Daniel Rothschild

The recent advances in AI are powered by learning algorithms that allow computers to develop abilities through training on data. These advances provide an unprecedented opportunity to study learning from a new angle: we now have powerful learning systems whose internals we can inspect, whose training we can control, and whose performance we can measure precisely. This gives us new traction on foundational questions about the nature of learning.

This module uses machine learning as a window into those questions. It covers the foundations of machine learning from a theoretical and conceptual perspective, develops a taxonomy of modern ML paradigms, and asks what the remarkable recent successes of AI tell us about how learning works — in machines and, perhaps, in biological minds.

Classes will mostly be on Tuesdays from 1-4pm in the seminar room, 19 Gordon Square, 101. We will always have a 20-30 minute break.

Assessment: Essay One (800 words – 30%, due 19 June), Essay Two (2,200 words – 70%, due 28 September)

All unlinked readings available here (ask instructor for password).

All staff and students are welcome at any sessions.

This class will cover quite a few topics in machine learning and some on human learning. If you want to read or listen to a semi-popular book that covers a lot of recent background, I recommend Tom Griffiths’ new book, Laws of Thought, which will give you useful background on symbolic AI, neural networks, language acquisition, and Bayesianism.

Other useful resources are various online courses on machine learning, such as Andrew Ng’s machine learning course, the classic version of which is on youtube. There are many online courses; the practical programming side will not be useful for this course, but the basic theory will be.

28 APRIL, 1-4pm: LEARNING AS SEARCH

Learning, across all its forms, can be understood as search through a space of possible systems guided by experience — a framework broad enough to encompass Bayesian updating, standard paradigms of machine learning, and human cognitive development.

• Rothschild, "Learning as Search" (2026)
• Plato, Meno (80d–86c) (c. 380 BCE)
  Raises the learning paradox — how can you seek what you don't already know? — and offers the geometry demonstration as Plato's own answer; the computational framework of the course will provide a different one.
• Fodor, "The Present Status of the Innateness Controversy" (1981), in Representations (see especially pp. 269–270)
  A concise statement of Fodor's argument that new concepts cannot be learned — the modern version of the Meno paradox — and the nativist position that the rest of the course pushes back against.
• Margolis and Laurence, "Learning Matters" (2011), p. 529 (relevant passage only)
  Provides a working characterisation of learning as the acquisition of genuinely new representational content; used as a touchstone throughout the course.
• Newell and Simon, "Computer Science as Empirical Inquiry: Symbols and Search" (1976), pp. 120–123
  Introduces the search framework and the generator-plus-test picture that responds to the Meno paradox — showing how new knowledge can be extracted from the environment without presupposing it.
• Dehaene, How We Learn, Introduction and ch. 1 (2020)
  Develops learning-as-search directly, arguing that learning in both brains and machines is a massive search through parameter space guided by error and reward signals.

Supplementary: Leibniz, New Essays (selections) (1765); Rothschild, “The Scope of Bayesianism”; Easwaran, Bayesianism, Philosophy Compass (2011); Hinton and Nowlan, “How Learning Can Guide Evolution” (1987)

5 MAY, 1-4pm: LEARNING AS A COMPUTATIONAL PROCESS

This class discusses the relationship between the theory of computation and learning. We discuss the difference between theoretical limits in computation and practical ones. We dive into a bit the difference between discreet and continuous systems, and introduce neural networks as general purpopse systems (capable of contiunous adjustments).

