Abstract
When agentic sessions run to a million tokens with many sessions resident at once, the KV cache and the index that ranks it live in host memory, and the scan that ranks all n keys for a top-k step becomes the traffic that bounds decoding. We present Fathom, a key scan in which each query decides how many bits of each key channel to read. The 4-bit K cache is stored channel-major as bit planes, so a prefix of t planes is exactly the channel's t-bit quantizer, and the query spends its bit budget by reverse water-filling over the variance-weighted importance of its channels. At one million tokens on Qwen3-8B a decode step is 1.67x faster in GPU time than with the 136-bit scans of Double Sparsity, Loki and SparQ r=32, and in the same GPU time as SparQ's 68-bit read (r=16) Fathom reads 18% fewer bytes with lower attention error on six of seven model and context settings. On RULER-style tasks every per-token scan matches exact top-k decoding, and on real coding-agent sessions Fathom reaches the step agreement of the most accurate 136-bit scan at 92 bits. The store is the 4-bit K copy a quantized serving stack already holds, and the method is not faster when the index is resident in GPU memory.
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Publication details
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- Open access
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Cite this article
APA 7
Kalyanarangan, V. (2026). Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches. https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches
MLA 9
Kalyanarangan, Vivek. "Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches." https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches.
Chicago (author–date)
Kalyanarangan, Vivek. 2026. "Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches." https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches.
Harvard
Kalyanarangan, V. (2026) 'Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches', Available at: https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches.
Vancouver
Kalyanarangan V. Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches. https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches
IEEE
V. Kalyanarangan, "Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches," https://omanscience.com/en/articles/fathom-per-query-read-depth-for-sparse-decoding-over-offloaded-kv-caches.