Interactive method visualization

Explore MisKT's four
hyperparameters.

Interact with misconception association τmis, conditional wrong-answer temperature τans, prototype count M, and CWP loss weight λ. Mathematical illustrations only—no model retraining or real student data.

Temperature controls

Choose exact values or drag the sliders. Paper default: 0.10 for both parameters.

Misconception associations
τmis
0.10
0 (limit)2.00
Conditional wrong-answer prediction
τans
0.10
0 (limit)2.00
Important: In MisKT, temperature parameters must satisfy τ > 0. The selectable value 0 is shown only as the mathematical limit τ → 0⁺ (hard argmax, equal shares if tied); it is not a valid setting for the paper's training equations.
Stage 01 · Semantic associations

Wrong answer → misconception prototypes

Temperature controls how strongly a wrong answer is associated with the most similar shared prototypes.

αq,a,j = softmaxj(cos(dq,a, pj) / τmis)
Inspect wrong answer:
Highest association
Prototype 1
Distribution entropy
—
Stage 02 · Personalized choices

Student state → wrong-answer probabilities

Candidate scores depend on the student misconception state and answer associations; τans controls the final probability sharpness.

s(a) = m⊤αq,a   ;   p(a | r = 0) = softmaxa(s(a) / τans)
Top predicted wrong answer
Answer A
Top-1 probability
—

The scores above are m⊤αq,a before the τans Softmax. Changing τmis also changes these scores.

Architecture & objective

Beyond temperatures

Adjust the prototype-space capacity or the joint-loss weighting. These controls illustrate structure and objective terms, not predictions of retrained-model accuracy.

MODEL DESIGN · TWO MORE CONTROLS
Control 03 · Shared prototype space

Number of misconception prototypes

M sets the number of shared prototype vectors and dimensions in each student's misconception state.

50
1050 · paper default100
Shared prototype space50 prototypes
Prototype matrix P · 768 × M
38,400Trainable elements in P
Student misconception state
50Activation dimensions

Changing M changes the model architecture and requires retraining. The five-prototype temperature example above is kept fixed for clarity.

Control 04 · Joint optimization

CWP loss weight

λ balances the correctness and CWP objectives during training; it does not directly rescale inference probabilities.

0.30
0.000.30 · paper default1.00
L = Lkt + λLcwp

Fixed illustrative losses: Lkt = 0.50 and Lcwp = 0.80

0.50 + 0.30 × 0.80= 0.740
KT term 67.6%
Weighted CWP term 32.4%

The percentages show shares of this illustrative scalar loss, not shares of gradient magnitude or measured training performance.

What τmis changes

It sharpens or smooths the prototype associations of every candidate wrong answer. Since those associations enter both misconception-state updates and wrong-answer matching, changing τmis can also change candidate scores and rankings.

What τans changes

At fixed trained scores, a positive τans changes probability sharpness without changing candidate rankings. During model training, however, τans affects the loss gradients and may change the learned scores.