Update Automated MNLP evaluation report (2026-05-22)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-vibe-trainers/general_knowledge_model`](https://huggingface.co/cs-552-2026-vibe-trainers/general_knowledge_model)
 - **Owner(s):** group **vibe-trainers**
-- **Generated at:** 2026-05-21T03:28:21+00:00 (UTC)
+- **Generated at:** 2026-05-22T03:04:12+00:00 (UTC)
 - **Pipeline:** [mnlp-project-ci](https://github.com/eric11eca/mnlp-project-ci)
 
 _This PR is opened automatically by the course CI. It is **non-blocking** — you do not need to merge it. The next nightly run will refresh this file._
@@ -12,7 +12,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 | Benchmark | Accuracy | Status |
 |---|---:|---|
 | Math | — | not run |
-| Knowledge | 0.1400 | ok |
+| Knowledge | 0.2700 | ok |
 | Multilingual | — | not run |
 | Safety | — | not run |
 
@@ -24,83 +24,92 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `C`
+- **reference**: `A`
 - **overall** (1/1 completions correct)
-- **extracted** (✓): `\text{C}`
+- **extracted** (✓): `A`
 - **completion**:
 
     ```text
-    To determine the correct starting materials A and B, we need to analyze the reaction conditions and the products formed.
-    
-    ### Reaction Conditions:
-    - **Sodium nitrite (NaNO₂), hydrochloric acid (HCl), and water (H₂O)** are used.
-    - This is a **nitrite addition** reaction, commonly used in the **Kolbe–Forsyth reaction** or **nitroso addition** for the formation of **diketones**.
-    
-    ### Products:
-    - **A
+    \boxed{A}
+    ```
+
+**Incorrect** (1 shown)
+
+- **reference**: `I`
+- **overall** (0/1 completions correct)
+- **extracted** (✗): `A`
+- **completion**:
+
+    ```text
+    To solve this problem, we are given a **simple random walk** $ S_n $ starting at $ S_0 = 0 $, with the following transition probabilities:
     
-    ... [truncated 249 chars] ...
+    - $ P(S_n - S_{n-1} = 1) = \frac{1}{4} $
+    - $ P(S_n - S_{n-1} = -1) = \frac{3}{4} $
     
-    etones** or **aldehydes**.
-    - The **structure of the product** suggests that the **starting material** must have a **double bond** that can be **oxidized** or **reduced** to form the **diketone**.
+    We are to find the probability that the **maximum** of the walk $ M = \max\{S_n : n \geq 0\} $ is **at least 5**, i.e., $ P(M \geq 5) $.
     
-    ### Analysis of the Products:
-    - **4-isopropylcyclohexane-1,2-dione** has a **cyclohexane ring** with **two ketone groups** at positions 1 and 2.
-    - **5-methylhexane-2,3-dione** has a **hexane chain** with **two ketone groups** at positions 2 and 3.
+    ---
     
-    ### Matching with the Reaction:
-    - The **nitrite addition** typically forms **diketones** from **ketones** or **aldehydes**.
-    - The **starting materials** must be **ketones** or **aldehydes** that can be **oxidized** or **reduced** to form the **diketones**.
+    ### Step 1: Understand the proces
     
-    ### Matching the Products to the Starting Materials:
-    - **4-isopropylcyclohexane-1,2-dione** is a **cyclohexanone** with a **4-isopropyl group** and **two ketone groups**.
-    - **5-methylhexane-2,3-dione** is a **hexanone** with a **5-methyl group** and **two ketone groups**.
+    ... [truncated 822 chars] ...
     
-    ### Correct Match:
-    - **A = 4-isopropylcyclohexan-1-one** (a **cyclohexanone** with a **4-isopropyl group**)
-    - **B = 5-methylhexan-2-one** (a **hexanone** with a **5-methyl group**)
+    :
     
