analogy-making. In Copycat, computational temperature is used both to measure the amount and quality of perceptual organization created by the program as processing proceeds, and, reciprocally, to continuously control the degree of randomness in the system. W e discuss these roles in two aspects of perception central to Copycat's behavior: (1) the emergence of a parallel terraced scan, in which many possible courses of action are explored simultaneously, each at a speed and to a depth proportional to moment-to-moment estimates of its promise, and (2) the ability to restructure initial perceptions — sometimes radically — in order to arrive at a deeper understanding of a situation. W e compare our notion of temperature to similar notions in other computational frameworks. Finally, we give an example of how temperature is used in Copycat's creation of a subtle and insightful analogy.

A central question about cognition is how, faced with a situation, one explores possible ways of understanding and responding lo it In particular, how do concepts initially considered irrelevant, or not even considered at all, become relevant in response to pressures evoked by the understanding process itself We describe a model of concepts and high-level perception in which concepts consist of a central region surrounded by a dynamic nondeterministic "halo of potential associations, in which relevance and degree of association change as processing proceeds. As the representation of a situation is built, associations arise and are considered in a probabilistic fashion according to a parallel terraced scan, in which many routes toward understanding the situation are tested in parallel, each at a rate and to a depth reflecting ongoing evaluations of its promise. We describe a computer program that implements this model in the context of analogy-making, and illustrate, using screen dumps from a run, how the program's ability to flexibly bring in appropriate concepts for a given situation emerges from the mechanisms we are proposing.

We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how machine-learning processes can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation.

We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's lambda parameter (Langton, 1990), and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near ``critical'' lambda values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with lambda values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to lambda, dynamical-behavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.