Update README.md

README.md

@@ -30,6 +30,66 @@ The Alpaca dataset is a set of 52k instruct-response pairs designed to enhace th
 The GALACTICA model card specifies that the primary indended users of the GALACTICA models are researchers studying language models applied to the scientific domain, and it cautions against production use of GALACTICA without safeguards due to the potential for the model to produce inaccurate information.
 The original GALACTICA models are available under a non-commercial CC BY-NC 4.0 license, and the GALPACA model is additionally subject to the [OpenAI Terms of Service](https://openai.com/policies/terms-of-use).
 
+<details>
+  <summary> Example Outputs </summary>
+  
+*__Full Prompt:__*
+```
+Below is an instruction that describes a task. As a scientist, write a response that appropriately completes the request, citing specific papers whenever possible.
+
+### Instruction:
+Write out Maxwell's equations and explain each one.
+
+### Markdown and LaTeX Response:
+```
+
+*__Response:__*
+
+Maxwell's equations are a set of four equations that describe the behavior of electromagnetic fields. These equations are:
+$$\nabla \times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}$$
+$$\nabla \times \textbf{B} = \mu_0 \epsilon_0 \frac{\partial \textbf{E}}{\partial t} + \mu_0 \textbf{J}$$
+$$\nabla \bullet \textbf{E} = \frac{\rho}{\epsilon_0}$$
+$$\nabla \bullet \textbf{B} = 0$$
+The first two equations describe how the electric and magnetic fields, E and B, are related to each other. The third and fourth equations are Gauss's law for electric and magnetic fields, respectively. These equations describe the behavior of the electric and magnetic fields when there are charges and currents in the space. Each equation has a specific purpose and together they form a complete description of the behavior of electromagnetic fields.
+
+*__Full Prompt:__*
+```
+Below is an instruction that describes a task. Write a response that appropriately completes the request.
+
+### Instruction:
+Write a python function implements the Sherman-Morrison matrix inversion lemma using numpy.
+
+### Response:
+```python
+```
+
+*__Response:__*
+```python
+def sm_inv_lemma(A, u, v):
+  """ Function implementing the Sherman-Morrison matrix inversion lemma using numpy.
+  
+  Parameters
+  ----------
+  A : numpy array
+      The original matrix.
+  
+  u : numpy array
+      The first vector in the Sherman-Morrison lemma.
+  
+  v : numpy array
+      The second vector in the Sherman-Morrison lemma.
+  
+  Returns
+  -------
+  The inverse matrix of A - uv^T.
+  """
+  A_inv = np.linalg.inv(A)
+  alpha = 1 / (1 + v.T @ A_inv @ u)
+  return A_inv - (alpha * A_inv @ u @ v.T @ A_inv)
+```
+
+</details>
+
 ## Training Data
 
 The GALPACA models are trained by fine-tuning pre-trained GALACTICA models on the Alpaca dataset. GALACTICA models were trained on 106 billion tokens of open-access scientific text and data, including papers, textbooks, scientific websites, encyclopedias, and more.
@@ -65,11 +125,11 @@ print(tokenizer.batch_decode(out_tokens, skip_special_tokens=False, clean_up_tok
 
 ## Training Resources
 
-GALPACA 30B was fine-tuned in about 6 hours using 16 A100 80GB GPUS, 16-bit mixed-precision, an effective batch-size of 1024, and with a maximum context window of 384 tokens. This model was trained using DeepSpeed Stage 3 optimizations.
+GALPACA 30B was fine-tuned in about 6 hours using 16 A100 80GB GPUS, 16-bit mixed-precision, an effective batch-size of 1024, and with a maximum context window of 384 tokens. This model was trained using DeepSpeed ZeRO Stage 3 optimizations.
 
 ## Performance and Limitations
 
-More information about the performance and limitations of this family of models can be found on the original GALACTICA model card.
+Qualitative evaluation suggests that Galpaca frequently outperforms LLaMA-based Alpaca models on tasks related to technical knowledge and programming, while it underperforms on natural langauge tasks such as generating prose. More information about the performance and limitations of the GALACTICA family of models can be found on the original GALACTICA model card.
 
 ## Works Cited