> Obviously not, which is why I didn't say it did!

But you sneak it into your assumptions on what a memory must be.

> However, if you want to identify where long-term memories are stored

And why do you assume there is a specific “where” for the memory?

> then that is in the cortex

There’s good deal of evidence disproving this in the way you’re stating this. The cortex is involved in sensing, and yes, the sensory information associated with a memory will recruit appropriate cortical cells. This doesn’t mean the memory resides in the cortex. And detailed episodic recall keeps recruiting the hippocampus even for old memories, which is odd if the memory were somehow only in the cortex.

> I'm not sure what you are trying to say.

Let me restate what I’m saying then:

There are four claims bundled together in the way you were describing biological memory: that a specific ensemble is activated when a given memory forms; that it’s the same ensemble that gets activated over time when that memory is retrieved; that it’s spatially compact, like a column in region of the brain; and that this ensemble it’s dedicated to that memory, or similar memories .

The first is well supported. An engram, a network of neurons, is indeed activated when a memory first forms, and gets stabilized due to repeated stimulus. Re-activating these neurons in a different context can make the subject (a mouse) behave as it would if it had contextual signals to evoke said memory.

However: 1. This engram is not in one particular part of the brain. There’s a cortical part that overlaps the sensory regions that were involved. But plenty of other regions are part of the engram 2. There’s turnover, over the course of weeks, when the specific cells involved in the engram drift, while the behavior remains stable. 3. The same synapses participate in many memories.

> Memories are presumably stored as embeddings

No. Let’s consider songbirds, which are an excellent worked out example (in an animal without the complex columnar cortical architecture mammals show, by the way).

What’s learned is a temporal sequence, with neurons in a nucleus in their brains each firing one brief burst at a fixed point in the motif, so the content of the memory is its dynamics rather than any value. The circuit that evaluates the match against the tutor template is the same circuit generating the output being evaluated. Song degrades overnight during sleep replay and recovers the next day, and in seasonal species the song nuclei change size across the year with neurons added and lost while the song persists. There’s no read that leaves the item untouched, no persistent address, and no substrate holding still. “Stored as” imports all three.

And it goes below the neuron or synapse. Hearing a tutor song drives immediate early gene expression that habituates with familiarity, and singing drives large transcriptional changes in the song nuclei that differ by social context for the same motor output. Since transcription runs on minutes to hours and the proteins turn over, any persistent state has to be actively regenerated rather than deposited.

TLDR: the memory isn’t a static store. There’s no persistent “location” for it, distributed or otherwise, though specific locations can be in the chain that’s activated for retrieval/production. Instead, memory, over time, is driven by a dynamical regime that adjusts its dynamics to account for the temporal pattern in the salient stimulus.

Nothing, down to the epigenetic changes in the chromatin of these neurons, can be seen as “the” location of “a” memory, especially over time.

> if you are saying that individual memories/chunks are not confined to one set of cells (some localized neural assembly such as a cortical column).

That is indeed the case.