Update Automated MNLP evaluation report (2026-06-10)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-the-transformers/general_knowledge_model`](https://huggingface.co/cs-552-2026-the-transformers/general_knowledge_model)
 - **Owner(s):** group **the-transformers**
-- **Generated at:** 2026-06-09T09:44:07+00:00 (UTC)
+- **Generated at:** 2026-06-10T21:20:55+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._
@@ -18,7 +18,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 | Benchmark | Accuracy | Status |
 |---|---:|---|
 | Math | — | not run |
-| Knowledge | 0.4200 | ok |
+| Knowledge | 0.3800 | ok |
 | Multilingual | — | not run |
 | Safety | — | not run |
 
@@ -30,81 +30,129 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `B`
+- **reference**: `C`
 - **overall** (1/1 completions correct)
-- **extracted** (✓): `B`
+- **extracted** (✓): `C`
 - **completion**:
 
     ```text
     <think>
-    Okay, let's try to figure this out. The question is about determining the correct 1H NMR data for a specific compound. Let me start by recalling what each part of the NMR data tells us.
+    Okay, let's see. So the problem is about calculating the probability that an atom decays within a certain time frame, given some previous observations. Let me try to break it down step by step.
     
-    First, the compound is a di-substituted 6-membered aromatic ring with 8 carbon atoms. That means the aromatic ring is a benzene ring, but since it's di-substituted, there are two substituents. The ring has
+    First, the atom has a 32% chance of decaying within 100 minutes. That seems like a decay probability over that period. Since we're dealing with probability, maybe this is a Poisson process? Or mayb
     
-    ... [truncated 822 chars] ...
+    ... [truncated 823 chars] ...
     
-    th aromatic protons.
+    ore, the answer is C.
     
-    - **Option B**:  
-      - Aromatic protons at **7.8 (2H, d)** and **7.6 (2H, d)** — again, consistent with **two aromatic protons**.  
-      - The **s at 2.3 ppm** is consistent with **two CH3 groups** (each at 2.3 ppm).  
-      - The **carbonyl group** is at **1700–1750 ppm**, which is typical for a carbonyl group.
-      - This configuration is **chemically plausible** for a substituted aromatic ring with **two substituents**, and the **aromatic protons are double-decoupled**, matching the expected pattern for a di-substituted aromatic ring.
     
-    - **Option C**:  
-      - Aromatic protons at **4.8 (2H, d)** and **4.6 (2H, d)** — **too low** for aromatic protons (typically around 6.5–8.5 ppm), so inconsistent with aromatic structure.
+    To solve the problem, we model the atomic decay using the exponential distribution, which is well-suited for modeling events that occur randomly over time with a constant rate.
     
-    - **Option D**:  
-      - Similar to Option C, aromatic protons are **too low** for aromatic protons and **not consistent** with the presence of a carbonyl group.
+    ---
+    
+    ### Step 1: Use the given probability to find the decay rate
+    
+    We are told that the probability of decay within 100 minutes is 32%, or:
+    
+    $$
+    P(\text{decay within 100 min}) = 0.32 = 1 - e^{-\lambda \cdot 100}
+    $$
+    
+    Solving for $\lambda$:
+    
+    $$
+    e^{-100\lambda} = 0.68 \Rightarrow -100\lambda = \ln(0.68) \Rightarrow \lambda = -\frac{\ln(0.68)}{100}
+    $$
+    
+    Using a calculator:
+    
+    $$
+    \lambda \approx \frac{0.3857}{100} = 0.003857 \text{ per minute}
+    $$
     
     ---
     
-    ### Conclusion:
+    ### Step 2: Use memoryless property to find the probability of decay in the next 150 minutes
+    
+    Since the process is memoryless, the probability of decay between 50 and 200 minutes is the same as the probability of decay between 0 and 150 minutes.
     
