Year 12 · 55 minutes · Seeded branching simulation
Sample continuations from a known branching process. Change rollout count, smoothing and early-exit confidence, then test a late reversal.
Student paper journal · Interactive notebook · Editable Python
Try the starting controls, save two runs and reopen a downloaded project. Print the student journal before class. If Python cannot load, use the supplied example below for a prediction and evidence critique; rerunning changed inputs requires the live or native notebook. Do not present paper discussion as a new model experiment. Keep an individual record even when you investigate in pairs. Record the exact settings, source and data split.
Start with 5–8 minutes of prediction, use about half the lesson for paired comparisons, then reserve at least 10 minutes for a counterexample and an individual explanation. The simulator reveals true probabilities so uncertainty estimates can be checked. Distinguish a monitor predicting an eventual answer from a monitor checking an external answer key.
Settings: {'rollouts': 50, 'smoothing': 1, 'threshold': 0.8, 'hard': 0, 'seed': 37}
Early exit at prefix 7: chooses A; the fixture answer is A. Later evidence can overturn an early high-confidence choice.
| prefix | true_p_A | sample_p_A | smoothed_p_A | estimated_standard_error |
|---|---|---|---|---|
| 0 | 0.5 | 0.54 | 0.54 | 0.07071067811865475 |
| 1 | 0.51 | 0.48 | 0.48 | 0.07069653456853454 |
| 2 | 0.52 | 0.62 | 0.62 | 0.07065408693062278 |
| 3 | 0.51 | 0.48 | 0.48 | 0.07069653456853454 |
| 4 | 0.53 | 0.56 | 0.56 | 0.07058328414008518 |
| 5 | 0.55 | 0.56 | 0.56 | 0.07035623639735145 |
| 6 | 0.87 | 0.76 | 0.76 | 0.04756048780237646 |
| 7 | 0.9 | 0.96 | 0.96 | 0.04242640687119285 |
The table shows up to eight rows. Inspect the notebook for all values, controls and denominators.
Method and scope: Each prefix draws N independent Bernoulli continuations from a known probability. A trailing mean smooths estimates. SE = √[p(1−p)/N]. These are simulated continuations; matching the eventual answer is distinct from matching an external answer key.
Assess four criteria, each 0–2: testable prediction; comparison identifying what stayed fixed; accurate use of exact evidence; counterexample and limited conclusion. 0 means absent or contradicted by the record, 1 means partly supported, and 2 means clear and supported. A surprising result earns no penalty.
Beginning response: ‘The picture looks right.’ Ask for a particular case. Developing response: names one number without its setting. Ask what comparison supports it. Secure response: states the setting and measured change and separates the notebook's result from the source paper's claim. Extending response: authors or reserves a new case, tests an alternative explanation, and revises the claim if needed. These are marking examples, not pupil data.
Extension: Repeat many seeds and plot error rate against average prefixes consumed.
System and data: Llama-3-8B-Instruct and DeepSeek-R1-Distill-Llama-8B on tinyMMLU
Method: Resamples continuations at shared prefixes and compares uncertainty estimates across sample budgets, spacing and smoothing.
Task: Compare sampled branch probabilities with a known distribution as rollout count and smoothing change. Record the source model/task, a baseline, the changed factor, a measurement and an alternative explanation. State exactly which part your notebook investigates and which part it does not reproduce.
Boundary: Our finite branching simulator is not a reasoning LLM. More samples reduce sampling noise, not model bias.
System and data: Gemma-2-2B activations from Pile-Uncopyrighted
Method: Compares temporal feature analysis with ReLU, TopK and BatchTopK SAEs, testing predictable versus innovation components and event structure.
Task: Contrast a static representation with a model of predictable state and residual novelty. Record the source model/task, a baseline, the changed factor, a measurement and an alternative explanation. State exactly which part your notebook investigates and which part it does not reproduce.
Boundary: Our Bayesian story model is explicit and hand-specified; it is not Temporal Feature Analysis applied to an LLM.
System and data: DeepSeek-R1 families and GPT-OSS-120B on MMLU-Redux and GPQA-Diamond
Method: Trains context-pooling probes to forecast eventual answers during reasoning and evaluates early-exit token cost versus benchmark accuracy.
Task: Evaluate early-exit cost against accuracy and distinguish answer prediction from correctness. Record the source model/task, a baseline, the changed factor, a measurement and an alternative explanation. State exactly which part your notebook investigates and which part it does not reproduce.
Boundary: Savings depend on task and paper version; the Goodfire post and later arXiv revision report different percentages. Our trajectories are simulated.
Independent Brightlab adaptations; no Goodfire endorsement or full reproduction claim. Source methods reviewed 7 September 2026. Curriculum connections are selected planning links; confirm your school syllabus.