Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning
neural ODEs;transformer;adaptive finetune
Yes
No ethics review needed.
1. Could you provide theoretical justification for the specific design of the time-dependent weight parametrization? What motivated these particular choices, and how do they relate to the model's performance?
2. The paper presents both analytical tools (spectral analysis, Lyapunov exponents) and empirical results, but the connection between them isn't clear. How do the insights from your analysis inform or explain the observed performance in the experiments?
3. The adaptive fine-tuning capability seems promising, but its benefits aren't fully explored. Could you elaborate on scenarios where this flexibility provides concrete advantages over traditional fine-tuning approaches?
4. Given that the Lyapunov exponent analysis is input-dependent, how generalizable are the insights gained from this analysis? What patterns or principles have you observed across different classes inputs that might provide more universal understanding of transformer behavior?
- The paper makes an interesting attempt to bridge the gap between theoretical analysis of transformers and practical implementations by using neural ODEs with depth-varying weights.
- The proposed adaptive fine-tuning approach, which leverages the discussed ODE formulation to enable flexible architecture changes during fine-tuning, presents a potentially useful direction for model adaptation.
- The presentation includes detailed visualizations of spectral dynamics and Lyapunov exponent analysis, which helps readers understand the model's behavior.
This paper proposes a novel approach to modeling transformer architectures using depth-varying neural ordinary differential equations (ODEs). The authors introduce time-dependent weights for attention and feed-forward blocks, implemented through neural networks that take a continuous layer index ($t$) as input. They analyze the model's dynamics through spectral analysis and Lyapunov exponents, aiming to provide insights into transformer behavior. The work also explores adaptive fine-tuning capabilities enabled by the ODE formulation, showing comparable performance to GPT models across various configurations and datasets.
1. Limited Technical Novelty:
- The core formulation of transformers as ODEs is directly borrowed from Lu et al. (2019) without significant theoretical advancement.
- The analysis methodology for the dynamics closely follows Geshkovski et al. (2023a,b) without introducing substantial new analytical tools or insights.
- The time-dependent weight parametrization, while interesting, lacks theoretical justification for its specific design choices.
2. Insufficient Analysis Rigor:
- The spectral analysis lacks formal theoretical guarantees or concrete connections to model performance.
- The Lyapunov exponent analysis is essentially equivalent to analyzing the Jacobian of transformer blocks, which varies with each input and doesn't provide generalizable insights.
- Many claims about model behavior are supported by cherry-picked empirical observations without theoretical justification.
3. Experimental Limitations:
- The performance improvements over baseline models are modest and inconsistent across different settings.
- The ablation studies don't sufficiently justify the architectural choices, particularly the dimension of time embeddings.
- The paper oscillates between being an analysis paper and an empirical paper without excelling in either direction.

4. Presentation Issues:
- The paper structure is somewhat disjointed, with early sections (1-4) largely reiterating existing work.
- Many design choices appear arbitrary and lack proper motivation or ablation studies.
- The relationship between the theoretical analysis and practical benefits isn't clearly established.
Yes
N/A
No ethics review needed.
Could the authors include evaluation on downstream tasks? This information would be valuable in assessing how well the model generalizes beyond the initial validation perplexity. They can show some zero and 5 shot evaluation on benchmarks from appendix of [2].

[2] Biderman, Stella, et al. "Pythia: A suite for analyzing large language models across training and scaling." International Conference on Machine Learning. PMLR, 2023.
1) This paper employs flexible computation and dynamically adjusts the step size of its ODE solvers to fine-tune the model with variable layer lengths, achieving competitive performance with vanilla transformers. This adaptation is particularly promising as it allows for post-pretraining adjustments to the model's architecture, which is a great direction for future research.

2) They demonstrate the model's capacity through spectral analysis, revealing that increasing eigenvalue magnitudes inhibit cluster formation compared to weight sharing based prior works. 

3) They also leverage the Lyapunov exponent to analyze token-level sensitivity for explainablity where they utilises both attention map and Jacobian which has similarity with the work in computer vision[1] for better faithfullness.

