Big Boxes, Not Black Boxes: What we can compute about LLMs, and what it may say about AGI
Deep networks are often thought of as black boxes. Their ability to encompass vast swathes of knowledge indeed makes them hard to explain. Yet many of their behaviours — generalization under overparametrization, grokking, OOD failures, neural scaling laws — recur across architectures and scales, and each, however surprising, can be reproduced and explained in controlled settings. I will review these efforts to identify and explain the universal phenomena of deep learning, and suggest that an LLM may amount to a sum of such tractable sub-phenomena, interpolative in nature. Finally, leaving scientific rigor aside, I'll argue that what separates this prosaic picture from the apparent magic of LLMs may well be the industrial scale of compute and human labour behind it, and that AGI in its deeper extrapolative sense may be much further away than claimed.
Learning representations of specifics and generalities over time
There is a fundamental tension between storing discrete traces of individual experiences, which allows recall of particular moments in our past without interference, and extracting regularities across these experiences, which supports generalization and prediction in similar situations in the future. One influential proposal for how the brain resolves this tension is that it separates the processes anatomically into Complementary Learning Systems, with the hippocampus rapidly encoding individual episodes and the neocortex slowly extracting regularities over days, months, and years. But this does not explain our ability to learn and generalize from new regularities in our environment quickly, often within minutes. We have put forward a neural network model of the hippocampus that suggests that the hippocampus itself may contain complementary learning systems, with one pathway specializing in the rapid learning of regularities and a separate pathway handling the region’s classic episodic memory functions. This proposal has broad implications for how we rapidly learn novel information of specific and generalized types, which we test across statistical learning, inference, and category learning paradigms. We also explore how this system interacts with slower-learning neocortical memory systems, with empirical and modeling investigations into how hippocampal replay shapes neocortical representations during sleep. Together, the work helps us understand how structured information in our environment is initially encoded and how it then transforms over time. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-12-03. Recording duration: 00:53:05.
Learning and prediction in artificial deep neural networks: scaling, data manifolds, and universality
Developing scientifically-grounded theories for representation learning and generalization in artificial deep neural networks remains a grand challenge of fundamental interest to theoretical neuroscience and machine learning. I will discuss our work on one facet of this challenge — namely understanding generalization or “scaling laws” in learned neural networks as a function of basic control variables. I’ll discuss a taxonomy we develop that classifies different regimes of scaling behavior. We identify regimes where generalization exhibits universal scaling behavior and others where it can be traced back to properties of the data and neural architecture. The theoretical analysis is enabled by leveraging exactly solvable models of deep neural networks that arise naturally in the limit of large hidden layers. Along the way, I’ll also discuss our work on these theoretical models, which have been a useful starting point for theoretical descriptions of neural network dynamics. Finally, I’ll discuss our findings connecting generalization in neural networks to properties of the learned data manifold. I’ll close by discussing future directions and new hypotheses that emerge from our findings Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-06-19. Recording duration: 00:46:53.
Learning representations of specifics and generalities over time
There is a fundamental tension between storing discrete traces of individual experiences, which allows recall of particular moments in our past without interference, and extracting regularities across these experiences, which supports generalization and prediction in similar situations in the future. One influential proposal for how the brain resolves this tension is that it separates the processes anatomically into Complementary Learning Systems, with the hippocampus rapidly encoding individual episodes and the neocortex slowly extracting regularities over days, months, and years. But this does not explain our ability to learn and generalize from new regularities in our environment quickly, often within minutes. We have put forward a neural network model of the hippocampus that suggests that the hippocampus itself may contain complementary learning systems, with one pathway specializing in the rapid learning of regularities and a separate pathway handling the region’s classic episodic memory functions. This proposal has broad implications for how we learn and represent novel information of specific and generalized types, which we test across statistical learning, inference, and category learning paradigms. We also explore how this system interacts with slower-learning neocortical memory systems, with empirical and modeling investigations into how the hippocampus shapes neocortical representations during sleep. Together, the work helps us understand how structured information in our environment is initially encoded and how it then transforms over time.
