Paper
The Anxiety of Influence: Bloom Filters in Transformer Attention Heads
Authors
Peter Balogh
Abstract
Some transformer attention heads appear to function as membership testers, dedicating themselves to answering the question "has this token appeared before in the context?" We identify these heads across four language models (GPT-2 small, medium, and large; Pythia-160M) and show that they form a spectrum of membership-testing strategies. Two heads (L0H1 and L0H5 in GPT-2 small) function as high-precision membership filters with false positive rates of 0-4\% even at 180 unique context tokens -- well above the $d_\text{head} = 64$ bit capacity of a classical Bloom filter. A third head (L1H11) shows the classic Bloom filter capacity curve: its false positive rate follows the theoretical formula $p \approx (1 - e^{-kn/m})^k$ with $R^2 = 1.0$ and fitted capacity $m \approx 5$ bits, saturating by $n \approx 20$ unique tokens. A fourth head initially identified as a Bloom filter (L3H0) was reclassified as a general prefix-attention head after confound controls revealed its apparent capacity curve was a sequence-length artifact. Together, the three genuine membership-testing heads form a multi-resolution system concentrated in early layers (0-1), taxonomically distinct from induction and previous-token heads, with false positive rates that decay monotonically with embedding distance -- consistent with distance-sensitive Bloom filters. These heads generalize broadly: they respond to any repeated token type, not just repeated names, with 43\% higher generalization than duplicate-token-only heads. Ablation reveals these heads contribute to both repeated and novel token processing, indicating that membership testing coexists with broader computational roles. The reclassification of L3H0 through confound controls strengthens rather than weakens the case: the surviving heads withstand the scrutiny that eliminated a false positive in our own analysis.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.17526v1</id>\n <title>The Anxiety of Influence: Bloom Filters in Transformer Attention Heads</title>\n <updated>2026-02-19T16:37:16Z</updated>\n <link href='https://arxiv.org/abs/2602.17526v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.17526v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Some transformer attention heads appear to function as membership testers, dedicating themselves to answering the question \"has this token appeared before in the context?\" We identify these heads across four language models (GPT-2 small, medium, and large; Pythia-160M) and show that they form a spectrum of membership-testing strategies. Two heads (L0H1 and L0H5 in GPT-2 small) function as high-precision membership filters with false positive rates of 0-4\\% even at 180 unique context tokens -- well above the $d_\\text{head} = 64$ bit capacity of a classical Bloom filter. A third head (L1H11) shows the classic Bloom filter capacity curve: its false positive rate follows the theoretical formula $p \\approx (1 - e^{-kn/m})^k$ with $R^2 = 1.0$ and fitted capacity $m \\approx 5$ bits, saturating by $n \\approx 20$ unique tokens. A fourth head initially identified as a Bloom filter (L3H0) was reclassified as a general prefix-attention head after confound controls revealed its apparent capacity curve was a sequence-length artifact. Together, the three genuine membership-testing heads form a multi-resolution system concentrated in early layers (0-1), taxonomically distinct from induction and previous-token heads, with false positive rates that decay monotonically with embedding distance -- consistent with distance-sensitive Bloom filters. These heads generalize broadly: they respond to any repeated token type, not just repeated names, with 43\\% higher generalization than duplicate-token-only heads. Ablation reveals these heads contribute to both repeated and novel token processing, indicating that membership testing coexists with broader computational roles. The reclassification of L3H0 through confound controls strengthens rather than weakens the case: the surviving heads withstand the scrutiny that eliminated a false positive in our own analysis.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CL'/>\n <published>2026-02-19T16:37:16Z</published>\n <arxiv:comment>13 pages, 8 figures, code at https://github.com/pbalogh/anxiety-of-influence v2: L3H0 reclassified as prefix-attention head following confound control. Capacity analysis updated. Duplicate-token head overlap experiment added v3: All experiments were independently validated on CPU to rule out hardware-specific computation artifacts. Results are consistent across backends</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Peter Balogh</name>\n </author>\n </entry>"
}