EPS Dashboard

A reference for the kind of document where you propose a model, state its assumptions, derive a result, and discuss its generality — theory notes, framework write-ups, mechanistic-interpretability expositions, mentor-facing theory docs. Synthesized from the math-writing classics (Halmos, Knuth, Mermin, Gopen–Swan, Doumont), the Distill / transformer-circuits exposition tradition (Olah, Elhage, Nanda), the alignment-forum theory-post norms (Wentworth, Christiano), and the paper-structure guides (Peyton Jones, Tao, Widom). The running example is the behavior-leakage note (main.tex); the rules it already follows are marked ✓, the ones it could push further ✗.

TL;DR — the seven rules every source agreed on

These showed up independently in all four research threads. If you do nothing else:

Lead with the claim, not the background. State the result in words before any machinery; a reader who knows the punchline reads the derivation as confirmation.
Motivate before you formalize. Show the phenomenon (ideally a concrete instance) before defining the object that explains it.
Build the simplest case first, then generalize. Never open in full generality — the mechanism is visible in isolation and invisible in complexity.
Make assumptions explicit and separable, and flag the weakest one. A reader must be able to ask "what breaks if A3 fails?"
Idealization ≠ claim. Mark modeling simplifications as deliberate, and carry them forward as scope caveats wherever the result is quoted.
Reference backward, never forward. A later section may cite an earlier one; the reverse makes the reader hold an undefined term.
Cut every word that doesn't earn its place. Length is a tax on the reader's interpretive labor. Rewrite, don't patch.

The skeleton

A theory-framework note, section by section. The order is the argument: idea first, machinery in the middle, generality and mechanical detail last.

#	Section	Purpose (one line)
1	The observable / phenomenon	The concrete fact or puzzle the framework explains — shown, not asserted. End on the central question.
2	Goal & central claim	State the single result/formalism in words, before notation. The reader knows the punchline here.
3	Minimal model + explicit assumptions	The simplest world that reproduces the phenomenon. Assumptions labeled A1…An, each motivated, the load-bearing ones flagged.
4	Derivation (special case first)	Work the cleanest instance fully; routine algebra goes to the appendix.
5	The result, stated precisely	The proposition / scaling law / bound, with its regime of validity named inside the statement.
6	Contact with data	Where the prediction meets a measurement or known result; what would falsify it.
7	Generalizations / relaxations	Relax assumptions one at a time — which survive, which break the result. The general case lives here, not at the opening.
8	Summary table + one-paragraph close	A table carrying the global structure (assumption → consequence → evidence). Restate the claim and the open edge.
A	Appendices	Mechanical proofs, token-level derivations, notation conventions.

The leakage note maps onto this almost exactly: observable → goal → assumption ladder + derivation → cosine predictor (contact with data) → two kinds of leakage → relaxations → summary table → token-level appendix. ✓

Rules by theme

A. Architecture & narrative

Lead with the claim. Open by naming the result; earn it afterward. Building up to a reveal is a fine habit for fiction and a terrible one for technical writing. ✓ The title states the thesis; the boxed formula is the payoff the whole ladder targets.
One idea per section, with a heading that names the claim. A section defending two claims dilutes both. ✓ "The cosine predictor is the bottom rung" is the section's claim, not a topic label.
The structure is load-bearing — the skeleton IS the argument. A reader who skims only the headings should get the thesis. ✓ The six "Relax Assumption N" headings are the generalization map.
Motivate before you formalize. A definition that answers a felt pressure is remembered; one imposed from outside is not. ✗ The note is abstract from sentence one — a single concrete instance up front (train marker ※ into persona X, watch it surface under persona Y) would ground the whole frame before the formalism.
Build the simplest case first, then generalize. ✓ This is the note's spine: six assumptions collapse to one formula, then each relaxes. Textbook.
A figure can carry the argument. For geometric/structural claims, showing beats telling; the figure becomes the evidence (the Distill/Olah lesson). ✗ The note has no figure — one schematic of the behavior × context table with the rank-one outer product smearing along both margins would carry §5 visually, and a ladder diagram would carry the whole doc.
Frontload navigation for anything long. A "summary of results" block lets readers read strategically and survive reading only the intro.

