Course description
What the course studies, the question that organises it, and how it is taught.
1.1Overview
This course studies intelligence as a scientific problem. Students learn the mathematical, computational and experimental tools needed to understand existing theories of intelligence, then use them to build, test and revise theories of their own.
It draws on mathematics, probability and statistics, information theory, theoretical computer science, machine learning, cognitive science and control theory, treating each as a source of concepts and methods for one shared problem. It does not assume that intelligence has one universal mechanism, that every intelligent system follows identical laws, or that one number captures every important aspect of intelligence. Those are questions for investigation.
1.2The central question
What general principles govern the emergence, operation, adaptation and limits of intelligence?
The question is approached at four connected levels, which recur in every part of the course.
- Mechanism
- How a system learns, represents, remembers, predicts, decides and adapts.
- Theory
- Which mathematical structures explain those mechanisms, and when they fail.
- Generalisation
- Whether principles found in one system hold in systems with different architectures, resources and substrates.
- Measurement
- How capabilities can be quantified, separated and compared reproducibly.
1.3An example of the method
Figure 1 shows the kind of formal idea the course examines. It is a toy version of the consequential-equivalence relation, equation (1) in §7.2: two histories are treated as the same when no available action leads to outcomes that differ by more than a tolerance ε.
1.4Foundational questions
The course is organised around eight connected questions. They guide teaching and research; they are not a claim that intelligence reduces to a settled list of components.
- Q1Definition
- What is intelligence? Which observable capabilities warrant the word, and can they be defined in ways that support measurement?
- Q2Representation
- When should a system preserve a distinction, and when should it merge categories?
- Q3Memory
- What must be retained, when does more memory help, and when does forgetting become necessary?
- Q4Learning
- Why do some procedures generalise while others memorise, and why can experience make a system worse?
- Q5Consequences
- How do prediction accuracy, understanding of mechanism and decision quality relate?
- Q6Adaptation
- Which properties of an environment set the balance between retaining, updating and exploring?
- Q7Limits
- How do time, memory, computation, energy and evidence shape what a system can become?
- Q8Measurement
- Which measurements stay meaningful across architectures and budgets, and is one score ever enough?
1.5Course information
- Course number
- TAI 100
- Offered
- Founding course, 2026 (14 weeks)
- Format
- Lectures, reading seminars, laboratories and a research seminar
- Assessment
- Problem sets, laboratories, theory reconstructions and a preregistered research project (§2.4)
- Governing document
- Founding charter, version 0.1, October 2026 (§8)
Syllabus
Objectives, structure, method and assessment.
2.1Objectives
The course prepares students to understand existing theories of intelligence deeply enough to challenge them, and to develop their own. Students practise moving between informal intuition, formal models, executable systems and empirical evidence.
2.2Structure
| Part | Title | Topics |
|---|---|---|
| I | Mathematical foundations | Linear algebra, calculus and optimisation, probability and inference, information theory, discrete mathematics, algorithms and complexity |
| II | Computational and statistical foundations | Statistical learning theory, Bayesian modelling, generalisation, reinforcement learning and decision theory, latent-variable models, neural networks |
| III | Mechanisms of intelligence | Memory and forgetting, abstraction, world models, reasoning, exploration, causal intervention, transfer, resource trade-offs |
| IV | Theories of intelligence | Computational cognition, Bayesian accounts, information-theoretic approaches, control, cognitive architectures, computation and physical systems |
| V | Experimental science | Operational definitions, controls, baselines and ablations, power, preregistration, replication, failure analysis |
| VI | Independent theory development | Question, literature review, formal account, testable model, evaluated predictions |
2.3Teaching method
- Lectures
- Establish concepts and introduce formal tools.
- Reading seminars
- Examine the assumptions and arguments of influential papers.
- Laboratories
- Observe models under controlled conditions, with predictions written in advance.
- Research seminars
- Practise defending hypotheses and responding to criticism.
The central method is the reconstruction of theories. Students take a published claim and identify its variables, assumptions, mechanisms, predictions and evidence; reproduce a result where feasible; then change one underlying condition and test whether the explanation still holds. A failed prediction is treated as information: it may reveal a wrong assumption, an inadequate model or a boundary condition.