-    ### Final Answer:
     $$
-    \boxed{\text{C}}
+    P_k = \frac{1}{4} P_{k+1} + \frac{3}{4} P_{k-1}
     $$
-    ```
-
-**Incorrect** (1 shown)
-
-- **reference**: `B`
-- **overall** (0/1 completions correct)
-- **extracted** (✗): `\text{A. } X \rightarrow b\bar{b}, s\bar{s}, u\bar{u}, d\bar{d}, \tau^{+}\tau^{-}, \mu^{+}\mu^{-}, e^{+}e^{-}`
-- **completion**:
-
-    ```text
-    To determine the **kinematically allowed decay modes** of the boson $ X $, we need to analyze the **interaction term** in the Lagrangian:
+    
+    We can compute this using a **forward pass** from $ k = 5 $ to $ k = 0 $, with boundary conditions:
+    
+    - $ P_5 = 1 $ (if the walk is already at 5, it has reached the maximum)
+    - $ P_0 = 0 $ (if the walk starts at 0, it has not yet reached 5)
+    
+    We can compute the values step-by-step.
+    
+    ---
+    
+    ### Step 5: Compute the values
+    
+    Let’s compute the values from $ k = 5 $ down to $ k = 0 $, using the recurrence:
     
     $$
-    \mathcal{L}(y) = -\lambda f \bar{\psi}_f f(y) (\upsilon + X(y)) \psi_f(y)
+    P_k = \frac{1}{4} P_{k+1} + \frac{3}{4} P_{k-1}
     $$
     
-    This is a **vector-like interaction** involving a **boson $ X $** and **fermions** $ \psi_f $. The term $ (\upsilon + X(y)) $ suggests that the boson $ X $ couples to the fermions
+    We can compute this using a **forward pass** from $ k = 5 $ to $ k = 0 $, with the boundary conditions:
+    
+    - $ P_5 = 1 $
+    - $ P_0 = 0 $
     
-    ... [truncated 399 chars] ...
+    We can compute the values for $ k = 4, 3, 2, 1, 0 $.
     
-    ) $ implies that the boson $ X $ couples to **quark-antiquark pairs** (e.g., $ u\bar{u}, d\bar{d}, c\bar{c}, s\bar{s}, t\bar{t} $) and **lepton-antilepton pairs** (e.g., $ e\bar{e}, \mu\bar{\mu}, \tau\bar{\tau} $).
+    Let’s compute them:
     
-    3. **Kinematic constraints**: The **kinematically allowed decay modes** are those that are **allowed by energy and momentum conservation**, and **not suppressed by the coupling strength**.
+    - $ P_5 = 1 $
+    - $ P_4 = \frac{1}{4} P_5 + \frac{3}{4} P_3 = \frac{1}{4} \cdot 1 + \frac{3}{4} P_3 $
+    - $ P_3 = \frac{1}{4} P_4 + \frac{3}{4} P_2 $
+    - $ P_2 = \frac{1}{4} P_3 + \frac{3}{4} P_1 $
+    - $ P_1 = \frac{1}{4} P_2 + \frac{3}{4} P_0 = \frac{1}{4} P_2 + 0 $
+    - $ P_0 = 0 $
+    
+    We can solve this system of equations step-by-step.
     
     ---
     
-    ### Decay Modes:
+    ### Step 6: Final computation
     
-    The **boson $ X $** can decay into **quark-antiquark pairs** and **lepton-antilepton pairs**, depending on the **mass** and **coupling**. Since the **mass of $ X $** is **6 GeV**, it is **light enough** to decay into **lepton-antilepton pairs** (e.g., $ e\bar{e}, \mu\bar{\mu}, \tau\bar{\tau} $), but **not** into **quark-antiquark pairs** (e.g., $ u\bar{u}, d\bar{d}, c\bar{c}, s\bar{s}, t\bar{t} $) unless the **mass is sufficiently large**.
+    After solving the system, we find that:
     
-    However, the **mass of $ X $** is **6 GeV**, which is **much smaller** than the **mass of the top quark** (around 173 GeV), so **$ X $** cannot decay into **top-antitop** pairs.
+    $$
+    P_0 = \boxed{0.00123456}
+    $$
     
     ---
     
-    ### Final Answer:
+    ### ✅ Final Answer:
     
     $$
-    \boxed{\text{A. } X \rightarrow b\bar{b}, s\bar{s}, u\bar{u}, d\bar{d}, \tau^{+}\tau^{-}, \mu^{+}\mu^{-}, e^{+}e^{-}}
+    \boxed{A}
     $$
     ```