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Symbolic systems are powerful frameworks for modeling cognitive processes as they encapsulate the rules and relationships fundamental to many aspects of human reasoning and behavior. Central to these models are systematicity, compositionality, and productivity, making them invaluable in both cognitive science and artificial intelligence. However, certain limitations remain. For instance, the integration of structured symbolic processes and latent sub-symbolic processes has been implemented at the computational level through fiat methods such as quantization or softmax sampling, which assume, rather than derive, the operations underpinning discretization and symbolicization. In this work, we introduce a novel neural stochastic dynamical systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT). Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. Moreover, like PLoT, our model learns to sample a diverse distribution of attractor states that reflect the mutual information between the input data and the symbolic encodings. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuro-plausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations.

Accounts of human language processing have long appealed to implicit ``situation models'' that enrich comprehension with relevant but unstated world knowledge. Here, we apply causal intervention techniques to recent transformer models to analyze performance on the Winograd Schema Challenge (WSC), where a single context cue shifts interpretation of an ambiguous pronoun. We identify a relatively small circuit of attention heads that are responsible for propagating information from the context word that guides which of the candidate noun phrases the pronoun ultimately attends to. We then compare how this circuit behaves in a closely matched ``syntactic'' control where the situation model is not strictly necessary. These analyses suggest distinct pathways through which implicit situation models are constructed to guide pronoun resolution., Comment: Findings of ACL

Out-of-distribution generalization (OODG) is a longstanding challenge for neural networks. This challenge is quite apparent in tasks with well-defined variables and rules, where explicit use of the rules could solve problems independently of the particular values of the variables, but networks tend to be tied to the range of values sampled in their training data. Large transformer-based language models have pushed the boundaries on how well neural networks can solve previously unseen problems, but their complexity and lack of clarity about the relevant content in their training data obfuscates how they achieve such robustness. As a step toward understanding how transformer-based systems generalize, we explore the question of OODG in small scale transformers trained with examples from a known distribution. Using a reasoning task based on the puzzle Sudoku, we show that OODG can occur on a complex problem if the training set includes examples sampled from the whole distribution of simpler component tasks. Successful generalization depends on carefully managing positional alignment when absolute position encoding is used, but we find that suppressing sensitivity to absolute positions overcomes this limitation. Taken together our results represent a small step toward understanding and promoting systematic generalization in transformers.

Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization of the transitions through intermediate solution steps to the goal state. We find that models that are supplied with such sequences as prompts can solve tasks with a significantly higher accuracy, and models that are trained to produce such sequences solve problems better than those that are trained with previously used human-generated sequences and other baselines. Our work thus takes several steps toward elucidating and improving how language models perform on tasks requiring multi-step mathematical reasoning.

Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional inputs. However, there is an ongoing debate about how and when transformers can acquire highly structured behavior and achieve systematic generalization. Here, we explore how well a causal transformer can perform a set of algorithmic tasks, including copying, sorting, and hierarchical compositions of these operations. We demonstrate strong generalization to sequences longer than those used in training by replacing the standard positional encoding typically used in transformers with labels arbitrarily paired with items in the sequence. We search for the layer and head configuration sufficient to solve these tasks, then probe for signs of systematic processing in latent representations and attention patterns. We show that two-layer transformers learn reliable solutions to multi-level problems, develop signs of task decomposition, and encode input items in a way that encourages the exploitation of shared computation across related tasks. These results provide key insights into how attention layers support structured computation both within a task and across multiple tasks., Comment: 18 pages

Reasoning is a key ability for an intelligent system. Large language models (LMs) achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect. For example, human reasoning is affected by our real-world knowledge and beliefs, and shows notable "content effects"; humans reason more reliably when the semantic content of a problem supports the correct logical inferences. These content-entangled reasoning patterns play a central role in debates about the fundamental nature of human intelligence. Here, we investigate whether language models $\unicode{x2014}$ whose prior expectations capture some aspects of human knowledge $\unicode{x2014}$ similarly mix content into their answers to logical problems. We explored this question across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task. We evaluate state of the art large language models, as well as humans, and find that the language models reflect many of the same patterns observed in humans across these tasks $\unicode{x2014}$ like humans, models answer more accurately when the semantic content of a task supports the logical inferences. These parallels are reflected both in answer patterns, and in lower-level features like the relationship between model answer distributions and human response times. Our findings have implications for understanding both these cognitive effects in humans, and the factors that contribute to language model performance., Comment: Published version of record: https://academic.oup.com/pnasnexus/article/3/7/pgae233/7712372

