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Authors: Ashish Sabharwal ×
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01.
arXiv (CS.CL) 2026-06-17

Olmo Hybrid: From Theory to Practice and Back

Recent work has demonstrated the potential of non-transformer language models, especially linear recurrent neural networks (RNNs) and hybrid models that mix recurrence and attention. Yet there is no consensus on whether the potential benefits of these new architectures justify the risk and effort of scaling them up. To address this, we provide evidence for the advantages of hybrid models over pure transformers on several fronts. First, theoretically, we show that hybrid models do not merely inherit the expressivity of transformers and linear RNNs, but can express tasks beyond both, such as code execution. Putting this theory to practice, we train Olmo Hybrid, a 7B-parameter model largely comparable to Olmo 3 7B but with the sliding window layers replaced by Gated DeltaNet layers. We show that Olmo Hybrid outperforms Olmo 3 across standard pretraining and mid-training evaluations, demonstrating the benefit of hybrid models in a controlled, large-scale setting. We find that the hybrid model scales significantly more efficiently than the transformer, explaining its higher performance. However, its unclear why greater expressivity on specific formal problems should result in better scaling or superior performance on downstream tasks unrelated to those problems. To explain this apparent gap, we return to theory and argue why increased expressivity should translate to better scaling efficiency, completing the loop. Overall, our results suggest that hybrid models mixing attention and recurrent layers are a powerful extension to the language modeling paradigm: not merely to reduce memory during inference, but as a fundamental way to obtain more expressive models that scale better during pretraining.

02.
arXiv (CS.CL) 2026-06-19

Efficiently Representing Algorithms With Chain-of-Thought Transformers

The increasing popularity of reasoning models – language models that output a series of reasoning or thought tokens before producing an answer – is justified, in part, by theoretical results showing that chain-of-thought (CoT) transformers can simulate Turing machines, and thus perform arbitrary computation. However, the Turing machine, while suitable for complexity-theoretic analysis, is not convenient, intuitive, or efficient for discussing algorithms. Algorithms are typically designed and analyzed at a higher level of abstraction, captured by the Word RAM model with random-access memory and unit-cost operations on $\bigO(\log n)$-bit words. As a result, Word RAM algorithms can be substantially more efficient than their Turing machine counterparts, raising the question: Can CoT transformers efficiently simulate Word RAM algorithms? For instance, can they sort $n$ items in $\bigO(n \log n)$ steps or run Dijkstra's algorithm in $\bigO(E + V \log V)$ steps? We answer affirmatively, up to poly-logarithmic overhead. We first establish this for finite-precision transformers with poly-logarithmic width and rightmost unique hard attention, then strengthen the result to two more practical settings with finite width and log-precision: continuous CoT, where reasoning takes the form of vectors rather than tokens, and a hybrid architecture in which transformer layers sit atop a recurrent (linear RNN) layer. In all three cases, we find that CoT can efficiently simulate any Word RAM algorithm with only a poly-logarithmic overhead in $n$. This overhead reduces to log-square when the Word RAM has a ``flat'' instruction set, and only logarithmic for multiplication-free flat instructions – in stark contrast to known CoT simulations of Turing machines, which require quadratic overhead over Word RAM.