Looped SSMs with shared parameters across depth match or exceed standard SSMs with more parameters on time series classification, with additional gains from input reshaping techniques.
A Mechanistic Analysis of Looped Reasoning Language Models
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Reasoning has become a central capability in large language models. Recent research has shown that reasoning performance can be improved by looping an LLM's layers in the latent dimension, resulting in looped reasoning language models. Despite promising results, few works have investigated how their internal dynamics differ from those of standard feedforward models. In this paper, we conduct a mechanistic analysis of the latent states in looped language models, focusing in particular on how the stages of inference observed in feedforward models compare to those observed in looped ones. To this end, we analyze cyclic recurrence and show that for many of the studied models each layer in the cycle converges to a distinct fixed point; consequently, the recurrent block follows a consistent cyclic trajectory in the latent space. We provide evidence that as these fixed points are reached, attention-head behavior stabilizes, leading to constant behavior across recurrences. Empirically, we discover that recurrent blocks learn stages of inference that closely mirror those of feedforward models, repeating these stages in depth with each iteration. We study how recurrent block size, input injection, and normalization influence the emergence and stability of these cyclic fixed points. We believe these findings help translate mechanistic insights into practical guidance for architectural design.
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2026 7representative citing papers
FPRM is a Transformer-based model using fixed-point convergence for adaptive halting in looped architectures, claimed effective on Sudoku, Maze, state-tracking, and ARC-AGI benchmarks.
MELT decouples reasoning depth from memory in looped language models by sharing a single gated KV cache per layer and training it via chunk-wise distillation from Ouro starting models.
Compressed looped Transformers with fixed small recurrent state cannot decide P-complete problems under logspace reductions, while polynomial-length chain-of-thought can.
Hyperloop Transformers outperform standard and mHC Transformers with roughly 50% fewer parameters by looping a middle block of layers and applying hyper-connections only after each loop.
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Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers
FPRM is a Transformer-based model using fixed-point convergence for adaptive halting in looped architectures, claimed effective on Sudoku, Maze, state-tracking, and ARC-AGI benchmarks.