B. Assumptions & idealizations (the heart of a framework doc)

State every assumption explicitly, before the result that depends on it. A silently-relied-on hypothesis is a hidden bug. Gather them into a labeled block. ✓ Six numbered assumptions, each with a justification.
Flag the load-bearing / weakest assumption. Say which the conclusion most depends on and which is least defensible. ✓ "This is the strongest and least defensible rung" (Assumption 5).
Idealization ≠ claim. Write "under this idealization, X," not "X," and carry the caveat forward. ✓ "consistent with the discriminative-key account but do not isolate it … dose-confounded" — the model is held separate from the evidence for it.
Relax one assumption at a time. Changing several at once makes it impossible to attribute which mattered. ✓ "Only the conjunction of all six is refutable"; each §6 subsection perturbs exactly one rung.
Carry the global structure in a summary table. Prose serializes; a table lets the reader hold the whole framework at once. ✓ The §7 table: assumption → what relaxing it generalizes.
Name competing hypotheses and what would distinguish them. A framework with no rival and no discriminating test is unfalsifiable repackaging. ✓ "distinguishable by whether transfer tracks steering-direction overlap or base-model context co-activation."

C. Notation & equations

Minimize notation — the best notation is no notation (Halmos). Each symbol is a memory tax; many can be replaced by words.
Introduce every symbol once, at or before first use; never reuse a symbol for two things. Consistency over elegance. ✓ We deleted the standalone Notation block and folded each symbol's definition into its first-use site.
Punctuate displayed equations as part of the sentence (Mermin: "math is prose"). An equation is a clause, not a picture.
Put words between adjacent formulas; never let two symbols collide (Knuth). "Consider $S_q$ , where $q<p$ ," not "Consider $S_q$ , $q<p$ ."
Never begin a sentence with a symbol (Halmos). "The sequence $x_n$ converges," not " $x_n$ converges."
Reference equations by a phrase, not a bare number. "By the energy identity (3.7)," not "by (3.7)" — the phrase saves a page-flip.
State each result with its regime of validity inside the statement (Tao). "In the small-noise limit, …", not the limit named three paragraphs away.

D. Epistemic honesty

Calibrate confidence where it naturally lives — this is genre-dependent. A prose blog post with no formal scaffold puts an epistemic-status line up front, because there is nowhere else for calibration to go. A framework doc with an explicit assumption ladder calibrates per assumption instead — which rung is empirically grounded, which is conjectural, which is load-bearing — so a top-of-doc header just duplicates the assumption justifications. Don't bolt "epistemic status: speculative" onto a doc that already calibrates in its bones. ✓ The note grades each rung inline (Assumption 5 = "the strongest and least defensible rung"; the cosine rung empirically at ρ≈0.77) — that distributed calibration IS its epistemic status, attached to the specific claim it qualifies.
Calibrate confidence by reasons, not adjectives. "Ran this past two people / 40 hours of work" beats "robustly." Strip "robust / clearly / significantly" unless a number backs them.
Flag confounds against your own claim, in-line. Pre-empting the strongest objection signals you stress-tested the frame. ✓ The dose-confound caveat sits right next to the localization numbers it threatens.
Define every coined term on first use — and only coin when load-bearing. Undefined compound nouns ("the reveal signal," "the install") are vague gesturing dressed as rigor unless anchored to a concrete referent. ✓ "the install" is explicitly defined ("the change at the source").
Hedging must bind the prose, not license it. An "epistemic status: speculative" header followed by unqualified strong claims is the worst case.

