fix: correct role of the beta hyperparameter on the DPO loss

Increasing beta leads to less divergence between the new model and the reference model.

Author: andreas-yin

ch07/04_preference-tuning-with-dpo/dpo-from-scratch.ipynb

@@ -156,8 +156,8 @@
     "- In the equation above,\n",
     "  - \"expected value\" $\\mathbb{E}$ is statistics jargon and stands for the average or mean value of the random variable (the expression inside the brackets); optimizing $-\\mathbb{E}$ aligns the model better with user preferences\n",
     "  - The $\\pi_{\\theta}$ variable is the so-called policy (a term borrowed from reinforcement learning) and represents the LLM we want to optimize; $\\pi_{ref}$ is a reference LLM, which is typically the original LLM before optimization (at the beginning of the training, $\\pi_{\\theta}$ and $\\pi_{ref}$ are typically the same)\n",
-    "  - $\\beta$ is a hyperparameter to control the divergence between the $\\pi_{\\theta}$ and the reference model; increasing $\\beta$ increases the impact of the difference between\n",
-    "$\\pi_{\\theta}$ and $\\pi_{ref}$ in terms of their log probabilities on the overall loss function, thereby increasing the divergence between the two models\n",
+    "  - $\\beta$ is a hyperparameter to control the divergence between the $\\pi_{\\theta}$ and the reference model; increasing $\\beta$ reduces the impact of the difference between\n",
+    "$\\pi_{\\theta}$ and $\\pi_{ref}$ in terms of their log probabilities on the overall loss function, thereby decreasing the divergence between the two models\n",
     "  - the logistic sigmoid function, $\\sigma(\\centerdot)$ transforms the log-odds of the preferred and rejected responses (the terms inside the logistic sigmoid function) into a probability score \n",
     "- To avoid bloating the code notebook with a more detailed discussion, I may write a separate standalone article with more details on these concepts in the future\n",
     "- In the meantime, if you are interested in comparing RLHF and DPO, please see the section [2.2. RLHF vs Direct Preference Optimization (DPO)](https://magazine.sebastianraschka.com/i/142924793/rlhf-vs-direct-preference-optimization-dpo) in my article [Tips for LLM Pretraining and Evaluating Reward Models](https://magazine.sebastianraschka.com/p/tips-for-llm-pretraining-and-evaluating-rms)"