Building a portfolio and research roadmap: Visual walkthrough

Before any symbol appears, let us agree on the plainest possible picture: you have a fixed amount of time (a bar), and an infinite pile of things you could learn (a mountain). The whole derivation is about how a bar meets a mountain.

Step 1 — The raw problem: a finite bar against an infinite mountain

WHAT. We draw the two facts of research life. On the left, your time budget — call it $T$ . Read $T$ as "total number of weeks you actually have" (say $T = 52$ for one year). It is a finite bar with a hard end. On the right, the set of all things one could learn in ML — call it $U$ (a fancy "U", short for Universe of skills). $U$ has no top; it grows faster than you can climb.

WHY these two objects and nothing else? Because every planning mistake comes from pretending one of them is different from what it is: pretending time is infinite (so you never prioritise) or pretending the skill-pile is small (so you think you'll "just learn everything"). Naming them forces honesty.

PICTURE. The bar on the left has a ceiling; the mountain on the right does not. That mismatch is the entire reason a roadmap must exist.

Figure — Building a portfolio and research roadmap

Step 2 — Value is not spread evenly: the 80/20 curve

WHAT. We ask: does every skill in $U$ give the same payoff? No. We assign each skill $s$ a value $v (s)$ — read " $v$ of $s$ " as "how much research capability this one skill unlocks." Because $U$ itself is infinite, "20% of an infinite set" is meaningless — so we first pass to a finite proxy: the shortlist $L$ , the $M$ skills that are even plausibly relevant to your target area (a big but finite number, say a few hundred). Everything from here on lives inside $L$ , never the raw infinite $U$ . When we sort the $M$ skills of $L$ from most to least valuable and plot them, we get a curve that is steep at the start and flat later.

WHY introduce $v (s)$ , a finite $L$ , and why sort? Because the parent note claims we should practise "the 20% you'll actually practise, not everything in the textbook." A percentage only makes sense against a finite denominator, which is exactly what $M = ∣ L ∣$ gives us. And the "20%" claim only bites if value is unevenly distributed — the sorted curve is the visual proof: the area under the first sliver of skills is huge; the area under the long tail is tiny.

PICTURE. The red curve drops fast. The shaded lavender region — the leftmost $\approx 20%$ of the $M$ shortlisted skills — already covers most of the total area (capability). The long flat tail to the right is the "nice to know, rarely unlocks anything" zone.

Step 3 — Choosing the steep slice: the constrained selection

WHAT. Now we combine Step 1 and Step 2. We must choose a subset $S \subseteq L$ of shortlisted skills to actually learn, where " $\subseteq$ " means "is contained in." Learning skill $s$ costs time $t (s)$ (weeks). The constraint is that total time cannot exceed the bar: $\sum_{s \in S} t (s) \leq T while maximising \sum_{s \in S} v (s) .$

WHY this exact shape? This is the classic "fill a fixed bag with the most valuable items" problem. It is why the roadmap has finitely many, deliberately chosen items rather than an open-ended wish list. The ceiling $T$ from Step 1 does the cutting; the value $v$ from Step 2 decides what survives the cut.

PICTURE. Items (skills) are boxes whose width = time cost and height = value. We pack boxes into the fixed-width bar $T$ , greedily preferring tall-and-narrow boxes (high value per week). Boxes that don't fit fall off the edge — those are the topics you consciously postpone.

Step 4 — Why phases: time has an order, not just a total

WHAT. So far $T$ was one bar and $S$ was one bag. But time is sequential — you learn attention before you can extend a Transformer. So we slice the bar into ordered chunks. Each chunk is a Phase. We index them $Phase_{1}, Phase_{2}, \dots, Phase_{N}$ , where the subscript is just a label saying "which chunk, in order."

WHY split an already-small bag into phases? Two reasons the parent note names: prevents drift (a phase has one focus, so you can't hop between shiny topics mid-chunk) and builds momentum (finishing a phase is a visible win). Ordering also respects prerequisites: later phases stand on earlier ones — exactly the dependency structure you see when interpretability work presupposes you can already train the model you want to explain.

PICTURE. The single bar $T$ is now cut into $N$ coloured segments laid end-to-end. Arrows point forward: skills flow from an earlier phase into the next, so nothing is attempted before its foundation exists.

Step 5 — What each phase must contain: earning the five fields

WHAT. A phase is a slice of time — but a bare slice tells you nothing about what to do in it. We now attach exactly five fields, and each answers one unavoidable question:

$Phase_{i} = (why? Goal_{i}, what artifact? Deliverable_{i}, practise what? Skills_{i}, how long? Duration_{i}, done or not? Metric_{i})$

WHY each is necessary — remove one and it breaks:

Drop $Goal_{i}$ → no direction; you drift (undoing Step 4's promise).
Drop $Deliverable_{i}$ → "I'll learn CNNs" stays vague forever; nothing enters your portfolio.
Drop $Skills_{i}$ → you don't know which slice of the curve (Step 2) this phase targets.
Drop $Duration_{i}$ → the phase eats all your time (Parkinson's Law), starving later phases (Step 4).
Drop $Metric_{i}$ → you never know whether to move on; no feedback, so no course-correction.

