Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.09412

MIRA: Mitigating Pole Geometry Bias in Recurrent Language Models

Róisín Luo·Ihsan Ullah·Christian Gagné·Dong Li·Karyn Morrissey
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that the Transformer's recurrent successors --- such as selective state-space models (SSMs), Receptance Weighted Key Value (RWKV), and Retentive Network (RetNet) --- can be characterized as infinite-impulse-response (IIR) systems. The zero--pole geometries of these IIR systems characterize the temporal modes they can represent. However, to trade parallelism, the algebraic structures of the parameterizations of these recurrent systems often give rise to poles constrained to the real axis, thereby inducing an architectural bias in their recurrent dynamics. To unify these recurrent architectures and eliminate their pole geometry bias, inspired by the lattice--ladder realization of general IIR systems, we present \textsc{Mira} (\textbf{M}odal \textbf{I}IR \textbf{R}ecurrent \textbf{A}rchitecture), a unified family of linear-time recurrent architectures for building large language models (LLMs) with a highly parallel algebraic structure. Each \textsc{Mira} block realizes a higher-order IIR system that represents temporal modes from token streams through a lattice--ladder structure, followed by a feed-forward network (FFN). This realization enables the model to represent the temporal modes associated with both real and complex-conjugate poles. We pretrain \textsc{Mira-S}, a 12-layer small-scale LLM with 0.14B parameters composed entirely of \textsc{Mira} blocks. Throughout the pretraining, \textsc{Mira-S} achieves lower perplexity than strong recurrent baselines, exhibits stronger context-window generalization beyond the training length, and attains higher throughput with a dedicated CUDA kernel.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Róisín Luo, Ihsan Ullah, Christian Gagné, Dong Li, Karyn Morrissey. 2026-11-06. MIRA: Mitigating Pole Geometry Bias in Recurrent Language Models. https://arxiv.org/abs/2611.09412

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Limit Analysis for Symbolic Multi-step Reasoning Tasks with Information Propagation Rules Based on Transformers

Transformers are able to perform reasoning tasks, however the intrinsic mechanism remains widely open. In this paper we propose a set of information propagation rules based on Transformers and utilize symbolic reasoning tasks to theoretically analyze the limit reasoning steps. We show that the limit number of reasoning steps is between $2^{L-1}-1$ and $\frac{3^{L-1}-1}{2}$ for a model with $L$ attention layers in a single-pass. In addition, we find that, for problems with a fixed number of reasoning steps, Transformers exhibit a preference for generating sequences that satisfy certain ordering relations. Ultimately, we construct a Transformer and prove that the limiting reasoning depth is achievable.

cs.AI↗
arXiv2026

Counterfactual Distillation: Internalizing Reflective Experience into LLM Agent

Large language models increasingly act as autonomous agents in long-horizon interactions, learning from final outcomes and environmental feedback. However, optimizing from such interaction experience remains challenging, as feedback is heterogeneous and rarely carries explicit reward information. Existing post-training approaches rely on outcome-driven methods, such as reinforcement learning with verifiable rewards (RLVR), which primarily exploit final success signals while leaving interaction experience and feedback underutilized. In sparse-reward, long-horizon tasks, this often results in distribution sharpening: the policy reinforces a narrow set of already-successful behaviors, without substantially improving the feedback-grounded agency needed for broader problem-solving capacity (e.g., Pass@k). We propose Counterfactual Distillation, a framework that converts exploration-derived experience into trainable policy supervision. Specifically, we organize exploration as a tree-structured search process, where the agent reflects on past decision points and makes new experience-guided decisions to form alternative branches. These corrections are then distilled as counterfactual targets: we train the model to predict the revised action from the original history without explicitly providing the experience, thereby introducing out-of-distribution behavior patterns and expanding exploration capacity. Across diverse interactive coding and agentic tasks, our method outperforms outcome-driven baselines such as GRPO and experience-based methods such as Early Experience, with gains of up to 14 percentage points over the base model on Pass@128. When interleaved with reinforcement learning updates, it further raises the performance ceiling, improving Pass@1 on Sokoban by 8 percentage points over extended GRPO. Our code is available at https://github.com/motigrez/Counterfactual-Distillation.

cs.AI↗
arXiv2026

Taming the Centaur(s) with LAPITHS: a framework for a theoretically grounded interpretation of AI performances

We introduce a framework called LAPITHS (Language model Analysis through Paradigm grounded Interpretations of Theses about Human likenesS) and use it to show that several major claims advanced by models such as CENTAUR, proposed as an artificial Unified Model of Cognition, are not theoretically or empirically justified. LAPITHS provides a principled reference point for counteracting the current behaviouristic tendency in AI research to interpret the human level performances of transformer based language models as evidence of human like underlying computation and, by extension, as signs of cognitive abilities. The novelty of LAPITHS lies in making explicit the arguments grounded in two quantitative assessments: (i) the Minimal Cognitive Grid, a theoretically motivated method for estimating the cognitive plausibility of artificial systems, and (ii) a behavioural comparison showing that results similar to those reported for CENTAUR like models can be reproduced by other systems that do not satisfy the structural constraints typically associated with cognitive plausibility, and whose outputs do not provide independent explanatory insight into human cognition.

cs.AI↗