A polar coordinate system represents syntax in large language models

Originally formalized with symbolic representations, syntactic trees may also be effectively represented in the activations of large language models (LLMs). Indeed, a 'Structural Probe' can find a subspace of neural activations, where syntactically related words are relatively close to one-another. However, this syntactic code remains incomplete: the distance between the Structural Probe word embeddings can represent the existence but not the type and direction of syntactic relations. Here, we hypothesize that syntactic relations are, in fact, coded by the relative direction between nearby embeddings. To test this hypothesis, we introduce a 'Polar Probe' trained to read syntactic relations from both the distance and the direction between word embeddings. Our approach reveals three main findings. First, our Polar Probe successfully recovers the type and direction of syntactic relations, and substantially outperforms the Structural Probe by nearly two folds. Second, we confirm that this polar coordinate system exists in a low-dimensional subspace of the intermediate layers of many LLMs and becomes increasingly precise in the latest frontier models. Third, we demonstrate with a new benchmark that similar syntactic relations are coded similarly across the nested levels of syntactic trees. Overall, this work shows that LLMs spontaneously learn a geometry of neural activations that explicitly represents the main symbolic structures of linguistic theory.

No Such Thing as a General Learner: Language models and their dual optimization

What role can the otherwise successful Large Language Models (LLMs) play in the understanding of human cognition, and in particular in terms of informing language acquisition debates? To contribute to this question, we first argue that neither humans nor LLMs are general learners, in a variety of senses. We make a novel case for how in particular LLMs follow a dual-optimization process: they are optimized during their training (which is typically compared to language acquisition), and modern LLMs have also been selected, through a process akin to natural selection in a species. From this perspective, we argue that the performance of LLMs, whether similar or dissimilar to that of humans, does not weigh easily on important debates about the importance of human cognitive biases for language.

What Makes Two Language Models Think Alike?

Do architectural differences significantly affect the way models represent and process language? We propose a new approach, based on metric-learning encoding models (MLEMs), as a first step to answer this question. The approach provides a feature-based comparison of how any two layers of any two models represent linguistic information. We apply the method to BERT, GPT-2 and Mamba. Unlike previous methods, MLEMs offer a transparent comparison, by identifying the specific linguistic features responsible for similarities and differences. More generally, the method uses formal, symbolic descriptions of a domain, and use these to compare neural representations. As such, the approach can straightforwardly be extended to other domains, such as speech and vision, and to other neural systems, including human brains.

What makes two models think alike?

Do architectural differences significantly affect the way models represent and process language? We propose a new approach, based on metric-learning encoding models (MLEMs), as a first step to answer this question. The approach provides a feature-based comparison of how any two layers of any two models represent linguistic information. We apply the method to BERT, GPT-2 and Mamba. Unlike previous methods, MLEMs offer a transparent comparison, by identifying the specific linguistic features responsible for similarities and differences. More generally, the method uses formal, symbolic descriptions of a domain, and use these to compare neural representations. As such, the approach can straightforwardly be extended to other domains, such as speech and vision, and to other neural systems, including human brains.

The Impact of Syntactic and Semantic Proximity on Machine Translation with Back-Translation

Unsupervised on-the-fly back-translation, in conjunction with multilingual pretraining, is the dominant method for unsupervised neural machine translation. Theoretically, however, the method should not work in general. We therefore conduct controlled experiments with artificial languages to determine what properties of languages make back-translation an effective training method, covering lexical, syntactic, and semantic properties. We find, contrary to popular belief, that (i) parallel word frequency distributions, (ii) partially shared vocabulary, and (iii) similar syntactic structure across languages are not sufficient to explain the success of back-translation. We show however that even crude semantic signal (similar lexical fields across languages) does improve alignment of two languages through back-translation. We conjecture that rich semantic dependencies, parallel across languages, are at the root of the success of unsupervised methods based on back-translation. Overall, the success of unsupervised machine translation was far from being analytically guaranteed. Instead, it is another proof that languages of the world share deep similarities, and we hope to show how to identify which of these similarities can serve the development of unsupervised, cross-linguistic tools.

Metric-Learning Encoding Models Identify Processing Profiles of Linguistic Features in BERT's Representations

We introduce Metric-Learning Encoding Models (MLEMs) as a new approach to understand how neural systems represent the theoretical features of the objects they process. As a proof-of-concept, we apply MLEMs to neural representations extracted from BERT, and track a wide variety of linguistic features (e.g., tense, subject person, clause type, clause embedding). We find that: (1) linguistic features are ordered: they separate representations of sentences to different degrees in different layers; (2) neural representations are organized hierarchically: in some layers, we find clusters of representations nested within larger clusters, following successively important linguistic features; (3) linguistic features are disentangled in middle layers: distinct, selective units are activated by distinct linguistic features. Methodologically, MLEMs are superior (4) to multivariate decoding methods, being more robust to type-I errors, and (5) to univariate encoding methods, in being able to predict both local and distributed representations. Together, this demonstrates the utility of Metric-Learning Encoding Methods for studying how linguistic features are neurally encoded in language models and the advantage of MLEMs over traditional methods. MLEMs can be extended to other domains (e.g. vision) and to other neural systems, such as the human brain.

Bridging the Empirical-Theoretical Gap in Neural Network Formal Language Learning Using Minimum Description Length

Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal language learning, we focus on one simple formal language and show that the theoretically correct solution is in fact not an optimum of commonly used objectives -- even with regularization techniques that according to common wisdom should lead to simple weights and good generalization (L1, L2) or other meta-heuristics (early-stopping, dropout). However, replacing standard targets with the Minimum Description Length objective (MDL) results in the correct solution being an optimum.

Minimum Description Length Hopfield Networks

Associative memory architectures are designed for memorization but also offer, through their retrieval method, a form of generalization to unseen inputs: stored memories can be seen as prototypes from this point of view. Focusing on Modern Hopfield Networks (MHN), we show that a large memorization capacity undermines the generalization opportunity. We offer a solution to better optimize this tradeoff. It relies on Minimum Description Length (MDL) to determine during training which memories to store, as well as how many of them.

Benchmarking Neural Network Generalization for Grammar Induction

How well do neural networks generalize? Even for grammar induction tasks, where the target generalization is fully known, previous works have left the question open, testing very limited ranges beyond the training set and using different success criteria. We provide a measure of neural network generalization based on fully specified formal languages. Given a model and a formal grammar, the method assigns a generalization score representing how well a model generalizes to unseen samples in inverse relation to the amount of data it was trained on. The benchmark includes languages such as $a^nb^n$, $a^nb^nc^n$, $a^nb^mc^{n+m}$, and Dyck-1 and 2. We evaluate selected architectures using the benchmark and find that networks trained with a Minimum Description Length objective (MDL) generalize better and using less data than networks trained using standard loss functions. The benchmark is available at https://github.com/taucompling/bliss.

Minimum Description Length Recurrent Neural Networks

We train neural networks to optimize a Minimum Description Length score, i.e., to balance between the complexity of the network and its accuracy at a task. We show that networks trained with this objective function master tasks involving memory challenges such as counting, including cases that go beyond context-free languages. These learners master grammars for, e.g., $a^nb^n$, $a^nb^nc^n$, $a^nb^{2n}$, and $a^nb^mc^{n+m}$, and they perform addition. They do so with 100% accuracy, sometimes also with 100% confidence. The networks are also small and their inner workings are transparent. We thus provide formal proofs that their perfect accuracy holds not only on a given test set, but for any input sequence.