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Dynamics of Spontaneous Topic Changes in Next Token Prediction with Self-Attention
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Theoretically characterizes spontaneous topic changes in a single-layer self-attention model via token-priority graphs, showing changes need lower-priority tokens to outnumber higher-priority ones and that longer context or ambiguity does not increase them, then checks this empirically with RAG on four frontier LLMs.
Problem
Self-attention models predict next tokens from structured input patterns and seem to lack the spontaneous topic shifts characteristic of human thought; it is unclear when and how such topic changes occur in self-attention and whether they resemble human cognition.
Approach
Defines a topic as a set of token-priority graphs (TPGs) and uses the Graph-SVM convergence result of a single-layer self-attention model trained on mixed-topic data to derive necessary conditions for topic change, showing that longer inputs and higher topic ambiguity do not increase change probability, unlike human cognition.
Key results
- In the toy model, the change-of-topic proportion drops from 1.40% at T=16 to 0.00% at T=512 (Table of varying T).
- In the toy model, change-of-topic proportion decreases from 1.52% at L=4 to 0.72% at L=18 while ambiguity rises from 0.26% to 1.26%.
- On frontier LLMs with RAG, cosine similarity between single-topic and mixed-topic continuations tends to increase with input length (10 to 150 words) across GPT-4o, Llama-3.3, Claude-3.7 and DeepSeek-V3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase test input length from T_test=4 to T_test=512 | Mixed-topic single-layer self-attention · Synthetic TPG test sequences | Change (%): 0.00 ± 0.00 -> 0.00 ± 0.00 | Hurt |
| Increase topic-overlap edge count L from 4 to 18 | Mixed-topic single-layer self-attention · Synthetic TPG test sequences | Change (%): 1.52 ± 1.31 -> 0.72 ± 0.86 | No clear effect |
| Increase input prompt length | GPT-4o, Llama-3.3, Claude-3.7, and DeepSeek-V3 · ArXiv paper abstracts; RAG with single-paper versus paired-paper context | Cosine similarity | Helped |
| Increase topic ambiguity | GPT-4o, Llama-3.3, Claude-3.7, and DeepSeek-V3 · ArXiv paper abstracts; five ambiguity bins | Cosine similarity | No clear effect |
Surprising findings
- Greater topic ambiguity does not increase spontaneous topic changes, contrary to human cognition where inter-connectivity promotes spontaneous thought.
- Longer prompts reduce rather than increase topic change in both the toy model and LLMs, opposite to human cognition.
Limitations
- Theory relies on a simplified single-layer self-attention model with log-loss and fixed classification head, which omits deep architectures and training heuristics.
- LLM experiments use a proxy (cosine similarity of RAG-based continuations) rather than the formal topic-continuity definition, and use a small set of 100 papers.
- Topic definition via TPGs and reconstruction assumption is idealized and not validated for real language.
Experimental setup
Datasets: 100 arXiv papers from March 2025 synthetic TPG-generated sequences
Benchmarks: synthetic TPG simulations 100 arXiv papers (March 2025)
Metrics: proportion keep topic / ambiguous / change of topic cosine similarity between single-topic and mixed-topic conti attention priority similarity
Baselines: GPT-4o Llama-3.3 Claude-3.7 DeepSeek-V3
Builds on: token-priority graph Graph-SVM implicit bias of self-attention attribution graphs retrieval-augmented generation
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