Annotated SSMs
July 11, 2026
Note: This is part of a series of personal notes on topics I’m trying to learn more deeply.
Why do we care about SSMs?
Each post has two parts: a short set of “teaching” notes (the order I’d introduce the ideas), then my handwritten notes (the main content). In my experience, having both matter a lot.
“Teaching” Notes:
Here’s my opinionated take on how to teach beginners about SSMs. The full PDF is at the bottom of this page.
The flow I’d use:
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Pitch. Why care about SSMs at all? Attention is quadratic in sequence length; an SSM step doesn’t grow with length.
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Showing SSMs in multiple angles. The S4 Hazy Research post frames SSMs as having “3 forms,” but they all reduce to one simple recurrence. I show that recurrence a few ways — RNN diagram, computation graph, expanding the equations — hoping at least one lands.
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Worked examples!!! Plug in small vectors and matrices and grind through the computation by hand. That does more for building intuition about shapes and mechanics than another round of abstractions. This is critically important! It grounds your audience to actually “think” like an LLM and actually do the computation themselves.
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The big “reveal” at the end (i.e. convolutions in this case). Once the recurrence clicks, expand and substitute: the convolutional form falls out of what you already know. That was the most satisfying bit for me.