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Free, open courses on the mathematics that has always underpinned AI and the research that is reshaping it now — written to the standard of our publications, with every claim sourced.
Foundations
The mathematics underneath every model — probability, geometry, information and optimization. These ideas predate deep learning and will outlast whatever architecture comes next.
Probability & Inference
Reasoning under uncertainty: the rules of probability, Bayes' rule, why averages concentrate, and how maximum likelihood turns a model into a loss function.
The Geometry of Learning
Linear algebra as the language of neural networks: vectors and similarity, matrices as maps, and the eigenvectors and singular vectors that reveal what a layer does.
Information Theory
Shannon's measure of surprise, the cross-entropy loss every language model minimizes, and the deep equivalence between predicting data and compressing it.
Optimization & Generalization
How networks learn and why they work on data they have never seen: gradient descent, backpropagation, stochastic optimizers, and the surprises of overparameterized models.
Frontier
How today's systems are built, trained, scaled, evaluated and aligned — researched against the current literature, with every claim sourced and dated.
Transformers & Language Models
What a language model is, how attention and the transformer block work, and what scaling laws do — and don't — tell us about training at frontier scale.
Reasoning Models & Reinforcement Learning
From human-preference training to reinforcement learning on verifiable rewards: how reasoning models are trained, and what the evidence says that training actually buys.
Test-Time Compute & Verification
Spending compute at inference — sampling, Best-of-N, majority vote — and why the verifier, not the generator, so often sets the ceiling. Built on NeuroGenesys's own research and tools.
Agents & Tool Use
Models that act: function calling, agent loops with memory and planning, and how to measure long-horizon autonomy without fooling yourself.
Interpretability & Alignment
Looking inside models — features, circuits, superposition — and the techniques and evaluations used to make capable systems behave as intended.
Efficient AI: Inference, Sparsity & Hardware
Where the cost of AI actually goes — memory bandwidth, KV caches, batching — and the methods and hardware that cut it, including the lab's own analog and photonic results.
Reference videos
60 curated lectures and 18full courses and series, for every course and for the lab's research threads: continual learning, verifiers and exploitability, memory and learning on the job.
Frontier lessons are dated and cite their sources; where the field disagrees, they say so. Lessons link into the research archive and evaluation tools wherever our own work bears on the topic.
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