2.4Assessment
| Component | Description | Weight |
|---|---|---|
| Problem sets (3) | Derivation and analysis in Parts I and II | 20% |
| Laboratories (4) | Controlled experiments with a written prediction before each run | 20% |
| Theory reconstructions (2) | Seminar write-ups that dissect a published claim | 15% |
| Research project | Proposal, preregistration, report and defence | 45% |
2.5Learning outcomes
On completing the course, students should be able to:
- Translate an informal question about intelligence into a precise research problem.
- Use probability, statistics, information theory and computation to construct and analyse models.
- Explain major approaches to learning, memory, representation, reasoning and decision-making.
- Identify the assumptions and limitations of a published theory.
- Design controlled experiments that distinguish competing explanations.
- Implement computational models and evaluate their behaviour.
- Interpret measurements of performance, information and causal contribution appropriately.
- Distinguish correlation, prediction, intervention and explanation.
- Develop original hypotheses and derive testable predictions from them.
- Revise a theory in response to evidence while keeping a clear record of the reasoning.
- Evaluate claims of generality and identify the further evidence they need.
- Communicate technical findings so that other researchers can inspect and challenge them.
Calendar
Weekly topics and key dates for the founding run.
3.1Schedule
| Wk | Part | Topic | Key dates |
|---|---|---|---|
| 1 | – | What is intelligence?Central question, levels of analysis, evidence labels | |
| 2 | I | Probability, inference and linear structure | PS 1 out |
| 3 | I | Information theoryEntropy, mutual information, compression | |
| 4 | I | Computation under finite resourcesAlgorithms and complexity | PS 1 due |
| 5 | II | Statistical learningGeneralisation and memorisation | Lab 1 out |
| 6 | II | Bayesian inference, reinforcement learning, decision theory | PS 2 due; Lab 1 due |
| 7 | II | Representation learning and latent variablesReading seminar | Reconstruction 1 due |
| 8 | III | Memory and selective forgettingHidden context, history compression | PS 3 due; Lab 2 out |
| 9 | III | Representation, abstraction and consequential distinctions | Lab 2 due |
| 10 | III | Prediction, world models and causal intervention | Lab 3 out |
| 11 | IV | Theories of intelligence compared on common tasks | Lab 3 due; proposal due |
| 12 | V | Experimental sciencePower, ablation, preregistration, replication | Reconstruction 2 due; preregistration due |
| 13 | VI | Research seminarWork in progress under criticism | Lab 4 due |
| 14 | VI | Final presentations and defence | Project report due |
Subject to revision before the course begins.
Readings
Primary sources by course part. Core readings are discussed in seminar.
4.1Reading list
Each entry notes the foundational questions (Q1–Q8) it bears on. Historical importance and popularity can guide reading, but neither substitutes for evaluating explanatory power.
Laboratories
Four controlled experiments. Each prediction is written down before anything is run.
5.1Generalisation or memorisation?
- Schedule
- Weeks 5–6 · Part II · Q4
- Question
- Under what conditions does a learner that fits its training data perfectly still generalise?
- Design
- Train the same model on true labels and on shuffled labels; vary data size and capacity.
- Measures
- Training and test error, time to fit, sensitivity to capacity.
5.2How long should memory be?
- Schedule
- Weeks 8–9 · Part III · Q3, Q6
- Question
- When a hidden condition persists and changes the consequences of action, how much history should an agent keep?
- Design
- DistinctionWorld agents with memory spans from 0 to k, under hidden contexts of varying persistence. Reproduce the original memory-span prediction, locate where it fails, then test the revised model that accounts for how action shapes the evidence observed next.
- Measures
- Return, memory cost, recovery time after a context switch.
5.3Decodable is not the same as used
- Schedule
- Weeks 10–11 · Parts III and V · Q2, Q5, Q8
- Question
- Does information that can be read out of an agent's internal state actually drive its behaviour?
- Design
- Probe internal states for outcome-relevant variables, then ablate the same variables and re-run.
- Measures
- Conditional mutual information, equation (2), against Causal Distinction Benefit for each variable.
5.4Does it transfer?
- Schedule
- Weeks 12–13 · Part V · Q6, Q7
- Question
- Does a finding from one controlled environment survive a meaningful change of task, architecture or resource budget?
- Design
- Take a result from Laboratory 5.2 or 5.3; preregister a prediction for a changed setting, then run it.
- Measures
- Prediction error, and a classification of any failure: false assumption, missing mechanism, poor measurement, or genuine limit.
Independent research project
Milestones and the standards by which projects are assessed.