• Turing, "Computing Machinery and Intelligence," Mind (1950), sections 1–5 and 7
  The founding statement of the computational approach to intelligence. Sections 1–3 set up the imitation game as an adequacy test; sections 4–5 introduce digital computers and the universality of the Turing machine; section 7 proposes building intelligence by learning rather than direct construction — the child-machine. Section 6 (the famous objections) is interesting but skippable for this week. The course's framing of AI as the working-out of two Turing ideas — universality and learning — starts here.
• Newell and Simon, "Computer Science as Empirical Inquiry: Symbols and Search" (1976), pp. 113–120 and 123–126
  Presents the Physical Symbol System Hypothesis — that symbolic manipulation is both necessary and sufficient for general intelligence — the theoretical manifesto for symbolic AI that PDP and the rest of the course systematically examine and challenge.
• Mitchell, Artificial Intelligence: A Guide for Thinking Humans (selections) (2019)
  Introduces the foundational symbolic/subsymbolic divide in AI; walks through perceptrons — the first neural network — from their biological inspiration through the learning rule (weight adjustment from examples) to multilayer networks and back-propagation; provides the accessible technical foundation the other readings presuppose.
• McClelland, Rumelhart and Hinton, "The Appeal of Parallel Distributed Processing" (1986, pp. 3–18, 31–45)
  The founding manifesto of connectionism: argues that many cognitive tasks are better captured by activation spreading across distributed representations than by symbolic rules, and introduces the core concepts — parallel processing, weighted connections, learning as weight adjustment — that underpin everything from backpropagation to modern deep learning.
• Karpathy, "Software 2.0" (2017)
  Reframes neural networks not as a new ML technique but as a new programming paradigm: in "Software 1.0" you write explicit code, in "Software 2.0" you specify an objective and let gradient descent search a continuous space of programs (the trained weights). A practitioner's view of exactly the discrete-to-continuous shift this session is about.

Supplementary: Aaronson, “Why Philosophers Should Care About Computational Complexity” (2013); Rescorla, “The Computational Theory of Mind,” Stanford Encyclopedia of Philosophy

12 MAY, 1-4pm: A TAXONOMY OF MACHINE LEARNING

I introduce a unifying engine behind the apparent diversity of modern AI successes — language models, image generation, game play: supervised learning. In the process this session develops a taxonomy of machine learning paradigms.

• Rothschild, "The New Associationism: Lessons from Deep Learning" (sections 1–6)
  Argues that supervised learning — training on labelled input-output pairs — is the unifying engine behind the apparent diversity of modern AI successes; shows how image generation, language modelling, and game-play all reduce to this single mechanism through clever reformulation; and draws from this the lesson that a modest, scaled-up associationism is far more powerful than twentieth-century cognitive science recognised.
• LeCun, Bengio and Hinton, "Deep Learning," Nature (2015)
  The landmark survey that introduced deep learning to a broad scientific audience: explains how deep architectures learn hierarchical representations automatically — without hand-engineered features — and surveys the striking successes in vision, speech, and language that this makes possible; provides the empirical backdrop for the theoretical claims of my paper above.

Supplementary: Smolensky, “On the Proper Treatment of Connectionism” (1988)

19 MAY, 1-4pm: ASSOCIATIONISM AND EMPIRICISM

• Rothschild, "The New Associationism: Lessons from Deep Learning" (sections 7–8)
  Section 7 argues that deep learning vindicates associationism via the uniformity of supervised learning across domains and its gradient-descent character. Section 8 qualifies this with three caveats: associationist training produces inference-time behaviour that looks nothing like conditioning; architectural structures (transformers, CNNs) go well beyond anything associationists envisaged; and domain-generality of mechanism does not settle empiricism about inductive biases.
• Buckner, From Deep Learning to Rational Machines, ch. 1 (2024)
  Frames deep learning within the empiricism-nativism debate; argues that its successes support a "moderate empiricism" — the view that rational cognition can be achieved without innate theories or domain-specific concepts — while resisting both the overclaiming of enthusiasts and the dismissals of nativists.
• Mandelbaum and Millière, "Associationist Theories of Thought," Stanford Encyclopedia of Philosophy (2025)
  Surveys the philosophical landscape of associationism — from classical and operant conditioning through connectionism to contemporary debates — providing the conceptual vocabulary the other readings presuppose.
• Dehaene, The Number Sense: How the Mind Creates Mathematics, chs. 1–3 (Oxford, 1997; 2nd ed. 2011) — skim
  The classic statement of the case for an evolved, pre-linguistic number sense. Chapter 1 surveys the numerical abilities of animals — rats, pigeons, chimpanzees, parrots — establishing that basic numerical discrimination is widespread across taxa. Chapter 2 reviews the developmental evidence in human infants, including Wynn's addition–subtraction looking-time experiments and the early Approximate Number System findings. Chapter 3 lays out the adult psychophysics: the distance effect, the size effect, the Weber–Fechner signature on numerosity discrimination, and the subitizing-versus-counting distinction. Together these chapters make the convergent empirical case for the number sense as an evolved cognitive system, with subitizing (small-set fast enumeration) and the Approximate Number System (Weber-fraction-scaled estimation of larger quantities) as its two main components.

