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1. Kernel and Rich Regimes in Overparametrized Models

   Woodworth, Blake; Gunasekar, Suriya; Lee, Jason D; Moroshko, Edward; Savarese, Pedro; Golan, Itay; Soudry, Daniel; Srebro, Nathan (February 2020, Conference on Learning Theory (COLT))

   A recent line of work studies overparametrized neural networks in the “kernel regime,” i.e. when during training the network behaves as a kernelized linear predictor, and thus, training with gradient descent has the effect of finding the corresponding minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized networks can induce rich implicit biases that are not RKHS norms. Building on an observation by \citet{chizat2018note}, we show how the \textbf{\textit{scale of the initialization}} controls the transition between the “kernel” (aka lazy) and “rich” (aka active) regimes and affects generalization properties in multilayer homogeneous models. We provide a complete and detailed analysis for a family of simple depth-D linear networks that exhibit an interesting and meaningful transition between the kernel and rich regimes, and highlight an interesting role for the \emph{width} of the models. We further demonstrate this transition empirically for matrix factorization and multilayer non-linear networks. 

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2. Self-Regularity of Non-Negative Output Weightsfor Overparameterized Two-Layer Neural Networks

   Gamarnik, David; Kızıldağ, Eren C.; Zadik, Ilias (January 2021, International Symposium on Information Theory)

   null (Ed.)

   We consider the problem of finding a two-layer neural network with sigmoid, rectified linear unit (ReLU), or binary step activation functions that "fits" a training data set as accurately as possible as quantified by the training error; and study the following question: \emph{does a low training error guarantee that the norm of the output layer (outer norm) itself is small?} We answer affirmatively this question for the case of non-negative output weights. Using a simple covering number argument, we establish that under quite mild distributional assumptions on the input/label pairs; any such network achieving a small training error on polynomially many data necessarily has a well-controlled outer norm. Notably, our results (a) have a polynomial (in d) sample complexity, (b) are independent of the number of hidden units (which can potentially be very high), (c) are oblivious to the training algorithm; and (d) require quite mild assumptions on the data (in particular the input vector X∈ℝd need not have independent coordinates). We then leverage our bounds to establish generalization guarantees for such networks through \emph{fat-shattering dimension}, a scale-sensitive measure of the complexity class that the network architectures we investigate belong to. Notably, our generalization bounds also have good sample complexity (polynomials in d with a low degree), and are in fact near-linear for some important cases of interest. 

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3. Graph Communal Contrastive Learning

   https://doi.org/10.1145/3485447.3512208  

   Li, Bolian; Jing, Baoyu; Tong, Hanghang (April 2022, Graph Communal Contrastive Learning)

   Graph representation learning is crucial for many real-world ap- plications (e.g. social relation analysis). A fundamental problem for graph representation learning is how to effectively learn rep- resentations without human labeling, which is usually costly and time-consuming. Graph contrastive learning (GCL) addresses this problem by pulling the positive node pairs (or similar nodes) closer while pushing the negative node pairs (or dissimilar nodes) apart in the representation space. Despite the success of the existing GCL methods, they primarily sample node pairs based on the node- level proximity yet the community structures have rarely been taken into consideration. As a result, two nodes from the same community might be sampled as a negative pair. We argue that the community information should be considered to identify node pairs in the same communities, where the nodes insides are seman- tically similar. To address this issue, we propose a novel Graph Communal Contrastive Learning (𝑔𝐶𝑜𝑜𝐿) framework to jointly learn the community partition and learn node representations in an end-to-end fashion. Specifically, the proposed 𝑔𝐶𝑜𝑜𝐿 consists of two components: a Dense Community Aggregation (𝐷𝑒𝐶𝐴) algo- rithm for community detection and a Reweighted Self-supervised Cross-contrastive (𝑅𝑒𝑆𝐶) training scheme to utilize the community information. Additionally, the real-world graphs are complex and often consist of multiple views. In this paper, we demonstrate that the proposed 𝑔𝐶𝑜𝑜𝐿 can also be naturally adapted to multiplex graphs. Finally, we comprehensively evaluate the proposed 𝑔𝐶𝑜𝑜𝐿 on a variety of real-world graphs. The experimental results show that the 𝑔𝐶𝑜𝑜𝐿 outperforms the state-of-the-art methods. 

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4. Robust Contrastive Learning Using Negative Samples with Diminished Semantics

   Songwei Ge, Shlok Mishra (January 2021, Advances in neural information processing systems)

   Unsupervised learning has recently made exceptional progress because of the development of more effective contrastive learning methods. However, CNNs are prone to depend on low-level features that humans deem non-semantic. This dependency has been conjectured to induce a lack of robustness to image perturbations or domain shift. In this paper, we show that by generating carefully designed negative samples, contrastive learning can learn more robust representations with less dependence on such features. Contrastive learning utilizes positive pairs which preserve semantic information while perturbing superficial features in the training images. Similarly, we propose to generate negative samples in a reversed way, where only the superfluous instead of the semantic features are preserved. We develop two methods, texture-based and patch-based augmentations, to generate negative samples. These samples achieve better generalization, especially under out-of-domain settings. We also analyze our method and the generated texture-based samples, showing that texture features are indispensable in classifying particular ImageNet classes and especially finer classes. We also show that the model bias between texture and shape features favors them differently under different test settings. 

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5. How neural networks extrapolate: from feedforward to graph neural networks

   Xu, Keyulu; Zhang, Mozhi; Li, Jingling; Du, Simon S.; Kawarabayashi, Ken-ichi; Jegelka, Stefanie (January 2021, International Conference on Learning Representations (ICLR))

   null (Ed.)

   We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) – structured networks with MLP modules – have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently “diverse”. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings. 

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