Evaluating $n$-Gram Novelty of Language Models Using Rusty-DAWG

How novel are texts generated by language models (LMs) relative to their training corpora? In this work, we investigate the extent to which modern LMs generate $n$-grams from their training data, evaluating both (i) the probability LMs assign to complete training $n$-grams and (ii) $n$-novelty, the proportion of $n$-grams generated by an LM that did not appear in the training data (for arbitrarily large $n$). To enable arbitrary-length $n$-gram search over a corpus in constant time, we develop Rusty-DAWG, a novel search tool inspired by indexing of genomic data. We compare the novelty of LM-generated text to human-written text and explore factors that affect generation novelty, focusing on the Pythia models. We find that, for $n > 4$, LM-generated text is less novel than human-written text, though it is more novel for smaller $n$. Larger LMs and more constrained decoding strategies both decrease novelty. Finally, we show that LMs complete $n$-grams with lower loss if they are less frequent in the training data. Overall, our results reveal factors influencing the novelty of LM-generated text, and we release Rusty-DAWG to facilitate further pretraining data research.

Let's Think Dot by Dot: Hidden Computation in Transformer Language Models

Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater computation that additional tokens allow. We show that transformers can use meaningless filler tokens (e.g., '......') in place of a chain of thought to solve two hard algorithmic tasks they could not solve when responding without intermediate tokens. However, we find empirically that learning to use filler tokens is difficult and requires specific, dense supervision to converge. We also provide a theoretical characterization of the class of problems where filler tokens are useful in terms of the quantifier depth of a first-order formula. For problems satisfying this characterization, chain-of-thought tokens need not provide information about the intermediate computational steps involved in multi-token computations. In summary, our results show that additional tokens can provide computational benefits independent of token choice. The fact that intermediate tokens can act as filler tokens raises concerns about large language models engaging in unauditable, hidden computations that are increasingly detached from the observed chain-of-thought tokens.

The Illusion of State in State-Space Models

State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill and Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). But do SSMs truly have an advantage (over transformers) in expressive power for state tracking? Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class $\mathsf{TC}^0$. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state" in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems.

Can You Learn Semantics Through Next-Word Prediction? The Case of Entailment

Do LMs infer the semantics of text from co-occurrence patterns in their training data? Merrill et al. (2022) argue that, in theory, probabilities predicted by an optimal LM encode semantic information about entailment relations, but it is unclear whether neural LMs trained on corpora learn entailment in this way because of strong idealizing assumptions made by Merrill et al. In this work, we investigate whether their theory can be used to decode entailment judgments from neural LMs. We find that a test similar to theirs can decode entailment relations between natural sentences, well above random chance, though not perfectly, across many datasets and LMs. This suggests LMs implicitly model aspects of semantics to predict semantic effects on sentence co-occurrence patterns. However, we find the test that predicts entailment in practice works in the opposite direction to the theoretical test. We thus revisit the assumptions underlying the original test, finding its derivation did not adequately account for redundancy in human-written text. We argue that correctly accounting for redundancy related to explanations might derive the observed flipped test and, more generally, improve linguistic theories of human speakers.

OLMo: Accelerating the Science of Language Models

Language models (LMs) have become ubiquitous in both NLP research and in commercial product offerings. As their commercial importance has surged, the most powerful models have become closed off, gated behind proprietary interfaces, with important details of their training data, architectures, and development undisclosed. Given the importance of these details in scientifically studying these models, including their biases and potential risks, we believe it is essential for the research community to have access to powerful, truly open LMs. To this end, this technical report details the first release of OLMo, a state-of-the-art, truly Open Language Model and its framework to build and study the science of language modeling. Unlike most prior efforts that have only released model weights and inference code, we release OLMo and the whole framework, including training data and training and evaluation code. We hope this release will empower and strengthen the open research community and inspire a new wave of innovation.

Transformers as Recognizers of Formal Languages: A Survey on Expressivity

As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring questions such as this will help to compare transformers with other models, and transformer variants with one another, for various tasks. Work in this subarea has made considerable progress in recent years. Here, we undertake a comprehensive survey of this work, documenting the diverse assumptions that underlie different results and providing a unified framework for harmonizing seemingly contradictory findings.

The Expressive Power of Transformers with Chain of Thought

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer? We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps make them recognize exactly the class of polynomial-time solvable problems -- the first exact characterization of a type of transformers in terms of standard complexity classes. Together, our results provide a nuanced framework for understanding how the length of a transformer's chain of thought or scratchpad impacts its reasoning power.

How Language Model Hallucinations Can Snowball

A major risk of using language models in practical applications is their tendency to hallucinate incorrect statements. Hallucinations are often attributed to knowledge gaps in LMs, but we hypothesize that in some cases, when justifying previously generated hallucinations, LMs output false claims that they can separately recognize as incorrect. We construct three question-answering datasets where ChatGPT and GPT-4 often state an incorrect answer and offer an explanation with at least one incorrect claim. Crucially, we find that ChatGPT and GPT-4 can identify 67% and 87% of their own mistakes, respectively. We refer to this phenomenon as hallucination snowballing: an LM over-commits to early mistakes, leading to more mistakes that it otherwise would not make.

A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure of networks undergoing grokking on the sparse parity task, and find that the grokking phase transition corresponds to the emergence of a sparse subnetwork that dominates model predictions. On an optimization level, we find that this subnetwork arises when a small subset of neurons undergoes rapid norm growth, whereas the other neurons in the network decay slowly in norm. Thus, we suggest that the grokking phase transition can be understood to emerge from competition of two largely distinct subnetworks: a dense one that dominates before the transition and generalizes poorly, and a sparse one that dominates afterwards.

Transparency Helps Reveal When Language Models Learn Meaning

Many current NLP systems are built from language models trained to optimize unsupervised objectives on large amounts of raw text. Under what conditions might such a procedure acquire meaning? Our systematic experiments with synthetic data reveal that, with languages where all expressions have context-independent denotations (i.e., languages with strong transparency), both autoregressive and masked language models successfully learn to emulate semantic relations between expressions. However, when denotations are changed to be context-dependent with the language otherwise unmodified, this ability degrades. Turning to natural language, our experiments with a specific phenomenon -- referential opacity -- add to the growing body of evidence that current language models do not well-represent natural language semantics. We show this failure relates to the context-dependent nature of natural language form-meaning mappings.