Supplementary: Dwarkesh Patel, Interview with Ilya Sutskever (podcast); Bubeck et al., “Sparks of Artificial General Intelligence” (2023, selections)

2 JUNE, 1-4pm: LANGUAGE AND LEARNING

Only AI systems trained extensively on natural language exhibit powerful domain-general reasoning, and this session argues that the explanation lies in language’s properties as a compression system — making general inference computationally tractable — with implications for the longstanding debate about the role of language in human thought.

• Rothschild, "Language and Thought: The View from LLMs" (2024)
  Argues that only AI systems extensively trained on natural language exhibit powerful domain-general reasoning, and that this is because language's abstraction and compression makes general inference computationally tractable; uses the evidence from LLMs to support the thesis that language has a transformative effect on cognition, not merely an expressive one.
• Fedorenko, Piantadosi and Gibson, "Language is Primarily a Tool for Communication Rather than Thought," Nature (2024)
  Argues from neuroscience and behaviour that the brain's language network is engaged in linguistic processing but largely inactive during non-linguistic reasoning tasks, and that aphasia leaves many forms of thought intact; concludes that language is shaped for communication rather than thought. An opposing view to mine.
• Lupyan and Bergen, "How Language Programs the Mind" (2016)
  Argues from cognitive psychology that language actively shapes thought rather than merely expressing it — linguistic labels influence perception, categorisation, and memory — provides a different view of the cognitive utility of language.

Supplementary: Mahowald et al., “Dissociating Language and Thought in Large Language Models,” Trends in Cognitive Sciences (2024); Griffiths et al., “Whither Symbols in the Era of Advanced Neural Networks?” (2025)

4 JUNE 1-3pm: STUDENT PRESENTATIONS

9 JUNE, 1-4pm: REINFORCEMENT LEARNING AND MOTIVATION

Reinforcement learning is introduced technically — temporal difference learning, value functions, Deep Q-learning — before the session pivots to ask what the reward signal actually is for human learners, whether understanding itself can be intrinsically rewarding, and what kind of values are coherent enough to specify an objective function at all.

• Sutton and Barto, Reinforcement Learning: An Introduction, Chapter 1 (2018)
  Introduces the reinforcement learning framework — agent, environment, state, reward, policy — and motivates it as the paradigm for goal-directed learning from interaction without labeled examples; frames RL as a third learning paradigm alongside supervised and unsupervised learning.
• Gopnik, "Explanation as Orgasm" (1998)
  Argues that explanation is intrinsically rewarding — the felt sense of understanding is a form of positive affect that motivates curiosity-driven learning — raising the question of what the reward signal actually is for human learners and whether it can be reduced to any simple objective function.
• Christian, The Alignment Problem (selections) (2020)
  Explores the difficulty of specifying reward functions that genuinely capture human values: the problem of reward hacking, Goodhart's law, and the gap between proxy objectives and what we actually want — raising the question of whether any formal objective function can adequately represent the goals that motivate biological learners.

Supplementary: Dwarkesh Patel, Interview with Richard Sutton (podcast)

Image: Hanna Hur, Visitor v, 2024. Collection of The Museum of Modern Art, New York.