Evaluation

Input	Output
Suppose we have a training set with m=3 examples,plotted below.Our hypothes is representation is $h_{\theta}(x) = \theta_1x$ , with parameter $\theta_1$ . The cost function $J(\theta_1)$ is $J(\theta_1)$ = ${1\over2m}\sum\nolimits_{i=1}^m(h_\theta(x^i) - y^i)^2$ . What is $J(0)$ ?<image 1> (A) 0 (B) 1/6 (C) 1 (D) 14/6 Answer with the option's letter from the given choices directly. No punctuation.	Google: Gemini Pro Vision 1.0 mmmu / Computer_SciencePublic (A) Difficulty: Medium Subfield: Artificial Intelligence

Input

Output

Suppose we have a training set with m=3 examples,plotted below.Our hypothes is representation is $h_{\theta}(x) = \theta_1x$ , with parameter $\theta_1$ . The cost function $J(\theta_1)$ is $J(\theta_1)$ = ${1\over2m}\sum\nolimits_{i=1}^m(h_\theta(x^i) - y^i)^2$ . What is $J(0)$ ?<image 1>

(A) 0

(B) 1/6

(D) 14/6

Answer with the option's letter from the given choices directly. No punctuation.

Google: Gemini Pro Vision 1.0

mmmu / Computer_SciencePublic

(A)

Difficulty: Medium

Subfield: Artificial Intelligence

Evaluation ID: d40f6ce8-3486-4d63-9210-799a1e816aba
Created: February 21, 2024

Raw Output

{
  "id": "gen-YrHbApIlwAYAjdNnCje2M1rn2ZkI",
  "model": "google/gemini-pro-vision",
  "choices": [
    {
      "message": {
        "role": "assistant",
        "content": " (A)"
      },
      "finish_reason": "STOP"
    }
  ],
  "object": "chat.completion",
  "created": 1708555915,
  "usage": {
    "prompt_tokens": 1644,
    "completion_tokens": 12,
    "total_tokens": 1656
  }
}