Kernelised Normalising Flows
Eshant English, Matthias Kirchler, Christoph Lippert
TL;DR
This paper introduces Ferumal flow, a kernelised normalising flow model that achieves competitive density estimation with fewer parameters, especially effective in low-data scenarios, by integrating kernels into the flow framework.
Contribution
The paper presents a novel kernelised normalising flow model that offers a parameter-efficient alternative to neural network-based flows, particularly excelling with sparse data.
Findings
Kernelised flows achieve comparable or better results than neural flows.
They are especially effective in low-data regimes.
The approach maintains parameter efficiency.
Abstract
Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in…
Peer Reviews
Decision·ICLR 2024 poster
I commend the authors for their dedicated focus on tackling the challenge of low-data scenarios in generative modeling. Furthermore, I value their efforts in quantifying the improvements brought about by their proposed architectures, particularly in terms of reducing computational demands for hyperparameter tuning and training convergence compared to other approaches.
It would have been beneficial if the authors had provided links to a repository containing their code and models for improved accessibility and reproducibility. Additionally, given the authors' initial reference to the potential application of their models in the medical field, it would have been valuable to include an evaluation of their models' performance on a medical dataset to demonstrate their practical applicability and potential benefits in that specific domain.
1. The paper introduce interesting concept in classical flow model 2. The paper has good theoretical fundaments.
1. In Fig 1, authors should add results from more methods, like FFJORD 2. How does the model work on a spiral 2D dataset? 3. In the main paper, we do not have any image datasets. In the appendix, we have Kuzushiji-MNIST dataset. Authors should evaluate the model on MNIST, CIFAR, and CELEBA data special when we compare methods with Glow. 4. In the paper, there is a lack of some illustration of the method. It can help to understand what exactly the kernels are in coupling layers. 5. Section 3.1 i
The proposed approach is novel and interesting. The paper correctly claims that normalizing flows which employ neural network based coupling layers are data and parameter hungry. The proposed kernel based approach in contrast is data and parameter efficient. · The results in Table 3 show that the proposed approach shines in the low data regime. It clearly outperforms FFJORD and obtains impressive results even when only 500 data samples are available. · The paper is well written
· Methods like FFJORD (\cf Figure 2 in FFJORD) report better results compared to the proposed approach (as shown in Table 1). The performance advantage of FFJORD is even more apparent in case of the challenging discontinuous checkerboard dataset in Figure 3 (supplementary). It is not clear if the proposed model has the modelling capacity to capture complex distributions. · The proposed method is outperformed significantly by FFJORD, although FFJORD uses more parameters as report
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · Music Technology and Sound Studies · Music and Audio Processing