Prediction Models for Brains and Machines
Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations. I will also cover work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. I will also talk about work applying this perspective to the deep RL setting, where we can study the effect of predictive learning on representations that form in a deep neural network and how these results compare to neural data. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-11-01. Recording duration: 00:50:44.
Relations and Predictions in Brains and Machines
Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations, while entorhinal cortex compresses these predictive representations with spectral methods that support smooth generalization among related states. I will also cover recent work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design.
Analogical Reasoning and Generalization for Interactive Task Learning in Physical Machines
Humans are natural teachers; learning through instruction is one of the most fundamental ways that we learn. Interactive Task Learning (ITL) is an emerging research agenda that studies the design of complex intelligent robots that can acquire new knowledge through natural human teacher-robot learner interactions. ITL methods are particularly useful for designing intelligent robots whose behavior can be adapted by humans collaborating with them. In this talk, I will summarize our recent findings on the structure that human instruction naturally has and motivate an intelligent system design that can exploit their structure. The system – AILEEN – is being developed using the common model of cognition. Architectures that implement the Common Model of Cognition - Soar, ACT-R, and Sigma - have a prominent place in research on cognitive modeling as well as on designing complex intelligent agents. However, they miss a critical piece of intelligent behavior – analogical reasoning and generalization. I will introduce a new memory – concept memory – that integrates with a common model of cognition architecture and supports ITL.
Parametric control of flexible timing through low-dimensional neural manifolds
Biological brains possess an exceptional ability to infer relevant behavioral responses to a wide range of stimuli from only a few examples. This capacity to generalize beyond the training set has been proven particularly challenging to realize in artificial systems. How neural processes enable this capacity to extrapolate to novel stimuli is a fundamental open question. A prominent but underexplored hypothesis suggests that generalization is facilitated by a low-dimensional organization of collective neural activity, yet evidence for the underlying neural mechanisms remains wanting. Combining network modeling, theory and neural data analysis, we tested this hypothesis in the framework of flexible timing tasks, which rely on the interplay between inputs and recurrent dynamics. We first trained recurrent neural networks on a set of timing tasks while minimizing the dimensionality of neural activity by imposing low-rank constraints on the connectivity, and compared the performance and generalization capabilities with networks trained without any constraint. We then examined the trained networks, characterized the dynamical mechanisms underlying the computations, and verified their predictions in neural recordings. Our key finding is that low-dimensional dynamics strongly increases the ability to extrapolate to inputs outside of the range used in training. Critically, this capacity to generalize relies on controlling the low-dimensional dynamics by a parametric contextual input. We found that this parametric control of extrapolation was based on a mechanism where tonic inputs modulate the dynamics along non-linear manifolds in activity space while preserving their geometry. Comparisons with neural recordings in the dorsomedial frontal cortex of macaque monkeys performing flexible timing tasks confirmed the geometric and dynamical signatures of this mechanism. Altogether, our results tie together a number of previous experimental findings and suggest that the low-dimensional organization of neural dynamics plays a central role in generalizable behaviors.
On the implicit bias of SGD in deep learning
Tali's work emphasized the tradeoff between compression and information preservation. In this talk I will explore this theme in the context of deep learning. Artificial neural networks have recently revolutionized the field of machine learning. However, we still do not have sufficient theoretical understanding of how such models can be successfully learned. Two specific questions in this context are: how can neural nets be learned despite the non-convexity of the learning problem, and how can they generalize well despite often having more parameters than training data. I will describe our recent work showing that gradient-descent optimization indeed leads to 'simpler' models, where simplicity is captured by lower weight norm and in some cases clustering of weight vectors. We demonstrate this for several teacher and student architectures, including learning linear teachers with ReLU networks, learning boolean functions and learning convolutional pattern detection architectures.