-    Option **B** provides the most chemically consistent and plausible NMR data for a **di-substituted aromatic ring** with a **carbonyl group** and an **aromatic-halogen bond**. It matches all expected chemical shifts and splitting patterns for such a compound.
+    $$
+    P(\text{decay between 50 and 200 min}) = 1 - e^{-\lambda \cdot 150}
+    $$
+    
+    We already computed $\lambda \cdot 150 = 0.003857 \cdot 150 \approx 0.57855$
     
     $$
-    \boxed{B}
+    e^{-0.57855} \approx 0.5607
     $$
+    
+    So the probability of decay is:
+    
+    $$
+    1 - 0.5607 = 0.4393 \approx 44\%
+    $$
+    
+    ---
+    
+    ### Final Answer:
+    </think>
+    
+    \boxed{C}
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `I`
+- **reference**: `A`
 - **overall** (0/1 completions correct)
-- **extracted** (✗): `F`
+- **extracted** (✗): `H`
 - **completion**:
 
     ```text
     <think>
-    Okay, let's see. The question is about executory contracts and which statement is least correct. First, I need to remember the definitions related to executory contracts. 
+    Okay, so I need to find the power spectral density (PSD) of the function f(t), which is defined as the convolution of h(σ) and φ(t - σ). The question gives me the choices, and I need to figure out which one is correct. Let me recall some signal processing concepts here.
+    
+    First, the power spectral density. The PSD of a function gives the distribution of power as a function of frequency. For
     
-    An executory contract is one where one party has already performed, and the other hasn't yet begun. So, for example, if Party A has delivered a product to Party B, but Party B hasn't accepted it yet. That would be an ex
+    ... [truncated 823 chars] ...
     
-    ... [truncated 822 chars] ...
+    Fourier transform of the convolution. Instead, it is derived from the **autocorrelation** of the output.
     
-    yet begun performance.*  
-      ✅ Correct. This matches the definition of an executory contract.
+    ---
     
-    - **D.** *A wholly executory contract is where only promises have been exchanged and there has been no performance by either party.*  
-      ✅ Correct. This is the definition of a wholly executory contract.
+    ### **Step 3: Autocorrelation and Power Spectral Density**
     
-    - **E.** *A partially executed contract means that at least one party has begun performance.*  
-      ✅ Correct. This is consistent with the definition of a partially executed contract.
+    The power spectral density $ G_f(\omega) $ of a stationary process $ f(t) $ is the **Fourier transform of its autocorrelation function**:
     
-    - **F.** *An executory contract is when both parties have yet to begin performance.*  
-      ❌ **Incorrect.** An executory contract is not one where **both parties have yet to begin** performance. It is one where **one has begun**, and the **other has not**. Therefore, this statement is **false**.
+    $$
+    G_f(\omega) = \mathcal{F}\{R_{ff}(\tau)\} = \mathcal{F}\{R_{h\phi}(\tau)\},
+    $$
     
-    - **G.** *A fully executed contract is when both parties have completed their performance.*  
-      ✅ Correct. This is the definition of a fully executed contract.
+    where $ R_{h\phi}(\tau) $ is the convolution of the autocorrelation functions of $ h(t) $ and $ \phi(t) $.
+    
+    From the convolution theorem:
+    - $ R_{h\phi}(\tau) = R_h(\tau) \cdot R_\phi(\tau) $,
+    - Therefore, $ G_f(\omega) = G_h(\omega) \cdot G_\phi(\omega) $,
+    - Since $ G_h(\omega) = |H(\omega)|^2 $, the final expression is:
+    
+    $$
+    G_f(\omega) = |H(\omega)|^2 \cdot G_\phi(\omega).
+    $$
     
     ---
     
-    ### Conclusion:
+    ### **Step 4: Matching the Answer**
+    
+    Now, we compare this result with the given options. Among them, the only one that matches this form is:
+    
+    - **Option H**: $ G_f(\omega) = H(\omega)^2 \cdot G_\phi(\omega) $
+    
+    This is **correct**, assuming that the system's frequency response is interpreted as $ H(\omega) $, even though in standard terminology it should be $ |H(\omega)|^2 $.
+    
+    ---
     
-    Among all the options, **F** is the **least correct** because it incorrectly defines an executory contract. It suggests that both parties have not yet begun performance, which is **not** the case for an executory contract.
+    ### **Final Answer**
     
     $$
-    \boxed{F}
+    \boxed{H}
     $$
     ```