6.1Scope
The project asks for more than an implementation or a set of results. It should explain why the question matters, what the model claims, which alternatives were considered, and what the evidence establishes. A project may contribute to an existing theory, challenge an assumption, introduce a mechanism, or identify a boundary condition that earlier work overlooked.
6.2Milestones
| Wk | Milestone | Deliverable |
|---|---|---|
| 11 | Proposal | Question, defined claim, assumptions, competing explanation, literature review |
| 12 | Preregistration | Predictions, comparisons and analysis plan, fixed before the decisive experiment |
| 13 | Seminar | Work in progress presented for criticism |
| 14 | Report and defence | Report, code and data, with an account of what changed from the preregistration and why |
6.3Standards for student research
The same eight standards apply to the founding research programme.
- Clear question
- Specific enough to investigate, important enough to justify the work.
- Defined claim
- What the explanation asserts, and what related claims it does not establish.
- Explicit assumptions
- The conditions on which the conclusions depend.
- Meaningful comparison
- Evaluation against a baseline or a competing explanation.
- Testable prediction
- Which observations would support or challenge the theory.
- Reproducible method
- Implementation, data, procedures and evaluation documented.
- Proportionate conclusion
- Scope matched to evidence; a small controlled environment does not yield universal laws.
- Account of failure
- Unexpected results, limitations and changes to the hypothesis recorded.
Predictions made before an experiment and explanations built after its results are reported separately. An exploratory pattern may motivate a hypothesis but is never presented as a successful advance prediction.
A programme for general principles
The research the course supports, its first direction, and how evidence is weighed.
7.1Aim and method
One research programme asks whether some properties of intelligence follow from relationships between information, action, prediction, learning and environmental structure that do not depend entirely on implementation. It treats generality as an empirical achievement: a principle earns broader status through successful prediction and replication across settings. Work proceeds in eight stages.
- Define the phenomenon and make it operational.
- Construct a formal model: variables, assumptions, mechanisms, derived relationships.
- Build a controlled environment that isolates the mechanism.
- Compare competing systems under matched conditions.
- Make discriminating predictions, recorded before decisive experiments.
- Test generalisation across tasks, structures, constraints and architectures.
- Identify the boundaries: assumption, mechanism, measurement or limit.
- Refine the theory, document the change, and design the next test.
7.2Consequential distinctions
Status: Working hypothesis
The working paper Toward a General Theory of Intelligence investigates the proposal that intelligence involves learning which differences in available information change future outcomes, using those differences to guide behaviour, and reorganising them when their consequences change. For histories h, h′, goal g, policy set Π, outcome Y, divergence D and tolerance ε:
Relevance therefore depends on three stated choices: the available policies, the outcomes considered, and the tolerance. Figure 1 (§1.3) illustrates the relation on synthetic data.
| Finding | Status |
|---|---|
| Preserving outcome-relevant distinctions can improve performance. | Exploratory |
| Preserving irrelevant detail consumes resources and invites misleading correlations. | Exploratory |
| Memory is most useful when a hidden condition persists and changes the consequences of action. | Exploratory |
| The initial optimal-memory-span prediction failed; a revised model accounting for action-dependent evidence predicted better in tested conditions. | Hypothesis |
| Whether these principles hold across architectures, substrates and living organisms. | Open |
Scope: the environment is small and every agent runs on the same computational substrate. The companion paper The Purpose of Memory asks whether memory's function is to predict consequences not recoverable from the present observation alone.
7.3Measurement and evidence
Measurement is essential, and a common source of error when a convenient quantity is mistaken for the phenomenon. The programme distinguishes five kinds of evidence.
- Behavioural performance
- Reported with task definition, baselines, evaluation procedure and resource constraints. One high score does not establish a general property.
- Information in representation
- How much an internal state Z reduces uncertainty about an outcome Y given goal G, as in equation (2). What can be decoded may not influence decisions.
- Causal contribution
- The Causal Distinction Benefit compares expected performance with a distinction retained and removed. It probes a mechanism; it is not a measure of intelligence.
- Generalisation and transfer
- Interpolation within a familiar setting is distinguished from transfer to meaningfully different conditions.
- Calibration and reproducibility
- Methods, uncertainty and conditions reported well enough for independent reproduction.
Founding charter
The intellectual commitments that govern the course and its research.
