Zero-Shot Transfer of Neural ODEs

Summary

The work explores the use of neural ODEs as basis functions for function encoders. This requires dealing with the additional integration step, with the weighted combination of obtained ODEs representing the behaviour of the function to approximate via its integral. With an inner product and its tractable Monte Carlo estimation scheme, the authors derive an algorithm to train basis functions which span the space of dynamical systems, where each basis function is a neural ODE. The FE + ODE approach is put to the test against ODE and FE schemes for fitting a space of Van der Pol systems, long term prediction for RL, as well as quadrotor MPC control with improvements in zero-shot performance against the baselines used.

Strengths

The authors deal with a very important problem in machine learning and all the more in robotics: that of zero-shot generalisation to changes in dynamics/environment (here modelled via hidden parameters) - Interesting extension of the FE paradigm with a clear derivation of the required additions to adapt the basis function algorithm to neural ODEs - Good readability and presentation - Relatively significant combination of neural ODEs and Function Encoders with interesting performance improvements

Weaknesses

- Some clumsiness in the math notation: in equation (3) $N$ is used at the denominator when it should be $m$ instead. - The assumption of orthogonality for the validity of the coefficients is vital. However, both the authors in [13] and in this paper do not share any analysis on the validity of this assumption. It would be interesting to see how well this holds in practice (computing inner product of obtained basis functions/ODEs should be easy) and how many iterations are required to reach orthogonality in the examples provided. - The introductory paragraph of section 3 where the link between a new unknown function $f$, its observed trajectory $\mathcal{D}$ and ODE basis functions is made, could benefit from more motivation and explanation. It is not immediately clear why reasoning at the derivative level while dealing with integral trajectory data is more advantageous. Perhaps a figure would help as the manuscript is text heavy. - Explanations of the MuJoCo results are not very clear to me, they seem more like observations than interpretations. Why is the oracle unstable (does it require more data and training given the conditioning on hidden params)? What explains the differences between both experiments: FE + RES does well on half cheetah (better than FE + NODE) and terrible on ant? Where does the lack of inductive bias intervene in this case ?

Questions

- The term zero-shot does indeed refer to the ability of networks to perform in novel circumstances without retraining, and does apply here. However, it can be slightly misleading as adaptability here requires analysis of new data from the new setting. Can the authors elucidate the scales involved in the tradeoff? In other words, when does it become interesting to train 100 base models (on the 100 datasets) to gain a deployment advantage that still requires new data to function, versus fine-tuning one model or retraining? - Do the authors have any insights on changes in levels of performance whether the new ODE is in the convex hull of the available basis or outside it? (for example in the Van der Pol example, if the basis datasets contain trajectories for values of $\mu$ between 0.1 and 3, can the system perform for $\mu = 5$ ?

Rating

6

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

- A major numerical challenge working with continuous time neural networks is that of integration, with a plethora of solvers and schemes available. The authors touch upon this topic in their limitations sections and the impact of the integration horizon selection on behaviour predictability as well as the compute overhead involved (also in appendix C). It would have been interesting to give readers a better sense about the tradeoffs with numerical comparisons that go beyond verbal description.

Summary

The paper presents a novel framework for the zero-shot transfer of neural ODEs by leveraging function encoders to represent a space of dynamical systems. It demonstrates the method's effectiveness in adapting to unseen environments without retraining, using MuJoCo and quadrotor experiments.

Strengths

The paper demonstrates interesting ideas by introducing a novel framework for zero-shot transfer of neural ODEs using function encoders. This approach enables adaptation to unseen scenarios without retraining using the neural ODEs and function encoders. This research shows its potential to enhance the adaptability and safety of autonomous systems, bridging the gap between training and testing data.

Weaknesses

The paper presents a promising framework for zero-shot transfer of neural ODEs, but there are several areas for improvement. Firstly, the reliance on a large and diverse dataset for training is a significant limitation. The approach requires extensive data that spans the entire function space of possible dynamics, which may not always be feasible. This dependency on comprehensive datasets should be addressed by exploring data-efficient learning methods or leveraging transfer learning techniques. Secondly, the computational overhead involved in training multiple neural ODEs is substantial. This might hinder the scalability and real-time applicability of the proposed method. The authors could investigate more efficient training algorithms or consider approximations that reduce computational costs without compromising accuracy. Thirdly, the paper does not explicitly enforce the orthogonality of basis functions, relying instead on implicit regularization through the loss function. This might lead to suboptimal representation of the function space, affecting the model's performance. Moreover, the experiments lack diversity in evaluating the model's robustness to completely unseen environments or significantly different conditions. Including more varied test scenarios or stress tests could provide a deeper understanding of the model's adaptability and limitations.

