Demo learner profile

A seeded learner is ready for the Hoeffding bridge.

This page uses fixed demo evidence, not a real account. It shows the product loop we want to record: evidence creates a capability checkpoint, the checkpoint suggests the next goal, and the next goal opens the matching gold diagnostic set.

Start targeted diagnostic View proof evidence View simulation run

Seeded scenario

Foundations passed

The demo learner has enough probability and Markov/union-bound evidence to move forward.

Next checkpoint chosen

Sub-Gaussian to Hoeffding bridge

No production data

The state is deterministic and safe for demos, screenshots, and walkthroughs.

Capability path

Evidence toward Concentration Builder

builder

Use event algebra, moments, tail assumptions, and finite union bounds to decide when a finite-class generalization claim is properly scoped. This panel shows the recorded evidence, the next checkpoint, and what remains blocked by missing content or weak mastery evidence.

checkpoints

2/4

topic evidence

content gaps

Suggested next goal

Next checkpoint toward Concentration Builder

continue

2/4 checkpoints complete; next checkpoint is Sub-Gaussian to Hoeffding bridge.

Checkpoint

Sub-Gaussian to Hoeffding bridge

0/2 topic signals; 1/10 diagnostic questions; 0 content gaps

Diagnostic link

Probability and concentration bridge

Start targeted diagnostic Study Sub-Gaussian Random Variables

Checkpoint evidence trail

Next action: Sub-Gaussian to Hoeffding bridge.

2/4

✓

Event algebra

Probability event algebra and moments

complete

0/2 topic signals; 7/10 diagnostic questions; 0 content gaps

A short worked note deriving complement, union, expectation, and variance facts from probability assumptions.

✓

Tail setup

Markov and union-bound tail setup

complete

0/2 topic signals; 7/10 diagnostic questions; 0 content gaps

A solved diagnostic set showing when Markov and union bounds apply and when they do not.

Hoeffding bridge

Sub-Gaussian to Hoeffding bridge

nextin progress

0/2 topic signals; 1/10 diagnostic questions; 0 content gaps

A compact derivation note or diagnostic review connecting sub-Gaussian MGF assumptions to Hoeffding-style tails.

Finite-class readiness

Finite-class uniform-convergence readiness

in progress

0/3 topic signals; 1/10 diagnostic questions; 0 content gaps

A finite-class generalization checklist that names the bounded-loss, sample-size, and union-bound assumptions.

Project unlocks

Build an event-risk checklist that separates probability algebra from tail assumptions.

Estimate finite-class sample-size requirements from Hoeffding-style bounds.

Audit whether an ERM or uniform-convergence claim has the bounded-loss and union-bound scope it needs.

Next checkpoint

Sub-Gaussian to Hoeffding bridge

in progress

2/4 checkpoints complete; next checkpoint is Sub-Gaussian to Hoeffding bridge.

Evidence required

Recognize the MGF assumption that makes a random variable sub-Gaussian.
Explain why bounded or sub-Gaussian terms support Hoeffding-style finite-sum control.

0/2 topic signals; 1/10 diagnostic questions; 0 content gaps · mixed

Gold diagnostic

Probability / concentration bridge gold set v1

1/10 correct · 1 answered · more evidence needed

Open diagnostic

Evidence already seen

No checkpoint topics have strong evidence yet.

Still needed

Sub-Gaussian Random Variables
Concentration Inequalities

Study Sub-Gaussian Random Variables

Capability badges are internal learning checkpoints for now. They are not public credentials and do not imply source or Lean verification of every related claim.

Other tracked capability paths

Tiny MLP Builder

Next checkpoint: Linear-layer and activation shape fluency.

Tiny LM Builder

Next checkpoint: Bigram baseline on a toy corpus.