Towards a Theory of Human Visual Reasoning
Many tasks that are easy for humans are difficult for machines. In particular, while humans excel at tasks that require generalising across problems, machine systems notably struggle. One such task that has received a good amount of attention is the Synthetic Visual Reasoning Test (SVRT). The SVRT consists of a range of problems where simple visual stimuli must be categorised into one of two categories based on an unknown rule that must be induced. Conventional machine learning approaches perform well only when trained to categorise based on a single rule and are unable to generalise without extensive additional training to tasks with any additional rules. Multiple theories of higher-level cognition posit that humans solve such tasks using structured relational representations. Specifically, people learn rules based on structured representations that generalise to novel instances quickly and easily. We believe it is possible to model this approach in a single system which learns all the required relational representations from scratch and performs tasks such as SVRT in a single run. Here, we present a system which expands the DORA/LISA architecture and augments the existing model with principally novel components, namely a) visual reasoning based on the established theories of recognition by components; b) the process of learning complex relational representations by synthesis (in addition to learning by analysis). The proposed augmented model matches human behaviour on SVRT problems. Moreover, the proposed system stands as perhaps a more realistic account of human cognition, wherein rather than using tools that has been shown successful in the machine learning field to inform psychological theorising, we use established psychological theories to inform developing a machine system.
Analogical encodings and recodings
This talk will focus on the idea that the kind of similarity driving analogical retrieval is determined by the kind of features encoded regarding the source and the target cue situations. Emphasis will be put on educational perspectives in order to show the influence of world semantics on learners’ problem representations and solving strategies, as well as the difficulties arising from semantic incongruence between representations and strategies. Special attention will be given to the recoding of semantically incongruent representations, a crucial step that learners struggle with, in order to illustrate a promising path for going beyond informal strategies.
Transforming task representations
Humans can adapt to a novel task on our first try. By contrast, artificial intelligence systems often require immense amounts of data to adapt. In this talk, I will discuss my recent work (https://www.pnas.org/content/117/52/32970) on creating deep learning systems that can adapt on their first try by exploiting relationships between tasks. Specifically, the approach is based on transforming a representation for a known task to produce a representation for the novel task, by inferring and then using a higher order function that captures a relationship between the tasks. This approach can be interpreted as a type of analogical reasoning. I will show that task transformation can allow systems to adapt to novel tasks on their first try in domains ranging from card games, to mathematical objects, to image classification and reinforcement learning. I will discuss the analogical interpretation of this approach, an analogy between levels of abstraction within the model architecture that I refer to as homoiconicity, and what this work might suggest about using deep-learning models to infer analogies more generally.
Generalizing theories of cerebellum-like learning
Since the theories of Marr, Ito, and Albus, the cerebellum has provided an attractive well-characterized model system to investigate biological mechanisms of learning. In recent years, theories have been developed that provide a normative account for many features of the anatomy and function of cerebellar cortex and cerebellum-like systems, including the distribution of parallel fiber-Purkinje cell synaptic weights, the expansion in neuron number of the granule cell layer and their synaptic in-degree, and sparse coding by granule cells. Typically, these theories focus on the learning of random mappings between uncorrelated inputs and binary outputs, an assumption that may be reasonable for certain forms of associative conditioning but is also quite far from accounting for the important role the cerebellum plays in the control of smooth movements. I will discuss in-progress work with Marjorie Xie, Samuel Muscinelli, and Kameron Decker Harris generalizing these learning theories to correlated inputs and general classes of smooth input-output mappings. Our studies build on earlier work in theoretical neuroscience as well as recent advances in the kernel theory of wide neural networks. They illuminate the role of pre-expansion structures in processing input stimuli and the significance of sparse granule cell activity. If there is time, I will also discuss preliminary work with Jack Lindsey extending these theories beyond cerebellum-like structures to recurrent networks.