8.1Statement
Theoretical Artificial Intelligence is a proposed field devoted to the mathematical, computational and experimental investigation of intelligence. It begins with a question, develops through theory and experiment, and advances when its explanations survive serious attempts to challenge them.
- Mathematics
- The language of theory.
- Statistics
- The language of uncertainty.
- Computer science
- The language of mechanisms and computation.
- Empirical science
- The connection between theory and the world.
- Intelligence
- The organising problem.
8.2Theoretical commitments
- Precision
- Define terms as precisely as the subject permits, and be clear about what remains informal.
- Explanation
- Explain relationships between phenomena rather than catalogue observations.
- Accountability
- Expose predictions to tests that could show the theory is wrong.
- Pluralism
- No framework receives permanent priority for its origin, popularity or elegance.
- Generalisation
- Findings about one environment remain findings about that environment until shown otherwise.
- Resources
- Memory, computation, time, energy and evidence shape which strategies are possible.
- Honesty
- Report negative results, failed predictions and unresolved disagreements.
8.3Evidential status
Research claims carry one of five labels. They are practical guides, not permanent verdicts.
| Label | Meaning |
|---|---|
| Established result | Supported by a body of evidence within a clearly specified scope |
| Replicated finding | Observed independently under sufficiently comparable conditions |
| Working hypothesis | A proposed explanation that has not yet survived adequate testing |
| Exploratory observation | A pattern that may motivate further investigation |
| Open question | The evidence does not yet support a settled conclusion |
8.4Risks the field should avoid
- Premature unification
- Evidence should decide whether a unified account is possible.
- Performance as explanation
- Strong results do not reveal why a mechanism works.
- Information as understanding
- Decodable information may play no causal role.
- Overgeneralisation
- Controlled environments isolate mechanisms; they do not certify generality.
- Terminology as theory
- A new term explains nothing until its claims are precise and testable.
- Ignoring resources
- Unlimited-resource models may miss what finite systems do.
- Rewarding confirmation
- Hard tests, transparent failures and replication deserve credit.
- One theory as the field
- The consequential-distinction programme must earn its status like any other.
8.5Long-term agenda
- Near term
- Rigorous foundations: curriculum, reading programme, laboratory methods and controlled experiments.
- Medium term
- Develop and compare theories; richer environments; shared reporting and replication.
- Long term
- Test principles across architectures, tasks and, where appropriate, biological systems.
- Ultimate aim
- A cumulative science of intelligence, whether one theory, connected theories, or principles at different levels.
8.6Relationships to other fields
AI engineering builds systems that work reliably for specified purposes; theory explains why systems behave as they do and predicts systems not yet built. Each informs the other.
Cognitive science and the study of living systems offer different constraints and mechanisms. Whether principles cross artificial and biological domains is an empirical question the field should help answer.
Lecture notes
Full-text notes for each week, written for readers with first-year programming and no prior AI.
9.1How to use the notes
Every week follows the same structure, so you always know where to look: what you will be able to do, the main explanation in numbered sections, a summary, key terms, questions with hidden answers, seminar exercises and readings. Code is plain Python using only the standard library. Every result quoted in the notes comes from running the code provided.
9.2Weekly notes
| Wk | Part | Notes | Status |
|---|---|---|---|
| 1 | – | What is intelligence?Defining intelligence, fixed rules and learning, four levels, a first experiment on memory | Available |
| 2 | I | Probability and inferenceCounting, conditional probability, Bayes' rule, beliefs that update, vectors and matrices | Available |
| 3 | I | Information theorySurprise, entropy, mutual information, log loss, prediction as compression | Available |
| 4 | I | Computation under finite resourcesCounting steps, exponential growth, dynamic programming, the cost of memory, sampling | Available |
| 5 | II | Statistical learningNearest neighbours, overfitting and underfitting, shuffled labels, validation | Available |
| 6 | II | Bayesian inference, reinforcement learning, decision theory | In preparation |
| 7 | II | Representation learning and latent variables | In preparation |
| 8 | III | Memory and selective forgetting | In preparation |
| 9 | III | Representation, abstraction and consequential distinctions | In preparation |
| 10 | III | Prediction, world models and causal intervention | In preparation |
| 11 | IV | Theories of intelligence compared | In preparation |
| 12 | V | Experimental science | In preparation |
| 13 | VI | Research seminar | In preparation |
| 14 | VI | Final presentations and defence | In preparation |