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Lumi

Lumi Research

The science of learning, encoded

The models behind Lumi's practice engine, explained: Item Response Theory for ability, FSRS for revision timing, and knowledge tracing concept by concept.

Item response · 2PL
00.51-4-2θ 0+2+4EASYMEDIUMHARD

Easy

P 0.83

Medium

P 0.65

Hard

P 0.20

+0.5

P(correct) = σ(a(θ − b)) for three items. Drag θ: the hard, sharply discriminating item moves from near 0 to near 1 over a narrow band of ability.

Whitepapers

Featured publications

Deep dives into the mathematical models driving the platform, with the maths written out and the figures drawn from the engine's own code.

  1. Whitepaper 012PL IRT

    Predictive Validity using Item Response Theory (IRT)

    Classical Test Theory treats all questions equally. How Lumi implements a two-parameter logistic (2PL) model to estimate latent ability from which questions a student answers, not just how many.

    Read paper

  2. Whitepaper 02FSRS

    Modeling Memory Decay with FSRS

    Memory fades on a predictable curve. How the Free Spaced Repetition Scheduler (FSRS) tracks each card's stability and books the review for the day recall would fall to 90%.

    Read paper

Methodology

Transparent algorithms

Our engineering and academic teams publish how the models work, so the platform can be held to its maths rather than its marketing.

01

Data Integrity
Every answer a student submits is validated before it updates their ability estimate, their revision schedule and the difficulty of the questions they see next.

02

Empirical Validation
Item difficulty and discrimination are calibrated incrementally from real student answers, for NEET and JEE alike, so the parameters track the students actually using Lumi.

03

Privacy-Preserving ML
We use isolated vector embeddings for clustering (K-Means) without compromising PII. Insights are generated while strictly maintaining user anonymity.

The plain-language version of both papers, with the live figures.

How Lumi works