[1] Chefer, Hila, Shir Gur, and Lior Wolf. "Transformer interpretability beyond attention visualization." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.
This paper presents a neural ODE-based approach for generating transformer weights. Unlike existing methods that use weight-sharing, this approach employs hyper-networks to produce the attention and feed-forward layer weights as functions of a continuous layer index (or time).
1) No evaluation of downstream performance is conducted.

2) Training is computationally and memory-intensive; for instance, training a GPT-medium model requires 1.8B (with d_emb=144) parameters to achieve competitive performance, while the original GPT-2 medium model has only 345M parameters.
Yes
No ethics review needed.
The time-dependent weight parameterization in your approach introduces additional parameters compared to standard transformer architectures. While you demonstrate comparable throughput, I'm concerned about the memory efficiency. Could you clarify the actual memory overhead during training and inference? Specifically, how does the memory usage scale with model size and demb.
1. The paper is exceptionally well-organized with a clear progression from theory to implementation. Complex mathematical concepts are presented in an accessible manner with effective visualizations.
2. The paper introduces an innovative approach using non-autonomous neural ODEs with time-dependent weights to model transformers, effectively overcoming limitations of previous weight-sharing methods. The comprehensive analysis through spectral dynamics of QK/OV pairs and investigation of clustering behavior provides deep theoretical insights into transformer dynamics while achieving competitive performance.
3. The introduction of Lyapunov exponents for analyzing token-level sensitivity is highly innovative. This provides new tools for model interpretability that go beyond traditional attention visualization methods.
This paper presents DIFFEQFORMER, an innovative framework that reformulates transformer architectures through the lens of non-autonomous neural ordinary differential equations (ODEs). The approach conceptualizes transformer layers as a continuous-time dynamical system, with the distinguishing feature of parameterizing attention and feed-forward weights as continuous functions of layer depth via neural networks.The authors conduct rigorous spectral analysis of the attention mechanisms, demonstrating increasing eigenvalue magnitudes across layers—a finding that challenges current theoretical frameworks predicated on weight-sharing assumptions. They further advance model interpretability by incorporating Lyapunov exponent analysis for examining token-level sensitivity.
1. The model's performance degradation at GPT-large scale raises concerns about its viability for larger architectures. The lack of experiments on billion-parameter scale models leaves uncertainty about whether this approach can effectively scale to sizes relevant for state-of-the-art language models.
2. While perplexity results are promising, the paper lacks zero-shot evaluation results which are crucial for understanding the model's practical capabilities. Additional metrics would better demonstrate the framework's advantages over traditional transformers.
3. The performance appears sensitive to the $d_{emb}$, but the paper provides limited guidance on how to optimally set this hyperparameter for different model scales.
Yes
No ethics review needed.
**Questions**:

* I encourage the authors to add a section (main body or appendix) about the computational differences betwee DiffEqFormer and a vanilla Transformer. For example, ML practitioners could be interested in training time, total number of parameters, FLOPs, GPU memory required and any other significant parameter the authors might think of, given their expertise in the field.

* In Section 5.2, I suggest including interpretability results using attention matrices, to make the differences claimed evident to the reader.

* In Section 6, can the authors elaborate on the choice of experimental setup? Why is GPT2 chosen among the breadth of language models available? Unless the constraints are compute-related, I believe this work could be much more impactful if DiffEqFormer was compared to a recent LLM architecture.
  * If some recent LLM was used, I am really intrigued in knowing about other metrics related to "_emergent capabilities_" are for DiffEqFormer. For example, does it perform better at 0-shot reasoning, on MMLU, etc? I am not asking the authors to provide all this analysis, but I definitely encourage them to include at least a comparison with a recent LLM.

* As far as I understand, the model is trained at fixed time intervals. I wonder whether the authors have thought about training at randomized time steps, as it is typically done for diffusion models.  Is it even feasible? Could this allow a more flexible adaptive fine-tuning later on? I would appreciate some discussion on this aspect during the rebuttal, for my better understanding of the work.

**Comments**:

* Overall, I believe this is a nice piece of research work. I enjoyed the reading and learnt throughout. My main concern is about the experimental setup. A comparison with some modern LLM would be very important to convince the community that DiffEqFormer is _equivalent_ to Transformer with the additional unique advantage of adaptability+interpretability. I am completely open to increase my review score upon a fruitful rebuttal.

