Lexinvariant Language Models (2305.16349v1)

Abstract: Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any LLM (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a LLM to be performant without \emph{any} fixed token embeddings? Such a LLM would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the \textit{a priori} identity of any token. To answer this, we study \textit{lexinvariant}LLMs that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true LLM at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard LLM, given a sufficiently long context. We further explore two properties of the lexinvariant LLMs: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard LLMs towards lexinvariance and potential practical applications.

• The paper introduces lexinvariant language models that forgo fixed token embeddings in favor of dynamic contextual roles, achieving competitive performance with longer contexts.
• The paper develops a rigorous theoretical framework and transformer-based experiments that demonstrate polynomial convergence rates and sublinear complexity relative to vocabulary size.
• The paper shows that lexinvariant models excel in in-context deciphering and symbolic reasoning tasks, outperforming traditional models by up to 4x in synthetic benchmarks.

Analysis of Lexinvariant LLMs

The paper introduces a novel framework termed "Lexinvariant LLMs" (LLMs), which challenges the conventional reliance on fixed token embeddings in LLMs. Traditional LLMs rely heavily on token embeddings as a mapping from discrete symbols to continuous vectors, effectively capturing lexical meaning based on pre-defined vocabularies. The authors propose an alternative approach where a model's performance is not contingent on fixed token embeddings but rather on the structural role of tokens within a given context. This model assigns the same probability to all lexical permutations of a sequence, effectively ignoring the identity of individual symbols.

Key Contributions

1. Theoretical Foundations: The paper provides a rigorously defined formalism for LLMs, proving their capability to converge to the true LLM at a rate polynomial in context length, with complexities sublinear in vocabulary size. This is foundational, showing that a lack of stable lexical mapping does not preclude language comprehension.
2. Empirical Validation: Employing a transformer architecture, the lexinvariant approach achieved perplexity comparable to conventional LLMs, especially with longer contexts. The gap in perplexity between standard models and lexinvariant models decreased significantly with increased context length, exemplified by experiments on The Pile dataset.
3. In-context Deciphering and Symbol Manipulation: The LLM demonstrated robust capabilities in deciphering substitution ciphers in-context and symbol manipulation tasks, outperforming standard models by up to 4x in synthetic reasoning tasks. This highlights the model's potential in applications requiring dynamic context-based symbol reasoning.
4. Practical Implications and Regularization: The paper discusses ways to leverage lexinvariance as regularization in conventional LLMs, potentially enhancing robustness and generalization across various tasks and domains.

Numerical Results and Key Observations

• The empirical analysis revealed that the perplexity of lexinvariant LMs was initially 9x that of standard LMs but converged to within 1x with increased context. Specifically, with a 150M parameter transformer and character-level vocabulary, the LLM's perplexity dropped to 3.38 after observing 512 tokens, closely aligning with a standard LM's perplexity of 2.00.
• Further, in synthetic reasoning tasks, LLMs achieved significant accuracy improvements over standard models, particularly in tasks that involved symbolic reasoning like lookups and permutation tasks, reinforcing the strength of LLMs in handling symbolically structured tasks.

Implications and Future Directions

The introduction of LLMs prompts reevaluation of the role of token embeddings in LLMing. The demonstrated efficacy of LLMs suggests that model performance may be enhanced through architectural innovations that emphasize contextual dependency over static embeddings. Future work may explore hybrid models combining lexinvariance with traditional methods to leverage the strengths of both approaches. Additionally, the potential use of LLMs in real-world applications could involve tasks where flexibility and symbolic reasoning are paramount, such as real-time data processing and dynamic symbol interpretation in multilingual environments.

Moreover, the integration of lexinvariance as a regularization mechanism offers a promising avenue for enhancing model robustness against adversarial attacks and cross-linguistic generalization. This presents further opportunities for inquiry into hybrid modeling techniques, potentially broadening the applicability of LLMs in diverse computational linguistics fields.

In conclusion, the exploration of LLMs sets a precedent for alternative LLMing methodologies that eschew fixed lexical representations, thereby opening pathways for innovative approaches in natural language processing and artificial intelligence research.