Add Hopfield (1982) — mathematical bridge between Pavlov and CRI

Dot-product pattern completion is the same operation at biological,
theoretical, and computational abstraction levels.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

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paper.md

@@ -281,6 +281,8 @@ This is privacy by representation, not encryption — an architectural consequen
 
 **Pavlov (1927)** described hypnotic suggestion as the best example of a conditioned reflex in humans — learned associations triggered by words. **"Hypnosis and the Conditioned Reflex" (1930)** formalized this: suggestion installs stimulus-response links that fire without the subject's awareness. CRI implements the same mechanism on transformers: activation pattern (CS) paired with logit biases (US) produces token sequence (CR). **Weitzenhoffer (1957)** modeled hypnosis through conditioning and inhibition principles. **Raz et al. (2005)** showed post-hypnotic suggestion reduces conflict in human brains by modulating activity in specific regions — external behavioral modification without the subject's awareness, analogous to CRI's logit injection. **Skinner (1938)**: operant conditioning — responses shaped by consequences. CRI currently performs respondent conditioning only, but bias magnitude modulation via reward is a natural extension.
 
+**Hopfield (1982)**: formalized associative memory as pattern completion via dot-product similarity — store patterns as attractors, retrieve by nearest match. CRI's cosine similarity matching is the same computation at a different abstraction level.
+
 **CAMELoT** (Jang et al., 2024): training-free associative memory, stores KV pairs from attention layers, injects as attention prefixes. **EM-LLM** (Fountas et al., 2024): KV pairs from attention heads, k-NN retrieval, KV cache extension. **Larimar** (Das et al., 2024): memory matrix with pseudo-inverse retrieval, requires training. All inject at the attention level. CRI injects at the output logits — simpler, cheaper, no attention recomputation.
 
 **RAG** (Lewis et al., 2020): retrieves text, re-encodes into context. RAG informs; CRI conditions. **ROME/MEMIT** (Meng et al., 2022, 2023): rank-one weight edits. CRI modifies zero weights. **NTM/DNC** (Graves et al., 2014, 2016): gradient-trained read/write controllers. CRI requires no training.
@@ -313,6 +315,7 @@ Capture activation pattern, store logit biases, match by cosine similarity, inje
 - Fountas, Z. et al. (2024). EM-LLM. arXiv:2407.09450.
 - Graves, A. et al. (2014). Neural Turing Machines. arXiv:1410.5401.
 - Graves, A. et al. (2016). DNC. Nature 538, 471-476.
+- Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. PNAS 79(8), 2554-2558.
 - Jang, J. et al. (2024). CAMELoT. arXiv:2402.13449.
 - Lewis, P. et al. (2020). RAG. NeurIPS 2020.
 - Meng, K. et al. (2022). ROME. NeurIPS 2022.

paper.tex

@@ -363,6 +363,13 @@ operating in the model's internal space.
 CRI implements the Pavlovian mechanism on transformers: activation pattern (CS)
 paired with logit biases (US) produces token sequence (CR).
 
+\subsection{Associative Memory}
+
+\textbf{Hopfield}~\citep{hopfield1982}: formalized associative memory as
+pattern completion via dot-product similarity---store patterns as attractors,
+retrieve by nearest match. CRI's cosine similarity matching is the same
+computation at a different abstraction level.
+
 \subsection{Training-Free External Memory}
 
 \begin{itemize}
@@ -415,6 +422,10 @@ Das, P. et~al. Larimar. \emph{ICML}, 2024. arXiv:2403.11901.
 \bibitem[Fountas et~al.(2024)]{fountas2024emllm}
 Fountas, Z. et~al. EM-LLM. arXiv:2407.09450, 2024.
 
+\bibitem[Hopfield(1982)]{hopfield1982}
+Hopfield, J.~J. Neural networks and physical systems with emergent collective
+computational abilities. \emph{PNAS}, 79(8):2554--2558, 1982.
+
 \bibitem[Jang et~al.(2024)]{jang2024camelot}
 Jang, J. et~al. CAMELoT. arXiv:2402.13449, 2024.