Reinforcement learning from human feedback (RLHF) and AI-generated feedback (RLAIF) have become prominent techniques that significantly enhance the functionality of pre-trained language models (LMs). These methods harness feedback, sourced either from humans or AI, as direct rewards or to shape reward models that steer LM optimization. Nonetheless, the effective integration of rewards from diverse sources presents a significant challenge due to their disparate characteristics. To address this, recent research has developed algorithms incorporating strategies such as weighting, ranking, and constraining to handle this complexity. Despite these innovations, a bias toward disproportionately high rewards can still skew the reinforcement learning process and negatively impact LM performance. This paper explores a methodology for reward composition that enables simultaneous improvements in LMs across multiple dimensions. Inspired by fairness theory, we introduce a training algorithm that aims to reduce disparity and enhance stability among various rewards. Our method treats the aggregate reward as a dynamic weighted sum of individual rewards, with alternating updates to the weights and model parameters. For efficient and straightforward implementation, we employ an estimation technique rooted in the mirror descent method for weight updates, eliminating the need for gradient computations. The empirical results under various types of rewards across a wide range of scenarios demonstrate the effectiveness of our method.

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for symbolic programming. To understand the mechanism of reasoning of LMs, we curate synthetic datasets containing equivalent (natural, symbolic) data pairs, where symbolic examples contain first-order logic rules and predicates from non-parametric knowledge bases (KBs), supporting automated verification of intermediate reasoning results. Then we revisit neuro-symbolic approaches and propose to learn from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs, recovering Prolog’s backward chaining algorithm and supporting automated verification of LMs’ outputs. Comprehensive experiments are included to systematically compare LMLP with CoT in deductive reasoning settings, showing that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks even with smaller model sizes.

Accurate uncertainty quantification is crucial for the safe deployment of machine learning models, and prior research has demonstrated improvements in the calibration of modern language models (LMs). We study in-context learning (ICL), a prevalent method for adapting static LMs through tailored prompts, and examine the balance between performance and calibration across a broad spectrum of natural language understanding and reasoning tasks. Through comprehensive experiments, we observe that, with an increasing number of ICL examples, models initially exhibit increased miscalibration before achieving better calibration and miscalibration tends to arise in low-shot settings. Moreover, we find that methods aimed at improving usability, such as fine-tuning and chain-of-thought (CoT) prompting, can lead to miscalibration and unreliable natural language explanations. Furthermore, we explore recalibration techniques and find that a scaling-binning calibrator can reduce calibration errors consistently.

Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a Differentiable Symbolic Reasoning framework where pre-trained LMs govern the perception of factual knowledge, and a symbolic module performs deductive reasoning. In contrast to works that rely on hand-crafted logic rules, our differentiable symbolic reasoning framework efficiently learns weighted rules and applies semantic loss to further improve LMs. DSR-LM is scalable, interpretable, and allows easy integration of prior knowledge, thereby supporting extensive symbolic programming to robustly derive a logical conclusion. The results of our experiments suggest that DSR-LM improves the logical reasoning abilities of pre-trained language models, resulting in a significant increase in accuracy of over 20% on deductive reasoning benchmarks. Furthermore, DSR-LM outperforms a variety of competitive baselines when faced with systematic changes in sequence length.