CMU 11-785 Lecture 3: Training I: Learning and Empirical Risk Minimization

TL;DR Spring 2026 Lecture 3 focuses on data distributions, hypotheses, losses, empirical risk, and their roles in generalization. This guide follows the official slides and recording and adds a small self-check that does not depend on the enrolled-course grader.

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Table of Contents

What this lecture addresses
Conceptual thread
Reproduce one small example
Boundary with official homework
After the lecture
References

Series: Reading CMU 11-785 Deep Learning (3 / 29)

CMU 11-785 Lecture 2: Neural Nets as Universal Approximators CMU 11-785 Lecture 4: Training II: Gradient Descent

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This article covers CMU 11-785 Spring 2026 Lecture 3: Training I: Learning and Empirical Risk Minimization. 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 It reconstructs only what those materials support and does not invent classroom dialogue or unpublished remarks.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 data distributions, hypotheses, losses, empirical risk, and their roles in generalization. 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 3, 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: write the per-example loss and mean empirical risk for a binary classifier. 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.