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Transformers Generalize Hierarchically Without Explicit Structural Bias: Understanding the Role of Training Objectives


Core Concepts
Transformer language models trained with the language modeling objective consistently learn to generalize hierarchically, even without any explicit structural bias, unlike models trained with other objectives like sequence-to-sequence or prefix language modeling.
Abstract
The paper investigates the sources of inductive bias in transformer models that lead to hierarchical generalization in language tasks. The key findings are: The choice of training objective significantly impacts hierarchical generalization in transformers. Among five objectives studied (language modeling, sequence-to-sequence, prefix language modeling, sequence classification, and cloze completion), only the language modeling objective consistently leads to strong hierarchical generalization across different tasks. Pruning experiments reveal the existence of subnetworks within the trained transformer language models that exhibit different generalization behaviors - some corresponding to hierarchical rules and others to linear rules. These subnetworks continue to coexist throughout training, despite the overall model performing closer to one type of generalization. Using a Bayesian framework, the paper shows a correlation between transformers generalizing hierarchically and the hierarchical grammars having higher posterior probability compared to regular grammars that follow linear rules. This suggests that transformers generalize hierarchically because the hierarchical grammars that fit the data are often "simpler" than the regular grammars. The paper concludes that modeling the entire sequence of tokens, as in the language modeling objective, is critical for learning hierarchical structure, and that transformers' preference for hierarchical generalization can be explained by a simplicity bias.
Stats
Transformers trained with the language modeling objective consistently achieve around 75% generalization accuracy on tasks like question formation and tense reinflection. Pruning experiments reveal the existence of subnetworks within the trained transformer language models that exhibit 100% generalization accuracy for hierarchical rules and 0% generalization accuracy for linear rules. When the training data is disambiguated to only contain examples consistent with the hierarchical rule, the subnetwork corresponding to the linear rule disappears.
Quotes
"Only the language modeling objective consistently obtains high generalization accuracy on all tasks." "We find joint existence of subnetworks within the model with different generalization behaviors (subnetworks corresponding to hierarchical structure and linear order)." "We establish a correlation between whether transformers generalize hierarchically on a dataset and whether the simplest explanation of that dataset is provided by a hierarchical grammar compared to regular grammars exhibiting linear generalization."

Deeper Inquiries

How do the findings of this paper generalize to more complex language tasks beyond the synthetic datasets studied here

The findings of this paper can be extended to more complex language tasks beyond the synthetic datasets studied here by considering the underlying principles of hierarchical generalization in neural network models. The key takeaway from the study is the importance of the training objective, specifically the language modeling objective, in inducing a bias towards hierarchical generalization in transformers. This insight can be applied to more complex language tasks by understanding the role of training objectives in shaping the model's ability to generalize hierarchically. For tasks such as natural language understanding, sentiment analysis, machine translation, and text generation, the choice of training objective could significantly impact the model's hierarchical generalization capabilities. By training models on diverse and challenging datasets that require hierarchical understanding of language structures, researchers can further explore how different training objectives influence the model's ability to generalize hierarchically in real-world language tasks. Additionally, the Bayesian framework used in the study can be applied to more complex language tasks to analyze the preference for hierarchical generalization in other neural network architectures. By constructing probabilistic generative grammars that model the data-generation process for specific tasks, researchers can investigate the simplicity bias and trade-off between goodness of fit and simplicity in different neural network models.

Can the Bayesian framework be extended to explain hierarchical generalization in other neural network architectures beyond transformers

The Bayesian framework used in this study can be extended to explain hierarchical generalization in other neural network architectures beyond transformers. The framework provides a systematic approach to understanding how neural networks generalize hierarchically by balancing the trade-off between the goodness of fit and simplicity of competing hypotheses. By constructing probabilistic generative grammars that represent different generalization behaviors, researchers can analyze the posterior probabilities of these hypotheses given the observed data and training objectives. This Bayesian approach can be applied to recurrent neural networks (RNNs), convolutional neural networks (CNNs), graph neural networks, and other neural network architectures to investigate their preference for hierarchical generalization. By modeling the data-generation process using probabilistic grammars and computing posterior probabilities, researchers can uncover the underlying biases and mechanisms that drive hierarchical generalization in diverse neural network models.

What other inductive biases, beyond the training objective, might influence hierarchical generalization in language models

Beyond the training objective, several other inductive biases might influence hierarchical generalization in language models. Some of these biases include architectural constraints, regularization techniques, dataset characteristics, and model hyperparameters. Architectural Constraints: The design of the neural network architecture, such as the number of layers, attention mechanisms, and connectivity patterns, can introduce biases towards hierarchical or linear generalization. Architectures that explicitly capture hierarchical structures, like tree-structured networks, may exhibit stronger hierarchical generalization compared to architectures without such constraints. Regularization Techniques: Regularization methods like dropout, weight decay, and early stopping can impact the model's preference for hierarchical generalization. Regularization techniques that encourage simpler models or prevent overfitting to the training data may influence the model's ability to generalize hierarchically. Dataset Characteristics: The complexity and diversity of the training data can also shape the model's inductive biases. Datasets with clear hierarchical structures and varying levels of ambiguity can influence the model's preference for hierarchical generalization. Introducing synthetic datasets with controlled hierarchical and linear rules can help analyze the impact of dataset characteristics on generalization behavior. Model Hyperparameters: Hyperparameters such as learning rate, batch size, and optimizer choice can affect how neural networks learn and generalize. Tuning these hyperparameters to encourage hierarchical learning or incorporating hierarchical priors in the model architecture can potentially enhance hierarchical generalization in language models. By considering these additional inductive biases alongside the training objective, researchers can gain a comprehensive understanding of the factors influencing hierarchical generalization in language models.
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