We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We train a proof-of-concept model from scratch with 3.5 billion parameters and 800 billion tokens. We show that this model can effortlessly use varying levels of compute, significantly improving with additional compute especially on reasoning tasks, such as math and coding. Further, this architecture naturally reduces compute costs via zero-shot per-token adaptive compute, KV-cache sharing and speculative decoding.

Scaling laws are typically fit using a family of models with a narrow range of frozen hyperparameter choices. In this work we study scaling laws using multiple architectural shapes and hyperparameter choices, highlighting their impact on resulting prescriptions. As a primary artifact of our research, we release the Gemstones: an open-source scaling law dataset, consisting of over 4000 checkpoints from transformers with up to 2 billion parameters and diverse architectural shapes; including ablations over learning rate and cooldown. Our checkpoints enable more complex studies of scaling, such as analyzing the relationship between width and depth. By examining our model suite, we find that the prescriptions of scaling laws can be highly sensitive to the experimental design process and the specific model checkpoints used during fitting.

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number. In addition to the boost these embeddings provide on their own, we show that this fix enables architectural modifications such as input injection and recurrent layers to improve performance even further. With positions resolved, we can study the logical extrapolation ability of transformers. Can they solve arithmetic problems that are larger and more complex than those in their training data? We find that training on only 20 digit numbers with a single GPU for one day, we can reach state-of-the-art performance, achieving up to 99% accuracy on 100 digit addition problems. Finally, we show that these gains in numeracy also unlock improvements on other multi-step reasoning tasks including sorting and multiplication.