Neural scaling laws for an uncertain world

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity

Generalizable Neural Fields as Partially Observed Neural Processes

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.Comment: To appear ICCV 202

A Recurrent Encoder-Decoder Approach with Skip-filtering Connections for Monaural Singing Voice Separation

The objective of deep learning methods based on encoder-decoder architectures for music source separation is to approximate either ideal time-frequency masks or spectral representations of the target music source(s). The spectral representations are then used to derive time-frequency masks. In this work we introduce a method to directly learn time-frequency masks from an observed mixture magnitude spectrum. We employ recurrent neural networks and train them using prior knowledge only for the magnitude spectrum of the target source. To assess the performance of the proposed method, we focus on the task of singing voice separation. The results from an objective evaluation show that our proposed method provides comparable results to deep learning based methods which operate over complicated signal representations. Compared to previous methods that approximate time-frequency masks, our method has increased performance of signal to distortion ratio by an average of 3.8 dB