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Register a new userEncoding Involutory Invariance in Neural Networks
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Added by
Anwesh Bhattacharya
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In certain situations, Neural Networks (NN) are trained upon data that obey underlying physical symmetries. However, it is not guaranteed that NNs will obey the underlying symmetry unless embedded in the network structure. In this work, we explore a special kind of symmetry where functions are invariant with respect to involutory linear/affine transformations up to parity $p=pm 1$. We develop mathematical theorems and propose NN architectures that ensure invariance and universal approximation properties. Numerical experiments indicate that the proposed models outperform baseline networks while respecting the imposed symmetry. An adaption of our technique to convolutional NN classification tasks for datasets with inherent horizontal/vertical reflection symmetry has also been proposed.
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While many existing graph neural networks (GNNs) have been proven to perform $ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $ell_1$-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on $ell_1$ and $ell_2$-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at url{https://github.com/lxiaorui/ElasticGNN}.
We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.
Creating aesthetically pleasing pieces of art, including music, has been a long-term goal for artificial intelligence research. Despite recent successes of long-short term memory (LSTM) recurrent neural networks (RNNs) in sequential learning, LSTM neural networks have not, by themselves, been able to generate natural-sounding music conforming to music theory. To transcend this inadequacy, we put forward a novel method for music composition that combines the LSTM with Grammars motivated by music theory. The main tenets of music theory are encoded as grammar argumented (GA) filters on the training data, such that the machine can be trained to generate music inheriting the naturalness of human-composed pieces from the original dataset while adhering to the rules of music theory. Unlike previous approaches, pitches and durations are encoded as one semantic entity, which we refer to as note-level encoding. This allows easy implementation of music theory grammars, as well as closer emulation of the thinking pattern of a musician. Although the GA rules are applied to the training data and never directly to the LSTM music generation, our machine still composes music that possess high incidences of diatonic scale notes, small pitch intervals and chords, in deference to music theory.
Reinforcement learning systems require good representations to work well. For decades practical success in reinforcement learning was limited to small domains. Deep reinforcement learning systems, on the other hand, are scalable, not dependent on domain specific prior knowledge and have been successfully used to play Atari, in 3D navigation from pixels, and to control high degree of freedom robots. Unfortunately, the performance of deep reinforcement learning systems is sensitive to hyper-parameter settings and architecture choices. Even well tuned systems exhibit significant instability both within a trial and across experiment replications. In practice, significant expertise and trial and error are usually required to achieve good performance. One potential source of the problem is known as catastrophic interference: when later training decreases performance by overriding previous learning. Interestingly, the powerful generalization that makes Neural Networks (NN) so effective in batch supervised learning might explain the challenges when applying them in reinforcement learning tasks. In this paper, we explore how online NN training and interference interact in reinforcement learning. We find that simply re-mapping the input observations to a high-dimensional space improves learning speed and parameter sensitivity. We also show this preprocessing reduces interference in prediction tasks. More practically, we provide a simple approach to NN training that is easy to implement, and requires little additional computation. We demonstrate that our approach improves performance in both prediction and control with an extensive batch of experiments in classic control domains.
Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.
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