Title: Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers
Venue: NeurIPS 2025
Accepted: yes
Keywords: language model

architecture design
Abstract: Understanding architectural differences in language models is challenging, especially at academic-scale pretraining (e.g., 1.3B parameters, 100B tokens), where results are often dominated by noise and randomness. To overcome this, we introduce controlled synthetic pretraining tasks that isolate and evaluate core model capabilities. Within this framework, we discover \emph{Canon layers}: lightweight architectural components—named after the musical term ``canon''—that promote horizontal information flow across neighboring tokens. Canon layers compute weighted sums of nearby token representations and integrate seamlessly into Transformers, linear attention, state-space models, or any sequence architecture.

We present 12 key results. This includes how Canon layers enhance reasoning depth (e.g., by $2\times$), reasoning breadth, knowledge manipulation, etc. They lift weak architectures like NoPE to match RoPE, and linear attention to rival SOTA linear models like Mamba2/GDN—validated both through synthetic tasks and real-world academic-scale pretraining.
This synthetic playground offers an \emph{economical, principled path} to isolate core model capabilities often obscured at academic scales. Equipped with infinite high-quality data, it may even \emph{predict} how future architectures will behave as training pipelines improve—e.g., through better data curation or RL-based post-training—unlocking deeper reasoning and hierarchical inference.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents a set of synthetic tasks to test architectural changes in LLMs in a more principled manner and further introduces Canon layers: 1d convolution with kernel size 4 + optional residual connections. Canon layers can be interleaved both in the attention and MLP part of a transformer. The authors present 12 empirical results highlighting differences in performance between Transformers and other architectures such as Mamba and GLA and the benefit of Canon layers. Canon layers are also shown to improve the performance in standard benchmarks under pre-training.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\nS1 Comprehensive experimental evaluation. The paper includes an impressive number of  experiments and for each of the synthetic tasks several different setups are evaluated: varying both the complexity of the task and the number of parameters for the models.\n\nS3 The proposed canon Layers are simple but impactful and justified both conceptually and experimentally,  although the novelty is limited given that Canon is similar to the 1d convolution present e.g. in Mamba.\n\nS2 The manuscript is clearly written, well organized and easy to follow.\n\n\n**Weaknesses**\n\nW1 Little related works concerning synthetic experiments previously proposed to test LLM architectures (See Q1 in Questions). \n\nW2. I found many figures (e.g Figure 4 and 5) too packed and therefore difficult to parse.\n\nQUESTIONS:\nQ1 Can you include, even if in the appendix, a related work section on synthetic tasks proposed to evaluate LLM architectures? For example [1,2] introduce formal language tasks which have been included in recent works concerning novel architectures. A deeper discussion on this would help contextualize the set of  tasks proposed in the paper. \n\nQ2 Figure 1 presents a compelling argument against relying on pretraining + benchmarks to assess architectural improvements: the difference by varying the data or init seed is larger than the one given by changing architecture. How does the difference in performance change when varying seed? Does fixing the seed to compute such a difference mitigate the huge variability of the results with the data and initialization seed?  Moreover, do you see these large differences even in perplexity on e.g. lambada or wikitext?\n\n\nQ3 Concerning canon layers, is there some intuition behind the choice of 4 for the kernel size?\n\n\n[1] Deletang, Gregoire, et al. \"Neural Networks and the Chomsky Hierarchy.\" The Eleventh International Conference on Learning Representations.\n\n[2] Akyürek, Ekin, et al. \"In-Context Language Learning: Architectures and Algorithms.\" International Conference on Machine Learning. PMLR, 2024.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-15"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents an intriguing exploration of synthetic pretraining tasks aimed at teasing apart architectural differences in large language models (LLMs). Using this framework, the authors identify Canon layers, lightweight components that enhance horizontal information flow across adjacent tokens, integrating seamlessly into diverse architectures, including Transformers, linear attention models, and state-space models. They validate these enhancements via both synthetic tasks and real-world academic-scale pretraining, demonstrating increased reasoning depth, reasoning breadth, and knowledge manipulation. \n\n\nI find this paper interesting with solid experiments that provide better readability than most current LLM-based benchmark papers. However, it still has several drawbacks, such as its difficulty to comprehend due to unclear writing. The authors present numerous findings, but I am curious about which one is the main finding the paper intends to highlight. Additionally, the Canon layer approach appears to me as a variant of sliding windows, and I wonder what additional computational overhead it might entail and why the window size is limited to 3. It seems this method might be particularly effective in certain scenarios, such as those demonstrated in lines 165-167 with the AB..A context. The effectiveness in other contexts remains uncertain, as the synthetic tasks designed by the authors naturally fit these scenarios, showcasing the Canon layer's promising results.