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Register a new userMeasuring Information Transfer in Neural Networks
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Quantifying the information content in a neural network model is essentially estimating the models Kolmogorov complexity. Recent success of prequential coding on neural networks points to a promising path of deriving an efficient description length of a model. We propose a practical measure of the generalizable information in a neural network model based on prequential coding, which we term Information Transfer ($L_{IT}$). Theoretically, $L_{IT}$ is an estimation of the generalizable part of a models information content. In experiments, we show that $L_{IT}$ is consistently correlated with generalizable information and can be used as a measure of patterns or knowledge in a model or a dataset. Consequently, $L_{IT}$ can serve as a useful analysis tool in deep learning. In this paper, we apply $L_{IT}$ to compare and dissect information in datasets, evaluate representation models in transfer learning, and analyze catastrophic forgetting and continual learning algorithms. $L_{IT}$ provides an information perspective which helps us discover new insights into neural network learning.
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Graph neural networks (GNNs) have been shown with superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards the transferability of GNNs. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of Ours, a novel GNN framework based on ego-graph information maximization to analytically achieve this goal. Secondly, we specify the requirement of structure-respecting node features as the GNN input, and derive a rigorous bound of GNN transferability based on the difference between the local graph Laplacians of the source and target graphs. Finally, we conduct controlled synthetic experiments to directly justify our theoretical conclusions. Extensive experiments on real-world networks towards role identification show consistent results in the rigorously analyzed setting of direct-transfering, while those towards large-scale relation prediction show promising results in the more generalized and practical setting of transfering with fine-tuning.
We study the flow of information and the evolution of internal representations during deep neural network (DNN) training, aiming to demystify the compression aspect of the information bottleneck theory. The theory suggests that DNN training comprises a rapid fitting phase followed by a slower compression phase, in which the mutual information $I(X;T)$ between the input $X$ and internal representations $T$ decreases. Several papers observe compression of estimated mutual information on different DNN models, but the true $I(X;T)$ over these networks is provably either constant (discrete $X$) or infinite (continuous $X$). This work explains the discrepancy between theory and experiments, and clarifies what was actually measured by these past works. To this end, we introduce an auxiliary (noisy) DNN framework for which $I(X;T)$ is a meaningful quantity that depends on the networks parameters. This noisy framework is shown to be a good proxy for the original (deterministic) DNN both in terms of performance and the learned representations. We then develop a rigorous estimator for $I(X;T)$ in noisy DNNs and observe compression in various models. By relating $I(X;T)$ in the noisy DNN to an information-theoretic communication problem, we show that compression is driven by the progressive clustering of hidden representations of inputs from the same class. Several methods to directly monitor clustering of hidden representations, both in noisy and deterministic DNNs, are used to show that meaningful clusters form in the $T$ space. Finally, we return to the estimator of $I(X;T)$ employed in past works, and demonstrate that while it fails to capture the true (vacuous) mutual information, it does serve as a measure for clustering. This clarifies the past observations of compression and isolates the geometric clustering of hidden representations as the true phenomenon of interest.
Parameters in deep neural networks which are trained on large-scale databases can generalize across multiple domains, which is referred as transferability. Unfortunately, the transferability is usually defined as discrete states and it differs with domains and network architectures. Existing works usually heuristically apply parameter-sharing or fine-tuning, and there is no principled approach to learn a parameter transfer strategy. To address the gap, a parameter transfer unit (PTU) is proposed in this paper. The PTU learns a fine-grained nonlinear combination of activations from both the source and the target domain networks, and subsumes hand-crafted discrete transfer states. In the PTU, the transferability is controlled by two gates which are artificial neurons and can be learned from data. The PTU is a general and flexible module which can be used in both CNNs and RNNs. Experiments are conducted with various network architectures and multiple transfer domain pairs. Results demonstrate the effectiveness of the PTU as it outperforms heuristic parameter-sharing and fine-tuning in most settings.
Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned for the node feature updating. However, existing propagation schemes are far from being optimal since they do not fully utilize the relational information between nodes. We propose the information maximizing graph neural networks (IGNN), which maximizes the mutual information between edge states and transform parameters. We reformulate the mutual information as a differentiable objective via a variational approach. We compare our model against several recent variants of GNNs and show that our model achieves the state-of-the-art performance on multiple tasks including quantum chemistry regression on QM9 dataset, generalization capability from QM9 to larger molecular graphs, and prediction of molecular bioactivities relevant for drug discovery. The IGNN model is based on an elegant and fundamental idea in information theory as explained in the main text, and it could be easily generalized beyond the contexts of molecular graphs considered in this work. To encourage more future work in this area, all datasets and codes used in this paper will be released for public access.
Compact neural networks are essential for affordable and power efficient deep learning solutions. Binary Neural Networks (BNNs) take compactification to the extreme by constraining both weights and activations to two levels, ${+1, -1}$. However, training BNNs are not easy due to the discontinuity in activation functions, and the training dynamics of BNNs is not well understood. In this paper, we present an information-theoretic perspective of BNN training. We analyze BNNs through the Information Bottleneck principle and observe that the training dynamics of BNNs is considerably different from that of Deep Neural Networks (DNNs). While DNNs have a separate empirical risk minimization and representation compression phases, our numerical experiments show that in BNNs, both these phases are simultaneous. Since BNNs have a less expressive capacity, they tend to find efficient hidden representations concurrently with label fitting. Experiments in multiple datasets support these observations, and we see a consistent behavior across different activation functions in BNNs.
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