Questions

1. The computational overhead for training multiple neural ODEs might be significant. How does this affect the scalability and real-time applicability of your method? 2. The paper does not enforce orthogonality explicitly for the basis functions, which might lead to suboptimal representation. Have you evaluated the levels of orthogonality (and their relationship with performance) in your method? 3. The experiments lack diversity in evaluating the model's robustness to completely unseen environments or significantly different conditions. How confident are you in your model’s adaptability in such scenarios? 4. The evaluation metrics used in the MuJoCo experiments are primarily focused on prediction accuracy. Have you considered additional metrics that might better capture your model's practical performance? For example, task-specific performance such as scores or cumulative rewards. 5. It seems to lack a sufficient variety of baselines for comparison. Have you considered additional zero-shot / few-shot or multitask / meta-learning studies?

Rating

5

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

Refer to Weaknesses and Questions.

Summary

This paper proposes a method to learn the dynamics of autonomous systems in a few shot manner. The core assumption is that the dynamics function dx/dt=f(x) of a new system can be modeled by a linear combination of basis dynamics functions. The method involves two stages. In the offline stage, the method learns a set of basis functions with neural ODE. In the online stage, the method uses incoming dynamics to fit the linear weights, which when combined with the learned basis, can be used to model the new system. The authors evaluated the effectiveness of the method on Van der Pol Oscillato system (with varying parameters) and Mujoco Ant.

Strengths

1. The writing is very clear. Readers with reasonable math background & ODE shall understand this paper reasonably well 2. The core of the method is intuitive, and the method is sound. Basis function with linear weighting for quick adaptation has been grounded in many fields. 3. I appreciate the fact that the authors explains the limitation and scope of the project, and there is no overclaim

Weaknesses

1. My main criticism of the paper is the technical contribution. The problems this system can solve seem to be constrained to systems limited variation in parameter, where the offline dataset & online system share a high level of similarity. While the authors explained how they apply NODE very clearly, I think using NODE is not a fundamental contribution because you can also have other sequence models trained to predict residue. The idea of basis function has also been explored by many prior literatures. 2. The title is misleading - you are doing quick online adaptation (few shot) instead of a zero-shot setting. A few trajectories of online data is required to adapt to the new system 3. There are a lot of baselines the authors should look into since few shot learning / quick adaptation is a long standing topic of research. For example, other basis function methods, meta learning methods. I understand that the authors picked a setting where time is continuous, but the mujoco Ant environment is also traditionally studied as discrete too, so a meta learning + some sequence prediction model should be applicable here. If you can provide a convincing argument about why those priors works aren't applicable it's also fine. 4. As I suggested in questions section, there could be many perspectives the author should dive deeper to improve the paper minor: 1. In line 114, the reasoning doesn't provide grounding to the orthogonality question - the training objective make them span the space assuming diverse enough dynamic systems - but this is unrelated to orthogonality! Are you saying that non orthogonal is okay as soon as they span the space? 2. It would be good to give more intuitive visualizations of estimation error in mujoco Ant. e.g. render the predicted trajectories as video 3. ablation about the number basis functions used would be helpful to understanding

Questions

1. In line 165, the authors said "Given data collected online from a single trajectory". I am curious to see ablations how the method improves as the amount of online data grow 2. In figure 3, error goes up as the number of look-ahead steps increases. While this is partially expected due to compounding error, how much of it shall be attributed to limited expressiveness of linear basis. e.g. I can do an experiment where I train a NODE with many many data, not just 200 example points, and roll it out. You will witness how MSE loss increases and gain insights about a upper bound for prediction accuracy that's not due to limited data / limited number of basis

Rating

5

Confidence

4

Soundness

3

Presentation

4

Contribution

2

Limitations

Please see my points in weakness

Summary

The paper aims to address the challenge of zero-shot transfer and adaptation. The authors propose tackling this challenge by learning a dynamics space spanned by neural ODE basis functions, which can then be used for rapid identification and adaptation to dynamics at inference time without additional training. The paper demonstrates the efficacy of the proposed approach, using both a simpler oscillator system and scaled up simulated robotics environments.

Strengths

- While this is not my area of expertise, to the best of my knowledge, the method proposed in the paper and the corresponding experiments are novel. - The paper is well written and clear, and fast adaptation is a crucial problem to the field, especially in the field of robotics and control. - The experiments seem well designed and thorough, showing the contribution of each of the method components when ablated, and demonstrating the efficacy of the approach for control via MPC.

Weaknesses

- To place the results in context with prior work, it would be additionally helpful for the robotics experiments to show comparisons to other methods that enable adaptation (e.g. training a model free method with domain randomized parameters). - It’s not clear how well the method will scale to more complex dynamics, or when trying to generalize beyond the learned basis functions (e.g., if they are not expressive enough or span the relevant spaces for a dynamical system, or if insufficient data is used to learn the dynamics space).

Questions

See suggestions in the Weaknesses section above.

Rating

6

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors address method limitations adequately in the paper.