The capabilities of large language models (LLMs) have been enhanced by training on data that reflects human thought processes, such as the Chain-of-Thought format. However, evidence suggests that the conventional scheme of next-word prediction may not fully capture how humans learn to think. Inspired by how humans generalize mathematical reasoning, we propose a new approach named ClozeMath to fine-tune LLMs for mathematical reasoning. Our ClozeMath involves a text-infilling task that predicts masked equations from a given solution, analogous to cloze exercises used in human learning. Experiments on GSM8K, MATH, and GSM-Symbolic show that ClozeMath surpasses the strong baseline Masked Thought in performance and robustness, with two test-time scaling decoding algorithms, Beam Search and Chain-of-Thought decoding. Additionally, we conduct an ablation study to analyze the effects of various architectural and implementation choices on our approach.

While decoder-only large language models (LLMs) have shown impressive results, encoder-decoder models are still widely adopted in real-world applications for their inference efficiency and richer encoder representation. In this paper, we study a novel problem: adapting pretrained decoder-only LLMs to encoder-decoder, with the goal of leveraging the strengths of both approaches to achieve a more favorable quality-efficiency trade-off. We argue that adaptation not only enables inheriting the capability of decoder-only LLMs but also reduces the demand for computation compared to pretraining from scratch. We rigorously explore different pretraining objectives and parameter initialization/optimization techniques. Through extensive experiments based on Gemma 2 (2B and 9B) and a suite of newly pretrained mT5-sized models (up to 1.6B), we demonstrate the effectiveness of adaptation and the advantage of encoder-decoder LLMs. Under similar inference budget, encoder-decoder LLMs achieve comparable (often better) pretraining performance but substantially better finetuning performance than their decoder-only counterpart. For example, Gemma 2B-2B outperforms Gemma 2B by $\sim$7\% after instruction tuning. Encoder-decoder adaptation also allows for flexible combination of different-sized models, where Gemma 9B-2B significantly surpasses Gemma 2B-2B by $>$3\%. The adapted encoder representation also yields better results on SuperGLUE. We will release our checkpoints to facilitate future research.

In this paper, we focus on addressing the constraints faced when applying LLMs to ASR. Recent works utilize prefixLM-type models, which directly apply speech as a prefix to LLMs for ASR. We have found that optimizing speech prefixes leads to better ASR performance and propose applying RNNT loss to perform speech prefix-tuning. This is a simple approach and does not increase the model complexity or alter the inference pipeline. We also propose language-based soft prompting to further improve with frozen LLMs. Empirical analysis on realtime testset from 10 Indic languages demonstrate that our proposed speech prefix-tuning yields improvements with both frozen and fine-tuned LLMs. Our recognition results on an average of 10 Indics show that the proposed prefix-tuning with RNNT loss results in a 12\% relative improvement in WER over the baseline with a fine-tuned LLM. Our proposed approches with the frozen LLM leads to a 31\% relative improvement over basic soft-prompting prefixLM.

Recent empirical evidence indicates that transformer based in-context learning performs better when using a prefix language model (prefixLM), in which in-context samples can all attend to each other, compared to causal language models (causalLM), which use auto-regressive attention that prohibits in-context samples to attend to future samples. While this result is intuitive, it is not understood from a theoretical perspective. In this paper we take a theoretical approach and analyze the convergence behavior of prefixLM and causalLM under a certain parameter construction. Our analysis shows that both LM types converge to their stationary points at a linear rate, but that while prefixLM converges to the optimal solution of linear regression, causalLM convergence dynamics follows that of an online gradient descent algorithm, which is not guaranteed to be optimal even as the number of samples grows infinitely. We supplement our theoretical claims with empirical experiments over synthetic and real tasks and using various types of transformers. Our experiments verify that causalLM consistently underperforms prefixLM in all settings.