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nInnovative Experimental Framework: The paper provides a new methodology for exploring language model architectures through synthetic tasks, presenting a novel approach for architectural understanding.\n\nRobust Experimental Design: The experiments cover multiple tasks and different architectures comprehensively, with clear comparisons and results.\n\nEnhanced Interpretability: By introducing Canon layers, the paper enhances the transparency of understanding how models perform reasoning and knowledge manipulation.\n\nWeaknesses:\n\nComplex and Lengthy Presentation: Although the experimental content is rich, the paper's narrative is somewhat challenging to decipher, lacking clear emphasis on primary findings.\n\nSimilar Design to Sliding Windows: The Canon layers resemble sliding window techniques, necessitating further exploration regarding computational overhead and the effectiveness of the fixed window size of 3.\n\nLimited Validation on Challenging Datasets: The validation utilizing GSM8k is relatively simple for current LLMs, thereby potentially restricting the paper's broader applicability and impact.\n\nQUESTIONS:\nWhat is the central contribution among the findings presented? Is there a particularly important conclusion?\n\nHow much computational overhead is introduced by the Canon layer? What rationale is given for the chosen window size?\n\nHow do the synthetic tasks relate to real-world complex tasks?\n\nLIMITATIONS:\nInsufficient Validation on Complex Tasks: Due to reliance on relatively simple validation tasks, the paper's applicability and impact in complex situations remain to be examined.\n\nOverly Technical Expression: The paper's technical language may limit rapid understanding and application of the methods by non-specialist readers.\n\nAs a Variant of Sliding Window: Canon layers, as a variant of sliding windows, are effective in specific scenarios, but their performance in other contexts is uncertain, especially without targeted task design.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nAcademic-scale pretraining (around 1.3 billion parameters and 100 billion tokens) yields results dominated by noise, making it difficult to discern true architectural differences. To overcome this, the authors design a controlled suite of five synthetic pretraining tasks, DEPO for reasoning depth, BREVO for breadth, CAPO for knowledge capacity, MANO for knowledge manipulation, and LANO for hierarchical structure, that cleanly isolate core capabilities. Based on insights from these tasks, they introduce Canon layers, lightweight horizontal residual links implemented as causal convolutions. Canon layers integrate into any sequence model and dramatically improve horizontal information flow, boosting reasoning depth by 2–4×, breadth by 30 percent, knowledge capacity by 10–15 percent, and enabling weaker architectures to match or exceed stronger baselines.\n\nSTRENGTHS AND WEAKNESSES:\n**Strength:** The paper presents a rigorous, cost-effective framework using synthetic benchmarks and extensive experiments that convincingly demonstrate how Canon layers improve core model capabilities and enable clearer architectural comparisons.\n\n**Weakness:** Real-world evaluations are limited to relatively small scale due to budget constraints, though the authors acknowledge and address this; the Canon concept itself is not particularly novel, though its systematic validation across diverse tasks is valuable and compelling.\n\nQUESTIONS:\n- The plots are overwhelming at first, and CAPO plots are particularly hard to read; Figure 8 could probably be simplified to highlight only the key insights.\n\n- It would be interesting to include a small-scale ablation study on different Canon kernel sizes.\n\n- For DEPO, the task may be too straightforward as a depth benchmark; would be good if we can also have a more demanding multi-step reasoning task. One example may be adding a variant of BREVO with a k-step limitation (output only vertices reachable in exactly k steps from the query).\n\n- Nit: on page 34 it should state “kernel size 4” rather than 3.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
Authors propose some synthetic pretraining tasks with the motivation that they will be helpful for doing architectural research, which at the moment is difficult to do for pretraining acc to them. 

5 tasks - DEPO (reasoning depth), BREVO (reasoning breadth), CAPO (knowledge capacity), MANO (knowledge manipulation), and LANO (hierarchical language structure.

To show effectiveness of these tasks, they propose Canon layers. Then they use these layers to show improvement on real world benchmarks.

STRENGTHS AND WEAKNESSES:
Strenghts:
- The paper is well written and easy to follow
- The authors have identified and are working on a very useful problem. Nice!

Weaknesses:
- I like the overall premise. But what is the guarantee that anything good on these tasks will be good on real world tasks? What is the guarantee that they are optimal tasks?
- How do you know that all we need is to measure performance on these 5 tasks and that is all to predict goodness of pre-training.
- Authors begin by saying that pre-training performance is more difficult to evaluate and it is correct. model has not been post-trained yet.
- Canon layers themselves are able to revive weaker models. Finding components using your framework that can improve upon state of art architectures will be the true test of this scheme.

QUESTIONS:
I think that the most important thing for such a framework is to establish correlation between the intermediate/psuedo tasks and the goodness of a pre-trained model (how many tasks does it take?) how will you establish it? 
I like the premise but I think there is more work needed.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-04