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This article covers CMU 11-785 Spring 2026 Lecture 2: Neural Nets as Universal Approximators. 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 It reconstructs only what those materials support and does not invent classroom dialogue or unpublished remarks.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 Boolean functions, how network depth and width affect representational capacity (including a multi-input XOR example), and the hand-off at the end to the next lecture's training problem. 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 2, 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: build a one-dimensional piecewise-linear function from ReLUs and mark its breakpoints. 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 2 official YouTube recording
Course and recording entries:
Checked: 2026-10-10.
Content check: verified against the video transcript (2026-10-10): Read the auto-generated transcript (about 84 minutes); sampled the start, middle and end and searched for Boolean functions, depth, width, XOR and activations. The transcript confirms a lecture on representational capacity and depth/width, but it does not argue that representation power is not trainability (it only says at the end that training comes next), so the description of the video's topic was rewritten. The English article had been written as Lecture 22 (VAE: latent variables, ELBO) and was corrected to this lecture.
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. Rewrote the description of the video's topic (the video does not argue that representation power is not trainability) and fixed the English version, whose tldr, summary and exercise had been written for Lecture 22 (VAE).
References
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