* I would like to share my opinion about the experiments in Tables 1-2. Although the authors try to explain why GPT2-large is slightly better in terms of PPL for OpenWebText, I believe the strength of these results lie in DiffEqFormer being similar (not necessarily better) to GPT. 

**Suggestions for readability + typos:**

* Very minor: Fig 1-b could have the arrow sin blue, as a connection with what is shown in Fig 1-a.
* L304: The OV matrix ~has~ have eigenvalues
* L322: model ~collapse~ collapses
* Fig 6 (legend) ~cratch~ scratch
**Originality:**

* The time-dependent implementation proposed is both elegant and original in my opinion. 
* Using the Lyapunov exponent for interpretability is an original idea, which is also very well adapted to the framework proposed.
* The idea of adaptive fine-tuning is also original to me, specially given how natural it is under the DiffEqFormer formulation.

**Quality:**

* The experimental setup related to interpretability of attention matrices and eigen-values is very complete. 

**Clarity:**

* The paper is well written, with clear language. The mathematical notation and formulation is also clear and easy to follow. I want to congratulate the authors for that, I honestly was hesitant before reading the paper since many ODE papers are too heavy in notation. I really enjoyed reading this manuscript!

**Significance:**

* I believe this Neural ODE approach can have impact and can serve as starting point for further research. Both the idea of adaptive fine-tuning and time-dependent weights have strong research potential.
This work proposes an architecture that implements a Transformer using a Neural ODE approach (DiffEqFormer). The main contribution over existing Neural ODE works is that DiffEqFormer has time-dependent weights, as opposed to traditional weight-sharing. This equips DiffEqFormer with the interesting property of adaptive fine-tuning, i.e. baing able to fine-tune a model with N layers as a M layer version of itself. The authors show competitive performance compared to GPT-S/M/L on two datasets. Additionally, interpretability results are obtained using the Lyapunov exponent of the proposed dynamical system.
**Quality:**

* The experimental setup related to Language Modelling (6.1) uses arguably old models (GPT2). Although the experiments are useful to understand how DiffEqFormer is able to match performance, I missed a comparison with a current SOTA model. I believe this work could have more impact if a recent model was included, not needing an extremely large model, but maybe a 1B parameter LLM. For example,  [Llama-3.2-1b](https://huggingface.co/meta-llama/Llama-3.2-1B) or [Gemma-2-2b](https://huggingface.co/google/gemma-2-2b) could be excellent candidates.

**Clarity:**

* I felt that the discussion about _attractive_ and _repulsive_ scenarios (5.1) is a little bit disconnected from the rest, and much harder to parse. For example, I could not directly understand why a $V=-I_d$ behavior leads to model collapse. Also, in the conclusion of this section (L336) the authors emphasize that "_positive values from the QK pairs in Figure 2a and the copying behavior observed in the OV pair_" hint to the presence of induction heads in the last layer(s). However, I understood that what is important is the magnitude of QK pairs, and the positiveness of OV pairs. There is a mismatch between this conclusion and the claims in the explanation.  I encourage the authors to revisit this section and provide a clearer explanation of why the QK, and specially the OV analysis, is important.

**Significance:**

* As said, this work can be impactful given the applicability of DiffEqFormer. However, lacking a comparison with SOTA LLMs can diminish such impact.
This paper introduces a new transformer architecture using non-autonomous neural ODEs that allows adaptive fine-tune. The paper analyze internal model dynamic using spectral analysis.
@inproceedings{
anonymous2024neural,
title={Neural {ODE} Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=XnDyddPcBT},
note={under review}
}
Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer architectures using highly flexible non-autonomous neural ordinary differential equations (ODEs). Our proposed model fully parameterizes all the weights of attention and feed-forward blocks through neural networks, with weights articulated as functions of a continuous layer index. We examine the model's dynamics through spectral analysis, uncovering an increase in eigenvalue magnitude offering a practical insights against weight-sharing assumption in existing theoretical studies. We also introduce the use of the Lyapunov exponent to examine token-level sensitivity, improving model interpretability. Our neural ODE transformer performs similarly to GPT across various configurations and datasets, while offering flexible fine-tuning capabilities under different architectures.
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Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning
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