J-space in practice: using Anthropic's Jacobian lens to decide what an LLM can forget

Anthropic published Verbalizable Representations Form a Global Workspace in Language Models on July 6, and the vocabulary it introduced is suddenly everywhere: J-space, the Jacobian lens, a global workspace inside Claude. Most of the discussion so far is about interpretability and alignment auditing, which is fair, since that is what the paper is about. I had a narrower and more mercenary question: can the workspace tell an inference runtime which parts of the KV cache it is safe to throw away? Three days after the paper landed, the first pre-registered gate on that question passed. As of this week the signal has replicated on three models and ships inside EVOKE , my KV cache memory manager built on a forked llama.cpp. This post covers what J-space is, why it makes a good KV cache eviction signal, the numbers across Qwen2.5-7B, Qwen3-8B, and Qwen3-4B, and the caveat that comes with them. What J-space is, in one paragraph The Jacobian lens is the instrument and J-space is the phenomenon. The lens isolates directions in a model's residual stream that encode a token the model could verbalize next, and those directions form a low-dimensional workspace: roughly 10% of activation variance, concentrated in the middle layers, carrying whatever the model is "holding in mind" at each position. Anthropic's headline application is alignment auditing, reading reasoning the model never voices. What makes independent work possible is that they released companion code under Apache-2.0 along with fitted lens matrices for open Qwen models on Hugging Face , so anyone can apply the lens to an open-weights model on a single GPU. The systems problem: KV cache eviction Every long-running LLM session eventually outgrows its KV cache budget. An agent session in a coding harness crosses tens of thousands of cached tokens within a few turns, and something has to decide which entries stay in GPU memory. The standard answers, H2O and SnapKV, rank cache blocks by accumulated attention history: k