Physical AI Foundations: The Math Behind VLMs, VLAs and WAM
Published 8/2026
MP4 | Video: h264, 1920×1080 | Audio: AAC, 44.1 KHz, 2 Ch
Language: English + subtitle | Duration: 5h 15m | Size: 1.35 GB
Master VLMs, VLAs and world models: transformers, attention, diffusion policies, and the control loop around them
What you’ll learn
Work scaled dot-product attention through numerically, cell by cell, and explain what query, key and value each compute inside a robot policy.
Explain how a VLA turns a camera frame and a sentence into a robot action, across three architecture families.
Derive why regression crashes robots, and how diffusion and flow matching policies fix it.
Run a 7 Hz learned model inside a 400 Hz control loop, with kinematics, contact and safety gates around it.
Requirements
Basic Python. No deep learning or robotics experience needed.
High-school linear algebra and calculus. The rest is re-derived in Section 2.
No GPU, no robot, no installs. Everything is derived on screen.
Description
This course contains the use of artificial intelligence.
Physical AI is the part of robotics where a model has to move something real. This course teaches the mathematics underneath it, from photons hitting a camera sensor to torque arriving at a motor, without hand-waving over the
steps in between.
You will not find a slide deck of model names here. Every mechanism is derived on screen, animated, and then connected back to a robot that has to act. By the end you will be able to open a VLA paper and know exactly which block
does what, and why the authors chose it.
What this course covers
– Robots as dynamical systems. Observation, hidden state, action, transition. Why embodiment changes what an “action” even means, and why latency is a design input rather than an implementation detail.
– The math you actually need. Tensors as robot data, embeddings as geometry, cosine similarity, distributions over actions, softmax and temperature. Only what the later sections use, nothing padded.
– Transformers, cell by cell. Tokens, patches, position, and query-key-value. Scaled dot-product attention is worked through numerically, not described. Multi-head attention, residuals, normalisation, autoregressive decoding.
– Vision language models. The camera pipeline honestly, patch embeddings and the real cost of resolution, contrastive alignment and what it does not give you, cross attention grounding a referring expression, and the difference
between what a VLM knows and what it only appears to know.
– Robot state and action. Proprioception, frames and transform chains, action spaces across four embodiments, tokenising a continuous action, and action chunking with its staleness problem.
– Vision language action models. Attaching an action head to a VLM, three architecture families, what a demonstration episode really contains, behaviour cloning derived from first principles, and how to evaluate a policy without
fooling yourself.
– Generative action policies. Diffusion from noise and back, diffusion policies for action chunks, flow matching as a learned velocity field, and the token-compression-latency tradeoff.
– World models and world action models. Action-conditioned dynamics, latent bottlenecks, imagined rollouts and planning, compounding error and why the horizon is short, and joint prediction of futures and actions.
– Physics, control and safety. Kinematics and the Jacobian, dynamics, force and contact, running a slow learned model inside a fast control loop, and runtime safety gates with honest demos.
Who this course is for
Robotics engineers who want to understand the learned models being bolted onto their stack.
ML engineers moving from language or vision into embodied AI.
Anyone who stalled at the architecture diagram in a VLA paper.
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