Generalization guided exploration
How do people learn in real-world environments where the space of possible actions can be vast or even infinite? The study of human learning has made rapid progress in past decades, from discovering the neural substrate of reward prediction errors, to building AI capable of mastering the game of Go. Yet this line of research has primarily focused on learning through repeated interactions with the same stimuli. How are humans able to rapidly adapt to novel situations and learn from such sparse examples? I propose a theory of how generalization guides human learning, by making predictions about which unobserved options are most promising to explore. Inspired by Roger Shepard’s law of generalization, I show how a Bayesian function learning model provides a mechanism for generalizing limited experiences to a wide set of novel possibilities, based on the simple principle that similar actions produce similar outcomes. This model of generalization generates predictions about the expected reward and underlying uncertainty of unexplored options, where both are vital components in how people actively explore the world. This model allows us to explain developmental differences in the explorative behavior of children, and suggests a general principle of learning across spatial, conceptual, and structured domains.
The geometry of abstraction in hippocampus and pre-frontal cortex
The curse of dimensionality plagues models of reinforcement learning and decision-making. The process of abstraction solves this by constructing abstract variables describing features shared by different specific instances, reducing dimensionality and enabling generalization in novel situations. Here we characterized neural representations in monkeys performing a task where a hidden variable described the temporal statistics of stimulus-response-outcome mappings. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for training. This type of generalization requires a particular geometric format of neural representations. Neural ensembles in dorsolateral pre-frontal cortex, anterior cingulate cortex and hippocampus, and in simulated neural networks, simultaneously represented multiple hidden and explicit variables in a format reflecting abstraction. Task events engaging cognitive operations modulated this format. These findings elucidate how the brain and artificial systems represent abstract variables, variables critical for generalization that in turn confers cognitive flexibility.
Abstraction and Analogy in Natural and Artificial Intelligence
In 1955, John McCarthy and colleagues proposed an AI summer research project with the following aim: “An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves.” More than six decades later, all of these research topics remain open and actively investigated in the AI community. While AI has made dramatic progress over the last decade in areas such as vision, natural language processing, and robotics, current AI systems still almost entirely lack the ability to form humanlike concepts and abstractions. Some cognitive scientists have proposed that analogy-making is a central mechanism for conceptual abstraction and understanding in humans. Douglas Hofstadter called analogy-making “the core of cognition”, and Hofstadter and co-author Emmanuel Sander noted, “Without concepts there can be no thought, and without analogies there can be no concepts.” In this talk I will reflect on the role played by analogy-making at all levels of intelligence, and on prospects for developing AI systems with humanlike abilities for abstraction and analogy.
Is Rule Learning Like Analogy?
Humans’ ability to perceive and abstract relational structure is fundamental to our learning. It allows us to acquire knowledge all the way from linguistic grammar to spatial knowledge to social structures. How does a learner begin to perceive structure in the world? Why do we sometimes fail to see structural commonalities across events? To begin to answer these questions, I attempt to bridge two large, yet somewhat separate research traditions in understanding human’s structural abstraction: rule learning (Marcus et al., 1999) and analogical learning (Gentner, 1989). On the one hand, rule learning research has shown humans’ domain-general ability and ease—as early as 7-month-olds—to abstract structure from a limited experience. On the other hand, analogical learning works have shown robust constraints in structural abstraction: young learners prefer object similarity over relational similarity. To understand this seeming paradox between ease and difficulty, we conducted a series of studies using the classic rule learning paradigm (Marcus et al., 1999) but with an analogical (object vs. relation) twist. Adults were presented with 2-minute sentences or events (syllables or shapes) containing a rule. At test, they had to choose between rule abstraction and object matches—the same syllable or shape they saw before. Surprisingly, while in the absence of object matches adults were perfectly capable of abstracting the rule, their ability to do so declined sharply when object matches were present. Our initial results suggest that rule learning ability may be subject to the usual constraints and signatures of analogical learning: preference to object similarity can dampen rule generalization. Humans’ abstraction is also concrete at the same time.
Analogy in Cognitive Architecture
Cognitive architectures are attempts to build larger-scale models of minds. This talk will explore how structure-mapping models of analogical matching, retrieval, and generalization are used in the Companion cognitive architecture. Examples will include modeling conceptual change, learning by reading, and analogical Q/A training.