Unveiling Divergent Inductive Biases of LLMs on Temporal Data

Unraveling the intricate details of events in natural language necessitates a subtle understanding of temporal dynamics. Despite the adeptness of Large Language Models (LLMs) in discerning patterns and relationships from data, their inherent comprehension of temporal dynamics remains a formidable challenge. This research meticulously explores these intrinsic challenges within LLMs, with a specific emphasis on evaluating the performance of GPT-3.5 and GPT-4 models in the analysis of temporal data. Employing two distinct prompt types, namely Question Answering (QA) format and Textual Entailment (TE) format, our analysis probes into both implicit and explicit events. The findings underscore noteworthy trends, revealing disparities in the performance of GPT-3.5 and GPT-4. Notably, biases toward specific temporal relationships come to light, with GPT-3.5 demonstrating a preference for "AFTER'' in the QA format for both implicit and explicit events, while GPT-4 leans towards "BEFORE''. Furthermore, a consistent pattern surfaces wherein GPT-3.5 tends towards "TRUE'', and GPT-4 exhibits a preference for "FALSE'' in the TE format for both implicit and explicit events. This persistent discrepancy between GPT-3.5 and GPT-4 in handling temporal data highlights the intricate nature of inductive bias in LLMs, suggesting that the evolution of these models may not merely mitigate bias but may introduce new layers of complexity.

SocREval: Large Language Models with the Socratic Method for Reference-Free Reasoning Evaluation

To comprehensively assess the capacity of current models for complex reasoning, it is crucial to assess their step-by-step reasoning in a scalable manner. Established reference-based evaluation metrics rely on human-annotated reasoning chains to assess the model-derived chains. However, such ``gold-standard'' human-written reasoning chains may not be unique and their acquisition is often labor-intensive. Existing reference-free reasoning metrics eliminate the need for human-crafted reasoning chains as references, but they typically require fine-tuning on datasets with human-derived reasoning chains, which complicates the process and raises concerns regarding generalizability across diverse datasets. To address these challenges, we harness GPT-4 to automatically evaluate reasoning chain quality, obviating the need for human-crafted references. Leveraging the Socratic method, we devise tailored prompts to enhance reference-free reasoning evaluation, which we term SocREval (Socratic method for Reasoning Evaluation). Empirical results from four human annotated datasets reveal that SocREval significantly improves GPT-4's performance, surpassing existing reference-free and reference-based reasoning evaluation metrics. Beyond its demonstrated efficacy, our proposed framework, large language models (LLMs) with the Socratic method, proves to be both cost-efficient and robust to prompt writing and example selection, as substantiated by our in-depth analysis.

On Regularization and Inference with Label Constraints

Prior knowledge and symbolic rules in machine learning are often expressed in the form of label constraints, especially in structured prediction problems. In this work, we compare two common strategies for encoding label constraints in a machine learning pipeline, regularization with constraints and constrained inference, by quantifying their impact on model performance. For regularization, we show that it narrows the generalization gap by precluding models that are inconsistent with the constraints. However, its preference for small violations introduces a bias toward a suboptimal model. For constrained inference, we show that it reduces the population risk by correcting a model's violation, and hence turns the violation into an advantage. Given these differences, we further explore the use of two approaches together and propose conditions for constrained inference to compensate for the bias introduced by regularization, aiming to improve both the model complexity and optimal risk.

Rethinking with Retrieval: Faithful Large Language Model Inference

Despite the success of large language models (LLMs) in various natural language processing (NLP) tasks, the stored knowledge in these models may inevitably be incomplete, out-of-date, or incorrect. This motivates the need to utilize external knowledge to assist LLMs. Unfortunately, current methods for incorporating external knowledge often require additional training or fine-tuning, which can be costly and may not be feasible for LLMs. To address this issue, we propose a novel post-processing approach, rethinking with retrieval (RR), which retrieves relevant external knowledge based on the decomposed reasoning steps obtained from the chain-of-thought (CoT) prompting. This lightweight approach does not require additional training or fine-tuning and is not limited by the input length of LLMs. We evaluate the effectiveness of RR through extensive experiments with GPT-3 on three complex reasoning tasks: commonsense reasoning, temporal reasoning, and tabular reasoning. Our results show that RR can produce more faithful explanations and improve the performance of LLMs.

A Law of Data Separation in Deep Learning

Multilayer neural networks have achieved superhuman performance in many artificial intelligence applications. However, their black-box nature obscures the underlying mechanism for transforming input data into labels throughout all layers, thus hindering architecture design for new tasks and interpretation for high-stakes decision makings. We addressed this problem by introducing a precise law that governs how real-world deep neural networks separate data according to their class membership from the bottom layers to the top layers in classification problems. This law shows that each layer roughly improves a certain measure of data separation by an \textit{equal} multiplicative factor. This law manifests in modern architectures such as AlexNet, VGGNet, and ResNet in the late phase of training. This law together with the perspective of data separation offers practical guidelines for designing network architectures, improving model robustness and out-of-sample performance during training, as well as interpreting deep learning predictions.

Weighted Training for Cross-Task Learning

In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy to implement, is computationally efficient, requires little hyperparameter tuning, and enjoys non-asymptotic learning-theoretic guarantees. The effectiveness of TAWT is corroborated through extensive experiments with BERT on four sequence tagging tasks in natural language processing (NLP), including part-of-speech (PoS) tagging, chunking, predicate detection, and named entity recognition (NER). As a byproduct, the proposed representation-based task distance allows one to reason in a theoretically principled way about several critical aspects of cross-task learning, such as the choice of the source data and the impact of fine-tuning

Layer-Peeled Model: Toward Understanding Well-Trained Deep Neural Networks

In this paper, we introduce the Layer-Peeled Model, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which in part explains the recently discovered phenomenon of neural collapse in deep learning training [PHD20]. Moreover, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto unknown phenomenon that we term Minority Collapse, which fundamentally limits the performance of deep learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before its confirmation by our computational experiments.

Label-Aware Neural Tangent Kernel: Toward Better Generalization and Local Elasticity

As a popular approach to modeling the dynamics of training overparametrized neural networks (NNs), the neural tangent kernels (NTK) are known to fall behind real-world NNs in generalization ability. This performance gap is in part due to the \textit{label agnostic} nature of the NTK, which renders the resulting kernel not as \textit{locally elastic} as NNs~\citep{he2019local}. In this paper, we introduce a novel approach from the perspective of \emph{label-awareness} to reduce this gap for the NTK. Specifically, we propose two label-aware kernels that are each a superimposition of a label-agnostic part and a hierarchy of label-aware parts with increasing complexity of label dependence, using the Hoeffding decomposition. Through both theoretical and empirical evidence, we show that the models trained with the proposed kernels better simulate NNs in terms of generalization ability and local elasticity.

Toward Better Generalization Bounds with Locally Elastic Stability

Classical approaches in learning theory are often seen to yield very loose generalization bounds for deep neural networks. Using the example of "stability and generalization" \citep{bousquet2002stability}, however, we demonstrate that generalization bounds can be significantly improved by taking into account refined characteristics of modern neural networks. Specifically, this paper proposes a new notion of algorithmic stability termed \textit{locally elastic stability} in light of a certain phenomenon in the training of neural networks \citep{he2020local}. We prove that locally elastic stability implies a tighter generalization bound than that derived based on uniform stability in many situations. When applied to deep neural networks, our new generalization bound attaches much more meaningful confidence statements to the performance on unseen data than existing algorithmic stability notions, thereby shedding light on the effectiveness of modern neural networks in real-world applications.