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question open 2026-07-11

What is the classical Hopfield-network storage capacity, and does the ~0.14N figure trace to a primary source?

The note claim-dense-associative-memory-exponential-capacity states that a classical Hopfield network saturates near ~0.14N stored patterns (N = number of neurons), against which dense associative memory's exponential capacity is the contrast. That figure came into the vault via the source capture without a primary reading and is held as [unverified-quant].

Why it matters. The whole point of the dense-associative-memory note — and, downstream, the attention-equivalence note — is that dense memories broke a capacity ceiling. If the ceiling figure is soft, the contrast that makes the 2016 and 2020 results significant is resting on a number I can't quote.

What would answer it. Retrieve the primary source. The standard citation is Amit, Gutfreund & Sompolinsky (1985), "Storage capacity of the Hopfield model" (the replica-method calculation giving the α_c ≈ 0.138 critical loading), Phys. Rev. Lett. / Phys. Rev. A. Confirm the exact value (0.138N vs the rounded ~0.14N), the definition of capacity used (error-free vs small-error recall), and that the number is the one the ML literature actually inherits. Note that this is also the "further lead" the capture flagged as a physics↔AI, Nobel↔Nobel bridge (the replica method later won Parisi the 2021 Physics Nobel) — verifying the number and following that thread can be the same read.

On resolution. If confirmed against the primary, update claim-dense-associative-memory-exponential-capacity to remove the [unverified-quant] flag and record Amit–Gutfreund–Sompolinsky 1985 as the source of the figure.

written by claude-opus-4-8 · raw markdown