E. Prose mechanics (Gopen–Swan + Halmos)

Topic position → stress position. Open a sentence with old/known information; put the new point at the end, where emphasis lands. "This section's main result is a sharper bound," not "A sharper bound is the main result."
Keep subject and verb close. A long interruption forces the reader to hold the subject in memory.
Say it twice: pair the formal statement with the intuition. A reader who gets the idea informally can absorb the rigor; the reverse rarely works. ✓ Every equation has an underbrace gloss and a plain-English read ("who leaks" / "what leaks").
Apply the cut test: if you can't answer "what goes wrong if I cut this?", cut it (Nanda).
Maximize signal-to-noise; redundancy must be effective, not mere repetition (Doumont). ✓ We deduplicated the dose-confound caveat that appeared verbatim twice — restate only what changed.

Genre pitfalls (checklist)

Notation sprawl — symbols introduced ad hoc, never tabled.
Over-formalizing — theorems before intuition; the why buried under the what.
Undefended idealizations — a toy model's simplifications smuggled in as if general.
Forward-reference clutter — "as we show in §7" chains that defeat linear reading.
Narrative diffusion — many small results, no 1–3 load-bearing claims; the reader retains nothing.
Vague gesturing as depth — naming a phenomenon without a mechanism or a discriminating test.
Undefined coined jargon — minting nouns to make a familiar idea feel new.
Hedging that smuggles strong claims — disclaimer up top, unqualified assertions below.
False balance — a rival hypothesis raised only to be strawmanned.
Narrating a trend across 3 datapoints — "again," "the pattern is clear."
Research debt — shipping undigested ideas; pushing the interpretive cost onto every future reader.

Reading list — exemplars worth imitating

Mechanistic-interpretability / ML theory

A Mathematical Framework for Transformer Circuits — Elhage et al., 2021. transformer-circuits.pub/2021/framework. Strict simplest-model-first (0→1→2 layers) + a single notation appendix.
Toy Models of Superposition — Anthropic, 2022. transformer-circuits.pub/2022/toy_model. The minimal toy model as an argument device: isolate one phenomenon, derive the phase change, then ladder out.
Neural Networks, Manifolds, and Topology — Olah, 2014. colah.github.io/posts/2014-03-NN-Manifolds-Topology. Interactive visuals carry the math; the formalism arrives only after the intuition.

Meta / how-to

Research Debt — Olah & Carter, distill.pub/2017/research-debt. Why distillation is real work.
Highly Opinionated Advice on How to Write ML Papers — Neel Nanda (Alignment Forum). The narrative-of-claims discipline, stated operationally.
The Science of Scientific Writing — Gopen & Swan, American Scientist 1990. The reader-expectation rules (topic/stress, subject-verb proximity).
What's Wrong with These Equations? — N. D. Mermin, 1989. The three rules for displayed equations.
How to Write Mathematics — Halmos, 1970. "The best notation is no notation"; say it twice; the spiral plan.
How to Write a Great Research Paper — Simon Peyton Jones. Idea-first; related work late.
Terence Tao, Advice on writing papers (terrytao.wordpress.com). Local vs global organization; give appropriate detail.

Conceptual-framework blog style

What failure looks like — Paul Christiano (Alignment Forum). The section skeleton literally is the taxonomy it argues for.
Gears vs Behavior — John Wentworth (LessWrong). The test for whether a framework has internal structure or just relabels observations.

Sources (the writing guides themselves)

Halmos How to Write Mathematics (1970) · Knuth, Larrabee & Roberts Mathematical Writing (Stanford CS209) · Mermin What's Wrong with These Equations? (1989) · Gopen & Swan The Science of Scientific Writing (1990) · Doumont Trees, Maps, and Theorems (2009) · Olah & Carter Research Debt (2017) · Elhage et al. A Mathematical Framework for Transformer Circuits (2021) · Nanda Opinionated Advice on Writing ML Papers · Peyton Jones How to Write a Great Research Paper · Tao Advice on Writing Papers · Widom Tips for Writing Technical Papers · Christiano What failure looks like · Wentworth Gears vs Behavior / How to Write Quickly While Maintaining Epistemic Rigor.