Language Models (LMs) can perform new tasks by adapting to a few in-context examples. For humans, explanations that connect examples to task principles can improve learning. We therefore investigate whether explanations of few-shot examples can help LMs. We annotate questions from 40 challenging tasks with answer explanations, and various matched control explanations. We evaluate how different types of explanations, instructions, and controls affect zero- and few-shot performance. We analyze these results using statistical multilevel modeling techniques that account for the nested dependencies among conditions, tasks, prompts, and models. We find that explanations can improve performance -- even without tuning. Furthermore, explanations hand-tuned for performance on a small validation set offer substantially larger benefits, and building a prompt by selecting examples and explanations together substantially improves performance over selecting examples alone. Finally, even untuned explanations outperform carefully matched controls, suggesting that the benefits are due to the link between an example and its explanation, rather than lower-level features. However, only large models benefit. In summary, explanations can support the in-context learning of large LMs on challenging tasks., Comment: Findings of EMNLP 2022

Inferring the abstract relational and causal structure of the world is a major challenge for reinforcement-learning (RL) agents. For humans, language--particularly in the form of explanations--plays a considerable role in overcoming this challenge. Here, we show that language can play a similar role for deep RL agents in complex environments. While agents typically struggle to acquire relational and causal knowledge, augmenting their experience by training them to predict language descriptions and explanations can overcome these limitations. We show that language can help agents learn challenging relational tasks, and examine which aspects of language contribute to its benefits. We then show that explanations can help agents to infer not only relational but also causal structure. Language can shape the way that agents to generalize out-of-distribution from ambiguous, causally-confounded training, and explanations even allow agents to learn to perform experimental interventions to identify causal relationships. Our results suggest that language description and explanation may be powerful tools for improving agent learning and generalization., Comment: ICML 2022; 23 pages

Neural networks have long been used to model human intelligence, capturing elements of behavior and cognition, and their neural basis. Recent advancements in deep learning have enabled neural network models to reach and even surpass human levels of intelligence in many respects, yet unlike humans, their ability to learn new tasks quickly remains a challenge. People can reason not only in familiar domains, but can also rapidly learn to reason through novel problems and situations, raising the question of how well modern neural network models capture human intelligence and in which ways they diverge. In this work, we explore this gap by investigating human adults' ability to learn an abstract reasoning task based on Sudoku from a brief instructional tutorial with explanatory feedback for incorrect responses using a narrow range of training examples. We find that participants who master the task do so within a small number of trials and generalize well to puzzles outside of the training range. We also find that most of those who master the task can describe a valid solution strategy, and such participants perform better on transfer puzzles than those whose strategy descriptions are vague or incomplete. Interestingly, fewer than half of our human participants were successful in acquiring a valid solution strategy, and this ability is associated with high school mathematics education. We consider the challenges these findings pose for building computational models that capture all aspects of our findings and point toward a possible role for learning to engage in explanation-based reasoning to support rapid learning and generalization., Comment: 27 pages, 108 references, 8 Figures, and one Table, plus Supplementary Materials

An important aspect of intelligence is the ability to adapt to a novel task without any direct experience (zero-shot), based on its relationship to previous tasks. Humans can exhibit this cognitive flexibility. By contrast, models that achieve superhuman performance in specific tasks often fail to adapt to even slight task alterations. To address this, we propose a general computational framework for adapting to novel tasks based on their relationship to prior tasks. We begin by learning vector representations of tasks. To adapt to new tasks, we propose meta-mappings, higher-order tasks that transform basic task representations. We demonstrate the effectiveness of this framework across a wide variety of tasks and computational paradigms, ranging from regression to image classification and reinforcement learning. We compare to both human adaptability and language-based approaches to zero-shot learning. Across these domains, meta-mapping is successful, often achieving 80-90% performance, without any data, on a novel task, even when the new task directly contradicts prior experience. We further show that meta-mapping can not only generalize to new tasks via learned relationships, but can also generalize using novel relationships unseen during training. Finally, using meta-mapping as a starting point can dramatically accelerate later learning on a new task, and reduce learning time and cumulative error substantially. Our results provide insight into a possible computational basis of intelligent adaptability and offer a possible framework for modeling cognitive flexibility and building more flexible artificial intelligence systems., Comment: 45 pages

Language is crucial for human intelligence, but what exactly is its role? We take language to be a part of a system for understanding and communicating about situations. The human ability to understand and communicate about situations emerges gradually from experience and depends on domain-general principles of biological neural networks: connection-based learning, distributed representation, and context-sensitive, mutual constraint satisfaction-based processing. Current artificial language processing systems rely on the same domain general principles, embodied in artificial neural networks. Indeed, recent progress in this field depends on \emph{query-based attention}, which extends the ability of these systems to exploit context and has contributed to remarkable breakthroughs. Nevertheless, most current models focus exclusively on language-internal tasks, limiting their ability to perform tasks that depend on understanding situations. These systems also lack memory for the contents of prior situations outside of a fixed contextual span. We describe the organization of the brain's distributed understanding system, which includes a fast learning system that addresses the memory problem. We sketch a framework for future models of understanding drawing equally on cognitive neuroscience and artificial intelligence and exploiting query-based attention. We highlight relevant current directions and consider further developments needed to fully capture human-level language understanding in a computational system.

Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of the same concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with deeply interconnected concepts and many distinct aspects of understanding of each concept, and we discuss difficulties with the idea that differences among presentations can be ordered on a concrete-abstract dimension. To move beyond this, we explore how different presentations of a concept can affect learning of subsequent concepts and assess several distinct aspects of understanding. Using the domain of elementary group theory, we teach adult participants a group operation using a visuospatial or an arithmetic presentation. We then teach them concepts that build upon this operation. We demonstrate that our presentations differentially support learning complementary aspects of the system presented. We argue that these differences arise from the fact that each presentation supports learning by connecting to different systems of reasoning learners are already familiar with, and that it is these connections to extant knowledge systems, rather than differences in concreteness vs abstractness that determine whether a presentation will be helpful. Furthermore, we show that presenting both presentations and encouraging participants to recognize the relationship between them improves performance without requiring additional time, at least for some participants. [This paper was published in "Journal of Educational Psychology" v110 n5 p664-682 2018 (EJ1184280).]

The question of whether deep neural networks are good at generalising beyond their immediate training experience is of critical importance for learning-based approaches to AI. Here, we consider tests of out-of-sample generalisation that require an agent to respond to never-seen-before instructions by manipulating and positioning objects in a 3D Unity simulated room. We first describe a comparatively generic agent architecture that exhibits strong performance on these tests. We then identify three aspects of the training regime and environment that make a significant difference to its performance: (a) the number of object/word experiences in the training set; (b) the visual invariances afforded by the agent's perspective, or frame of reference; and (c) the variety of visual input inherent in the perceptual aspect of the agent's perception. Our findings indicate that the degree of generalisation that networks exhibit can depend critically on particulars of the environment in which a given task is instantiated. They further suggest that the propensity for neural networks to generalise in systematic ways may increase if, like human children, those networks have access to many frames of richly varying, multi-modal observations as they learn.

After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning concepts efficiently in a continual learning setting remains an open challenge for current Artificial Intelligence algorithms as persistent model retraining is necessary. Inspired by the Parallel Distributed Processing learning and the Complementary Learning Systems theories, we develop a computational model that is able to expand its previously learned concepts efficiently to new domains using a few labeled samples. We couple the new form of a concept to its past learned forms in an embedding space for effective continual learning. Doing so, a generative distribution is learned such that it is shared across the tasks in the embedding space and models the abstract concepts. This procedure enables the model to generate pseudo-data points to replay the past experience to tackle catastrophic forgetting.

How can deep learning systems flexibly reuse their knowledge? Toward this goal, we propose a new class of challenges, and a class of architectures that can solve them. The challenges are meta-mappings, which involve systematically transforming task behaviors to adapt to new tasks zero-shot. The key to achieving these challenges is representing the task being performed in such a way that this task representation is itself transformable. We therefore draw inspiration from functional programming and recent work in meta-learning to propose a class of Homoiconic Meta-Mapping (HoMM) approaches that represent data points and tasks in a shared latent space, and learn to infer transformations of that space. HoMM approaches can be applied to any type of machine learning task. We demonstrate the utility of this perspective by exhibiting zero-shot remapping of behavior to adapt to new tasks., Comment: 27 pages

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? We address this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Thus, surprisingly, our simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep learning dynamics to give rise to these regularities.

Standard deep learning systems require thousands or millions of examples to learn a concept, and cannot integrate new concepts easily. By contrast, humans have an incredible ability to do one-shot or few-shot learning. For instance, from just hearing a word used in a sentence, humans can infer a great deal about it, by leveraging what the syntax and semantics of the surrounding words tells us. Here, we draw inspiration from this to highlight a simple technique by which deep recurrent networks can similarly exploit their prior knowledge to learn a useful representation for a new word from little data. This could make natural language processing systems much more flexible, by allowing them to learn continually from the new words they encounter., Comment: 15 pages, 7 figures, under review as a conference paper at ICLR 2018