Step 1: User Input

The user submits a question to the SLM-MUX system

Question: Which of the following physical theories never requires regularization at high energies?
(A) Superstring Theory
(B) Classical Electrodynamics
(C) Quantum Electrodynamics (QED)
(D) Quantum Chromodynamics (QCD)
Correct Answer: (A)
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Step 2: Query Multiple SLMs

The question is sent to 3 different SLMs. Each SLM generates 3 independent responses.

SLM 1

Output 1: ... the final answer is (A) ✔
Output 2: ... the final answer is (A) ✔
Output 3: ... therefor the correct answer is (B) ✖

SLM 2

Output 1: ... the final answer is (A) ✔
Output 2: ... the correct choice is (B) ✖
Output 3: ... I think the best answer is (B) ✖

SLM 3

Output 1: ... the final answer is (A) ✔
Output 2: ... the correct choice is (B) ✖
Output 3: ... I think the best answer is (C) ✖
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Step 3: Calculate Confidence Scores

Confidence is calculated by counting how many times each SLM gives the same answer.
SLM 1: 2/3 answers are (A) → 67% confidence
SLM 2: 2/3 answers are (B) → 67% confidence
SLM 3: Only 1/3 answers match → 33% confidence

SLM 1 SLM 2 SLM 3
Confidence 67% ✔ 67% ✔ 33% ✖
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Step 4: Tie-Breaker with Validation Accuracy

SLM 1 and SLM 2 both have 67% confidence (tie!).
We use Validation Accuracy as a tie-breaker: SLM 1 has higher validation accuracy.

SLM 1 SLM 2 SLM 3
Confidence 67% ✔ 67% ✔ 33% ✖
Validation Accuracy High ✔ Low ✖ Low ✖
Winner: SLM 1 is selected due to higher validation accuracy
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Step 5: Final Answer

The system outputs the most frequent answer from the selected SLM (SLM 1)

Final Answer

(A) Superstring Theory
Selected from SLM 1