PICTURE. One phase-block exploded into five labelled compartments, each tagged with the question it answers. This is precisely the parent note's tuple — now derived, not asserted.

Step 6 — The feedback loop: a roadmap is a hypothesis you update

WHAT. After each phase's metric fires, we do not blindly march on. We reflect: did the metric pass? Was $Duration_{i}$ realistic? Did the phase reveal a new high-value skill (moving the curve of Step 2)? Based on this, we edit the remaining phases. This is the arrow that loops back.

WHY a loop and not a straight line? Because $v (s)$ from Step 2 is only an estimate. Learning changes what you value: reproducing a paper might reveal you love alignment questions, or that federated learning is harder than you scored it. A straight plan can't absorb that; a loop can. The roadmap is a hypothesis about your learning path that you update with evidence — exactly the parent's phrase, now shown as a control loop.

PICTURE. A cycle: Plan phase → Execute → Measure metric → Reflect → adjust the next phases → back to Plan. The reflect arrow bends backward, and re-weights the value curve for the phases still ahead.

Step 7 — Degenerate and edge cases (never hit a scenario we didn't show)

WHAT & WHY. We stress-test the formula at its boundaries so no situation surprises you.

$T$ very small (a busy month, $T \approx 4$ ): then $N = 1$ . One phase, one deliverable, one metric. The structure doesn't break — it collapses to a single well-scoped project. Still better than an unstructured to-do list.
A phase's metric returns False: the loop (Step 6) does not mark it complete. You either extend $Duration_{i}$ (borrowing weeks from a later, lower-priority phase) or shrink the goal. The bar $T$ stays fixed; something else must give.
You discover a skill with huge $v (s)$ mid-year (e.g., an open problem catches fire): the reflect step reorders the remaining phases so this steep-left skill jumps forward. This is the loop earning its keep.
Value ties / equal-priority skills: when $v / t$ ratios tie, break ties by the prerequisite depth defined in Step 4 — learn the shallower (enabler) skill first, so every arrow of the prerequisite graph still points forward. E.g., learn a base model before studying its fairness properties.

PICTURE. The same bar under three regimes — tiny $T$ , a failed metric forcing a reflow, and a mid-year high-value insertion — side by side, so the shape's behaviour at the edges is visible at a glance.

The one-picture summary

Everything above compresses into a single diagram: a finite bar (Step 1) cut into ordered phases (Step 4), each phase a five-field block (Step 5) selected off the steep left of the value curve over the finite shortlist (Steps 2–3), with a feedback loop (Step 6) that re-weights the curve after every phase — robust even at the edges (Step 7).

Recall Feynman retelling — say it like you'd tell a friend

You've got a short ruler and an endless mountain. First honest move: admit the ruler is short and the mountain never ends (Step 1). But you can't do percentages on an endless mountain, so you first fence off a big-but-finite shortlist of skills that are even plausibly relevant (Step 2). Second honest move: notice the shortlist isn't uniform — a few skills near the front are worth almost everything, the rest of the climb barely adds anything (Step 2, the 80/20 curve). So you pack your short ruler with the tall-narrow, best-bang-per-week skills, and let the rest fall off the edge on purpose — knowing this "biggest ratio first" trick is a smart draft, not a guaranteed-best pack, because skills are all-or-nothing (Step 3). Because you can't learn attention after extending a Transformer, you cut your ruler into ordered chunks called phases, ordered so every prerequisite arrow points forward (Step 4). A bare chunk is useless, so you stamp five labels on each: why (Goal), what to show (Deliverable), what to practise (Skills), how long (Duration), and how you'll know you're done (Metric) — drop any one and it breaks (Step 5). After each chunk you stop, check the metric, and rewrite the chunks you haven't done yet, because doing the work changed what you think is valuable — that's the loop that makes a roadmap a living hypothesis, not a stone tablet (Step 6). And it still works when time is tiny, when a metric fails, or when a shiny new must-learn appears mid-year (Step 7). That whole story is the parent's formula $Phase_{i} = (Goal, Deliverable, Skills, Duration, Metric)$ — now you know exactly why every piece is there.

Recall

Why must a roadmap have a feedback loop and not be a straight line? ::: Because the value $v (s)$ of each skill is only an estimate; doing the work changes what you value, so you must periodically re-weight and reorder the remaining phases with the new evidence. What does the width vs height of a skill-box mean in the packing picture? ::: Width = time cost $t (s)$ in weeks; height = value $v (s)$ ; you prefer tall-narrow boxes (high $v / t$ ) until the fixed bar $T$ is full. If a phase's Metric returns False, what stays fixed and what must give? ::: The total bar $T$ stays fixed; you either extend that phase's Duration by borrowing weeks from a later lower-priority phase, or shrink the goal.