Notes and essays by Xingyu Zhu.https://ultimatejupiter.github.io/https://ultimatejupiter.github.io/blog/context-enhanced-learning/https://ultimatejupiter.github.io/blog/context-enhanced-learning/Training with helpful text in the context but no loss on it can be exponentially more sample-efficient than plain fine-tuning, and that text is hard to recover afterwards.Wed, 30 Sep 2026 00:00:00 GMTLLMslearning theoryinteractivehttps://ultimatejupiter.github.io/blog/eos-minimalist/https://ultimatejupiter.github.io/blog/eos-minimalist/A four-parameter scalar network reproduces edge-of-stability training, and a two-step parabola explains why gradient descent ends just below the stability threshold 2/η.Wed, 30 Sep 2026 00:00:00 GMToptimizationedge of stabilityinteractivehttps://ultimatejupiter.github.io/blog/t2mlr/https://ultimatejupiter.github.io/blog/t2mlr/T²MLR feeds a middle-layer state from the previous token into an earlier layer of the next, adding latent recurrence at almost no inference cost.Wed, 30 Sep 2026 00:00:00 GMTarchitecturelatent reasoninginteractivehttps://ultimatejupiter.github.io/blog/periodic-weak-spots/https://ultimatejupiter.github.io/blog/periodic-weak-spots/Chunked KV-cache compression gives every token a phase, and models that use it retrieve worse at some phases than others.Tue, 29 Sep 2026 00:00:00 GMTlong contextKV cacheinteractive