Upload README.md

README.md

@@ -13,14 +13,14 @@ license: apache-2.0
 
 EurusPRM-Stage2 is trained using **[Implicit PRM](https://arxiv.org/abs/2412.01981)**, which obtains free process rewards at no additional cost but just needs to simply train an ORM on the cheaper response-level labels. During inference, implicit process rewards are obtained by forward passing and calculating the log-likelihood ratio on each step.
 
-<img src="./figs/implicit.png" alt="prm" style="zoom: 33%;" />
+<img src="./figures/implicit.png" alt="prm" style="zoom: 33%;" />
 
 The key ingredient of Implicit PRM is the reward representation, as demonstrated below:
 
 <aside>
-✨ 
-  
-***Proposition***: Consider an ORM where the reward is parameterized by the log-likelihood ratio of two causal LMs, i.e. $r_\phi(\mathbf{y}):= \beta \log \frac{\pi_\phi(\mathbf{y})}{\pi_\text{ref}(\mathbf{y})}$. Define $q_\phi^t(\mathbf{y}_{<t}, y_t):= \sum_{i=1}^{t} \beta \log \frac{\pi_\phi(y_{i}|\mathbf{y}_{<i})}{\pi_\text{ref}(y_{i}|\mathbf{y}_{<i})}$. $q_\theta^t$ is the exponential average of $r_\theta$ at step $t$.*
+✨
+
+***Proposition**: Consider an ORM where the reward is parameterized by the log-likelihood ratio of two causal LMs, i.e. $r_\phi(\mathbf{y}):= \beta \log \frac{\pi_\phi(\mathbf{y})}{\pi_\text{ref}(\mathbf{y})}$. Define $q_\phi^t(\mathbf{y}_{<t}, y_t):= \sum_{i=1}^{t} \beta \log \frac{\pi_\phi(y_{i}|\mathbf{y}_{<i})}{\pi_\text{ref}(y_{i}|\mathbf{y}_{<i})}$. $q_\theta^t$ is the exponential average of $r_\theta$ at step $t$.*
 
 $$
 q_\phi^t(\mathbf{y}_{<t}, y_t) = \beta \log \mathbb{E}_{\pi_\text{ref}(\mathbf{y}|\mathbf{y}_{\leq t})} e^{\frac{1}{\beta}r_\phi(\mathbf{y})}