On Subquadratic Architectures: From Applications to Principles

Mechanistic studies of sequence models often treat layerwise state encodings as architectural traits: recurrent models concentrate readable state, attention-based models distribute it. We find that the same architecture reverses this profile when the task changes. Across Transformers, Mamba, Mamba-2, LSTMs, and GRUs, Parity is concentrated late in Mamba and the recurrent baselines and built gradually by Transformer; on bounded-depth Dyck-k the pattern flips. The same flip appears in fine-tuned Mamba-130M and Pythia-160M, and the Pythia Dyck bottleneck persists at 410M. Two explanations are conflated in the literature: algebraic structure (commutativity) versus computational structure (prefix update vs. stack). To separate them we add a third task: non-commutative S_3 permutation composition. S_3 groups with Parity, not Dyck, on layerwise probing across all five architectures and on Mamba-specific Conv1D attribution, so the grouping tracks computational structure rather than commutativity. Causal interventions show that, in the 4-layer formal models, linearly readable directions are often functionally necessary and can remain important at out-of-distribution lengths on Parity and Dyck. At pretrained scale the picture splits. Fine-tuned Pythia Dyck has a strong middle-layer bottleneck (L6-L7 ablation drops accuracy by roughly 81% at 160M; broader L4-L18 plateau at 410M), far weaker at the best-probe layer. Pretrained Mamba shows the complementary failure mode: its final layer is highly readable, no single probe direction breaks the task on Parity, Dyck, or S_3, yet mid-position activation patching there recovers about 97-98% of the clean-corrupted logit gap. Probing localizes where state is linearly available, not always where the computation is bottlenecked. Mechanistic signatures are properties of architecture and task together.

There have been numerous attempts to distill quadratic attention-based large language models (LLMs) into sub-quadratic linearized architectures. However, despite extensive research, such distilled models often fail to match the performance of their teacher LLMs on various downstream tasks. We set out the goal of lossless distillation, which we define in terms of tolerance-corrected Win-and-Tie rates between student and teacher on sets of tasks. To this end, we introduce an effective distillation pipeline for xLSTM-based students. We propose an additional merging stage, where individually linearized experts are combined into a single model. We show the effectiveness of this pipeline by distilling base and instruction-tuned models from the Llama, Qwen, and Olmo families. In many settings, our xLSTM-based students recover most of the teacher's performance, and even exceed it on some downstream tasks. Our contributions are an important step towards more energy-efficient and cost-effective replacements for transformer-based LLMs.

Looped Transformers (LT) have emerged as a powerful architecture by iterating their layers multiple times before decoding the final token. However, pairing them with full attention retains quadratic complexity, making them computationally expensive and slow. We introduce LT2 (Linear-Time Looped Transformers), a family of looped architectures that replace quadratic softmax attention with subquadratic, linear-time attention. We study two variants: LT2-linear with linear attention and LT2-sparse with sparse attention. We find that looping uniquely synergizes with these variants: it enables iterative memory refinement in linear attention and progressively expands the effective receptive field in sparse attention. We formalize these benefits theoretically and demonstrate consistent empirical gains across controlled recall, state-tracking, and language modeling tasks. We then explore LT2-hybrid, which combines different attention variants in a looped setting. Two variants are especially promising: LT2-hybrid (GDN+DSA), which interleaves linear and sparse attention to maximize efficiency and matches the standard looped transformer's quality at fully linear-time cost; and LT2-hybrid (Full+GDN), which interleaves GDN with a small fraction of full attention layers to maximize quality, surpassing the standard looped transformer in both performance and efficiency. We also show how to convert a pre-trained LT into an LT2-hybrid model. With about 1B tokens of training, our converted model, Ouro-hybrid-1.4B, outperforms industry-level 1B models and is competitive with industry-level 4B models while retaining the speed benefits of linear-time attention. Together, these results show a clear path toward making looped transformers more scalable and advancing efficient, capable small language models.