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Similarity Is a Decision

Mon, 07 Sep 2026 09:30:00 +0000

Part I — A Vector Is Not Meaning

Two vectors, four answers

Here are three document vectors, kept to three dimensions so every number is checkable:

x = ( 2.0, 0.0, 0.0 ) a short doc, one strong topic
y = ( 6.0, 0.1, 0.0 ) a long doc, same topic, much more of it
z = ( 0.0, 2.0, 0.0 ) a short doc, a different topic

Before computing anything, look at the geometry. x and y point in almost exactly the same direction but have very different lengths (norm 2 versus about 6). x and z have the same length but point ninety degrees apart. So “is x more like y or z?” comes down to a prior question: which kind of difference should count — a difference in direction, or a difference in size?

Memory and Selective Recall

Sat, 08 Aug 2026 17:14:00 +0100

The capability boundary gave the agent a defined action space and a rule for which capabilities are eligible at each step. Runtime state gave it an explicit working representation of what this run has established so far and how it reached that point. Together they govern the current execution, but neither gives information from an earlier run a controlled way to influence this one. There is a family of failures that requires exactly that.

From Similarity to Search

Mon, 07 Sep 2026 11:00:00 +0000

Part III — Retrieval Is an Experiment

Retrieval in four lines

# assume embed() returns L2-normalized vectors, so dot product == cosine (Chapter 4)
query_vec = embed(query) # one unit vector
scores = corpus_vecs @ query_vec # a cosine score for every document
order = np.argsort(-scores) # rank all n documents, best first
results = [corpus[i] for i in order[:k]] # keep the top k

That is the whole primitive for the simple policy shown here. A vector database may add several different kinds of machinery around it: an ANN index or quantization may approximate the same ranking more cheaply; sharding may distribute the computation; filtering may change the eligible candidate set; persistence and replication may make the system operable. Do not collapse all of those into “faster search” — some preserve the target policy, some approximate it, and some redefine it.

Agents From First Principles 07: AI Agent Forgets Previous Work? Add Working, Semantic and Episodic Memory

Sat, 08 Aug 2026 17:14:00 +0100

AI Agent Forgets Previous Work? Add Working, Semantic and Episodic Memory

An agent can use the right model, call the right tools, execute the right plan, and still behave as if nothing that happened five minutes ago matters.

You see the symptoms quickly:

it re-reads files it already inspected;
it repeats research it already completed;
it asks for information the user already supplied;
it forgets why a previous approach failed;
it loses decisions made earlier in a long task;
it treats every new run as if the system has never seen the problem before;
it retrieves an old answer and treats it as current truth;
it fills the prompt with so much history that the useful information is buried.

The usual response is:

RELATE: Searching Embeddings by Relation, Not Just Similarity

Wed, 05 Aug 2026 23:24:45 +0100

Embeddings are everywhere in modern AI.

They power semantic search, retrieval-augmented generation, recommendations, clustering, duplicate detection, code search, memory systems, and many of the mechanisms through which an AI system decides what information is relevant.

Yet most systems interrogate embeddings in essentially the same way:

Take two vectors and calculate cosine similarity.

That is useful. But it also makes a strong assumption.

It assumes that the information we care about is expressed directly through the default geometry of the embedding space.