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Why Are Linear RNNs More Parallelizable?

William Merrill, Hongjian Jiang, Yanhong Li, Anthony Lin, Ashish Sabharwal · Mar 4, 2026 · Citations: 0

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Extraction: Fresh

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Mar 5, 2026, 5:58 AM

Recent

Extraction refreshed

Mar 14, 2026, 6:23 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.20

Abstract

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what makes LRNNs -- but not traditional, nonlinear RNNs -- as easy to parallelize in practice as transformers. We answer this question by providing a tight connection between types of RNNs and standard complexity classes. We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that transformers admit. Furthermore, we show that nonlinear RNNs can solve $\mathsf{L}$-complete problems (and even $\mathsf{P}$-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them as efficiently as transformers. Our theory also identifies fine-grained expressivity differences between recent popular LRNN variants: permutation-diagonal LRNNs are $\mathsf{NC}^1$-complete whereas diagonal-plus-low-rank LRNNs are more expressive ($\mathsf{PNC}^1$-complete). We provide further insight by associating each type of RNN with a corresponding automata-theoretic model that it can simulate. Together, our results reveal fundamental tradeoffs between nonlinear RNNs and different variants of LRNNs, providing a foundation for designing LLM architectures that achieve an optimal balance between expressivity and parallelism.

Low-signal caution for protocol decisions

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  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.20 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.

Reported Metrics

partial

Precision

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: Furthermore, we show that nonlinear RNNs can solve $\mathsf{L}$-complete problems (and even $\mathsf{P}$-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them as efficiently as transformers.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.20
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

precision

Research Brief

Deterministic synthesis

We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that transformers admit. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Mar 14, 2026, 6:23 AM · Grounded in abstract + metadata only

Key Takeaways

  • We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that…
  • Furthermore, we show that nonlinear RNNs can solve L-complete problems (and even P-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them…
  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Validate metric comparability (precision).

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that transformers admit.
  • Furthermore, we show that nonlinear RNNs can solve L-complete problems (and even P-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them as efficiently as transformers.

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Pass: Metric reporting is present

    Detected: precision

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