Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism

Aviv Bick, Eric Xing, Albert Gu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:4324-4344, 2025.

Abstract

State-space models (SSMs) offer efficient alternatives to Transformers for long sequences, but their fixed-size recurrent state limits capability on algorithmic tasks, such as retrieving past context. In this work, we examine how in-context retrieval operates in Transformer- and SSM-based language models and find that both rely on a Gather-and-Aggregate (G&A) mechanism: a Gather Head extracts relevant information from context, which an Aggregate Head integrates into representation. In both architectures, G&A concentrates in a few heads, forming bottlenecks even for simple retrieval. For example, disabling a single Gather or Aggregate Head in a pruned Llama-3.1-8B impairs retrieving the correct answer letter in MMLU, reducing its accuracy from 66% to 25%. Moreover, this retrieval bottleneck can obscure knowledge demands of tasks as the pruned model succeeds on MMLU with functioning G&A heads yet fails on other knowledge benchmarks. The bottleneck similarly extends to tasks where SSMs typically underperform, like GSM8K, BBH, and dialogue. We show that SSMs’ retrieval challenges manifest in these heads, creating smoother attention patterns instead of the sharp transitions effective G&A requires. Thus, the Transformer-SSM retrieval gap exists in just a few heads, rather than the entire language model. % Result 3: Analyzing Hybrid models This suggests a unified explanation for Transformer vs. SSM performance gap while showing how to merge their strengths. We find that pretrained hybrid models, where SSMs are combined with attention layers, delegate the role of Aggregate Heads to attention. Similarly, replacing a single G&A head in a pretrained SSM with an attention variant boosts retrieval and benchmark scores.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bick25a, title = {Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism}, author = {Bick, Aviv and Xing, Eric and Gu, Albert}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {4324--4344}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bick25a/bick25a.pdf}, url = {https://proceedings.mlr.press/v267/bick25a.html}, abstract = {State-space models (SSMs) offer efficient alternatives to Transformers for long sequences, but their fixed-size recurrent state limits capability on algorithmic tasks, such as retrieving past context. In this work, we examine how in-context retrieval operates in Transformer- and SSM-based language models and find that both rely on a Gather-and-Aggregate (G&A) mechanism: a Gather Head extracts relevant information from context, which an Aggregate Head integrates into representation. In both architectures, G&A concentrates in a few heads, forming bottlenecks even for simple retrieval. For example, disabling a single Gather or Aggregate Head in a pruned Llama-3.1-8B impairs retrieving the correct answer letter in MMLU, reducing its accuracy from 66% to 25%. Moreover, this retrieval bottleneck can obscure knowledge demands of tasks as the pruned model succeeds on MMLU with functioning G&A heads yet fails on other knowledge benchmarks. The bottleneck similarly extends to tasks where SSMs typically underperform, like GSM8K, BBH, and dialogue. We show that SSMs’ retrieval challenges manifest in these heads, creating smoother attention patterns instead of the sharp transitions effective G&A requires. Thus, the Transformer-SSM retrieval gap exists in just a few heads, rather than the entire language model. % Result 3: Analyzing Hybrid models This suggests a unified explanation for Transformer vs. SSM performance gap while showing how to merge their strengths. We find that pretrained hybrid models, where SSMs are combined with attention layers, delegate the role of Aggregate Heads to attention. Similarly, replacing a single G&A head in a pretrained SSM with an attention variant boosts retrieval and benchmark scores.} }
Endnote
%0 Conference Paper %T Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism %A Aviv Bick %A Eric Xing %A Albert Gu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bick25a %I PMLR %P 4324--4344 %U https://proceedings.mlr.press/v267/bick25a.html %V 267 %X State-space models (SSMs) offer efficient alternatives to Transformers for long sequences, but their fixed-size recurrent state limits capability on algorithmic tasks, such as retrieving past context. In this work, we examine how in-context retrieval operates in Transformer- and SSM-based language models and find that both rely on a Gather-and-Aggregate (G&A) mechanism: a Gather Head extracts relevant information from context, which an Aggregate Head integrates into representation. In both architectures, G&A concentrates in a few heads, forming bottlenecks even for simple retrieval. For example, disabling a single Gather or Aggregate Head in a pruned Llama-3.1-8B impairs retrieving the correct answer letter in MMLU, reducing its accuracy from 66% to 25%. Moreover, this retrieval bottleneck can obscure knowledge demands of tasks as the pruned model succeeds on MMLU with functioning G&A heads yet fails on other knowledge benchmarks. The bottleneck similarly extends to tasks where SSMs typically underperform, like GSM8K, BBH, and dialogue. We show that SSMs’ retrieval challenges manifest in these heads, creating smoother attention patterns instead of the sharp transitions effective G&A requires. Thus, the Transformer-SSM retrieval gap exists in just a few heads, rather than the entire language model. % Result 3: Analyzing Hybrid models This suggests a unified explanation for Transformer vs. SSM performance gap while showing how to merge their strengths. We find that pretrained hybrid models, where SSMs are combined with attention layers, delegate the role of Aggregate Heads to attention. Similarly, replacing a single G&A head in a pretrained SSM with an attention variant boosts retrieval and benchmark scores.
APA
Bick, A., Xing, E. & Gu, A.. (2025). Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:4324-4344 Available from https://proceedings.mlr.press/v267/bick25a.html.

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