# Blog

- [Long LLM outputs hinge on a few decisions, not on their length](https://telegrapher.ai/blog/beyond-exponential-decay.md): About 9% of tokens carry long-range dependency and errors cluster, so the predicted decay of long LLM outputs is far gentler than (1 − e)^n. (October 9, 2026)
- [No finite fix list covers every LLM failure, and a deployment doesn't need one](https://telegrapher.ai/blog/architecture-of-errors.md): Open-ended LLM use has no finite fix list, but inside one deployment failures tend to recur, so a slowly growing library of fixes covers the most common ones. (October 9, 2026)
- [Production AI learns outside the weights, without the optimizer that layer needs](https://telegrapher.ai/blog/frontier-and-localhost.md): Teams fix LLM systems by editing prompts, memory, skills and tools. Across ~130 systems, that loop runs mostly as patchwork, its cross-org optimizer missing. (October 9, 2026)
- [Rewriting a prompt loses fewer details than deleting its tokens](https://telegrapher.ai/blog/telegraph-english.md): Telegraph English rewrites text one claim per line with explicit symbols. Against LLMLingua-2 it lost fewer answers, most visibly on fine-detail questions. (October 9, 2026)
- [Rewriting a retrieved passage beats cutting it to the same token budget](https://telegrapher.ai/blog/context-compression-is-not-one-thing.md): At a fixed token budget, rewriting passages as entity-relation clauses beat truncated and thinned text on three multi-hop datasets, and a summary on one. (October 9, 2026)
- [A compressed code can pass its own checker and still change the facts](https://telegrapher.ai/blog/what-survives-learned-symbolic-compression.md): Learned symbolic codes passed their own checker while changing what the source said. Scored against the source, a compact format kept more per byte. (October 9, 2026)
- [Asked for a quarter of the context, one encoder sent back two thirds](https://telegrapher.ai/blog/relational-context-compression.md): We followed Telegraph English rewrites from token budget to reader: 33 of 9,600 landed in band, and a compiler that held its ceiling still scored poorly. (October 9, 2026)
- [Finding most of what an edit changed is not finding all of it](https://telegrapher.ai/blog/ripplekb.md): We scored whether rankings recover every statement an edit changes, not just most. Recall and completion disagree, sometimes at the edited sentence itself. (October 9, 2026)
- [A linter that redoes the work catches injected errors that self-verification misses](https://telegrapher.ai/blog/telegraph-reasoning.md): Written in seven tags, a model's math reasoning can be checked by a SymPy-backed linter. It caught 195 of 196 injected errors; self-verification, 66.3%. (October 9, 2026)
- [A math trace that passes our checker is right about one time in three](https://telegrapher.ai/blog/answer-accuracy-and-trace-verifiability.md): We checked a small model's math traces with a program. Accepted traces were right about one time in three; switching to the trace format cost accuracy. (October 9, 2026)
- [In GRPO, the weight on an additive process reward acts like a switch, not a dial](https://telegrapher.ai/blog/additive-process-rewards.md): Group standardization cancels an additive process reward's weight when outcomes agree and swamps the term when they differ. We measured both, then tested fixes. (October 9, 2026)
- [An LLM labeler scores higher when its sibling wrote the answer key](https://telegrapher.ai/blog/same-family-halo.md): Hold an LLM labeler fixed and swap who wrote its answer key: agreement rises when the key comes from a sibling model, and no human gold is needed to see it. (October 9, 2026)
- [Most calls never reach the LLM, and the ones that do need a different prompt](https://telegrapher.ai/blog/high-load-call-categorization.md): A fine-tuned encoder answers roughly 87% of customer calls. The rest go to an LLM with five candidate labels, and that shortlist needs a prompt of its own. (October 9, 2026)
- [Rare call issues can get lost before an LLM ever sees them](https://telegrapher.ai/blog/clusters-are-proposals.md): A 1% call issue can be absent from the sample an LLM proposes topics from. Over-splitting each category found 234 subcategories; flat clustering found 111. (October 9, 2026)
- [Clarify a call once, then choose what each reader sees](https://telegrapher.ai/blog/clarify-then-focus.md): We rewrite each customer call once into short, tagged statements. An encoder gains from clearer text alone; weaker prompted readers also gain from selection. (October 9, 2026)