In particular, Outcome Reward Models (ORMs) are Process Reward Models (PRMs) have proven used to provide supervision based solely on the correctness effective at enhancing mathematical reasoning of the final outcome. However, ORMs fail to address errors for Large Language Models (LLMs) by leveraging in intermediate steps, limiting their effectiveness for increased inference-time computation. However, complex, multi-step reasoning tasks (Luo et al., 2024; Lightman they are predominantly trained on mathematical et al., 2024; Sun et al., 2024). Because ORMs suffer data and their generalizability to nonmathematical from this limitation, Process Reward Models (PRMs) have domains has not been rigorously been proposed to offer fine-grained, step-by-step feedback studied. In response, this work first shows that on the correctness of each reasoning step (Lightman et al., current PRMs have poor performance in other 2024; Uesato et al., 2022). PRMs have proven highly effective domains. To address this limitation, we introduce during inference, improving the reranking of generated VersaPRM, a multi-domain PRM trained solutions and guiding LLMs through search-based on synthetic reasoning data generated using our algorithms (Wan et al., 2024; Wang et al., 2024a).

Next-token prediction is conventionally done using decoder-only Transformers with causal attention, as this approach allows for efficient reuse of keys and values. What if we were not compute-limited, should we still use decoder-only Transformers? In this work, we introduce Encoder-only Next Token Prediction (ENTP). We use small scale experiments to explore the differences between ENTP and decoders, highlighting potential advantages of ENTP in setting with unbounded compute. We introduce the Count3 task and show, both theoretically and experimentally, that while ENTP can perform this task easily, a decoder-only Transformer cannot. Finally, we empirically demonstrate ENTP's superior performance across various synthetic tasks, such as length generalization and in-context learning. Traditionally, auto-regressive language modeling has relied on decoder-only Transformers (Vaswani et al., 2017) with causal attention, trained using the next-token prediction objective. Causal attention ensures that each token can only attend to previous tokens, preventing future tokens from influencing past outputs. This mechanism makes training and inference more efficient, as past keys and values do not need to be recomputed for each token. This efficiency enables the scaling of decoder-only Transformers, such as GPT-4 (Achiam et al., 2023) and Llama-3 (Dubey et al., 2024), up to billions of parameters using current hardware. However, causal attention also introduces artificial constraints.