Chalkless: recovering the logical structure of lectures

Why local classification is insufficient

A short clip from a math lecture rarely carries its own meaning. The same equation can be the definition an instructor is introducing, a line inside a worked example, or the identity that anchors a key result. What separates those roles is the segment's place in the lesson.

Take the coefficient formula a_n = (1/π) ∫ f(x) cos(nx) dx and the orthogonality fact ∫ sin(mx) sin(nx) dx = 0. Both are integrals of products of trigonometric functions. A classifier that reads one segment at a time sees nearly the same object in each, even though one belongs to a definition and the other is the idea that makes the definition work.

Recovering lecture structure is therefore a sequence problem. The role of a segment depends on the segments around it, so a method that labels each segment on its own cannot reconstruct the arc of the lesson.

A two-stage pipeline

Chalkless runs in two stages. The first makes a rough guess for every segment. The second reconciles those guesses using rules about how lectures tend to be ordered.

02.1The stabilization rules

The second stage encodes patterns that hold across board-based math lectures. A few examples of the kind of rule it applies:

• Lectures usually open with a topic segment.
• Examples tend to run in continuous spans rather than alternating with other roles.
• A key concept commonly follows the example that motivates it.
• Frequent back-and-forth switching between roles is usually inference noise.

These rules are written down by hand instead of learned by a model. Encoding them keeps the system legible and removes the need for labeled lectures. When a label changes, you can read the exact rule that caused it.

We do not claim this beats a trained CRF or a neural sequence model on accuracy. Its value is interpretability and running without annotated data.

What we have seen so far

These are early, qualitative observations from inspecting real lectures. They are not measured results, and we report no accuracy numbers at this stage.

• Applying the temporal rules appears to produce a more coherent sequence than the per-segment guesses on their own. On inspection, the stabilized labeling reads closer to how the lecture is actually organized.
• The key-concept role seems to be the hardest to identify locally. In the cases we looked at, it appears to need the surrounding sequence, the example before it and the transition after, to be recognized at all.

We treat both as directions to test properly. Neither is a settled conclusion yet.

What this does not yet show

• Scope is narrow. The system is built and tested on board-based mathematics lectures, and we do not expect it to transfer unchanged to other subjects or formats.
• The evidence is qualitative. With no labeled benchmark yet, the observations above come from manual inspection rather than measurement.
• The rules are hand-built. They encode patterns we have seen in math lectures and may not hold for other teaching styles.
• The approach is interpretable but unvalidated against trained baselines. Comparing it to CRFs or neural sequence models on a labeled set is future work.

Paper and status