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This article covers CMU 11-785 Spring 2026 Lecture 28: Boltzmann Machines. Its primary evidence is the official slide deck and official YouTube recording. It reconstructs only what those materials support and does not invent classroom dialogue or unpublished remarks.
What this lecture addresses
The lecture centers on energy-based probability models (the Gibbs distribution and its normalizing constant Z), stochastic neurons, and how to train such probabilistic networks. Keep three things separate while reading: the model or algorithm's definition, the objective it optimizes, and the actual computational flow. The first determines the allowed function family, the second states what training prefers, and the third controls memory, speed, and numerical stability.
As Lecture 28, this topic inherits the course's earlier language of representation and training while establishing components used later. Do not merely copy terminology. For each equation, label its input, output, learnable parameters, and gradient path.
Conceptual thread
Begin with a shape audit. Write the batch, feature, and sequence or spatial dimensions next to every tensor. Then ask whether parameters are shared, whether normalization is required, and whether training differs from inference. These questions expose the gap between recognizing an equation and implementing it correctly.
Place each local operation back inside the overall objective. A deep-learning system does not succeed because of one layer alone: data, representation, loss, optimizer, and evaluation jointly determine behavior. When a result changes, hold the other conditions fixed before diagnosing it.
Reproduce one small example
Tonight's minimum exercise is: enumerate every state of three binary units and normalize their energy probabilities. Work through a tiny input by hand, reproduce it in NumPy or PyTorch, and compare the results. If they differ, inspect shapes, indexing, and reductions before questioning the theory.
“Runs without an exception” is not a sufficient check. Record at least one invariant: probabilities sum to one, a loss should decline, an output shape remains fixed, or numerical and analytic gradients agree. This restores a feedback loop without the course's hidden grader.
Boundary with official homework
The Spring 2026 assignment table exposes HW1–HW4 titles, deadlines, and platform links, but the complete handouts, starters, data, Autolab tests, and Piazza guidance do not form an anonymously available same-version bundle. The exercise above is a reduced practice task derived from public lecture material, not a reproduction or solution of official homework.
For more implementation work, select a related notebook from the official recitation and bootcamp table. Those public resources support practice; they do not become official homework starters.
After the lecture
Close the slides and write the lecture's input, output, objective, and one failure mode on a blank page. Continue only when you can explain all four without notes. Otherwise return to the small example and reduce its input until every operation can be checked manually.
Course video sources
Recording links have been checked against the official course page for the edition used by this article.
Original videos: Lecture 28 official YouTube recording
Course and recording entries:
Checked: 2026-10-10.
Content check: verified against the video transcript (2026-10-10): The Lecture 28 video (about 81 minutes, YouTube title "Boltzmann Machines", the last lecture of the semester) covers the extension from Hopfield networks, the Gibbs distribution with its normalizing constant 1/Z, stochastic neurons (sigmoid probabilities), the temperature term, hidden units, and how to train probabilistic networks. The transcript only mentions a normalizing constant, never the term partition function, and has no dedicated discussion of learning difficulty, so the wording was changed. I sampled the beginning, middle, and end and searched by keyword; this is not a word-for-word check.
Update Log
- 2026-10-10: Added explicit video status and checked recording sources and access notes.
- 2026-10-10: Rechecked video status. Matched the embedded video against the live official lecture table for the same lecture; playback was not checked individually.
- 2026-10-10: Checked the video content against its transcript. The transcript only mentions a normalizing constant and has no dedicated learning-difficulty discussion; corrected the topic wording.
References
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