Fathom addresses the bottleneck of scanning offloaded KV caches during long agentic sessions by letting each query decide how many bits of each key channel to read, using a bit-plane-organized 4-bit K cache and reverse water-filling over channel importance. On Qwen3-8B at one million tokens, it decodes 1.67x faster than prior sparse-decoding methods reading full precision, and reads 18% fewer bytes than SparQ at matched GPU time while maintaining lower attention error. It matches exact top-k decoding accuracy on RULER-style tasks and real coding-agent sessions at a fraction of the read cost.
