We present a framework based on bilevel optimization for learning multilayer, deep data representations. On the one hand, the lower-level problem finds a representation by successively minimizing layer-wise objectives made of the sum of a prescribed regularizer as well as a fidelity term and some linear function both depending on the representation found at the previous layer. On the other hand, the upper-level problem optimizes over the linear functions to yield a linearly separable final representation. We show that, by choosing the fidelity term as the quadratic distance between two successive layer-wise representations, the bilevel problem reduces to the training of a feed-forward neural network. Instead, by elaborating on Bregman distances, we devise a novel neural network architecture additionally involving the inverse of the activation function reminiscent of the skip connection used in ResNets. Numerical experiments suggest that the proposed Bregman variant benefits from better learning properties and more robust prediction performance.

The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the notion of linearly disentangled representations, but there is currently no metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and to compare them to previous understandings of disentanglement. We propose D_LSBD, a mathematically sound metric to quantify LSBD, and provide a practical implementation for SO(2) groups. Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to learn LSBD representations. We demonstrate the utility of our metric by showing that (1) common VAE-based disentanglement methods don't learn LSBD representations, (2) LSBD-VAE, as well as other recent methods, can learn LSBD representations needing only limited supervision on transformations, and (3) various desirable properties expressed by existing disentanglement metrics are also achieved by LSBD representations.

Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular G-CNNs, and show considerable parameter redundancy in group convolution kernels. This finding motivates further weight-tying by sharing convolution kernels over subgroups. To this end, we introduce convolution kernels that are separable over the subgroup and channel dimensions. In order to obtain equivariance to arbitrary affine Lie groups we provide a continuous parameterisation of separable convolution kernels. We evaluate our approach across several vision datasets, and show that our weight sharing leads to improved performance and computational efficiency. In many settings, separable G-CNNs outperform their non-separable counterpart, while only using a fraction of their training time. In addition, thanks to the increase in computational efficiency, we are able to implement G-CNNs equivariant to the $\mathrm{Sim(2)}$ group; the group of dilations, rotations and translations of the plane. $\mathrm{Sim(2)}$-equivariance further improves performance on all tasks considered, and achieves state-of-the-art performance on rotated MNIST.

Steerable models can provide very general and flexible equivariance by formulating equivariance requirements in the language of representation theory and feature fields, which has been recognized to be effective for many vision tasks. However, deriving steerable models for 3D rotations is much more difficult than that in the 2D case, due to more complicated mathematics of 3D rotations. In this work, we employ partial differential operators (PDOs) to model 3D filters, and derive general steerable 3D CNNs, which are called PDO-s3DCNNs. We prove that the equivariant filters are subject to linear constraints, which can be solved efficiently under various conditions. As far as we know, PDO-s3DCNNs are the most general steerable CNNs for 3D rotations, in the sense that they cover all common subgroups of SO(3) and their representations, while existing methods can only be applied to specific groups and representations. Extensive experiments show that our models can preserve equivariance well in the discrete domain, and outperform previous works on SHREC'17 retrieval and ISBI 2012 segmentation tasks with a low network complexity.

We present an approach that incorporates expert knowledge for time-series representation learning. Our method employs expert features to replace the commonly used data transformations in previous contrastive learning approaches. We do this since time-series data frequently stems from the industrial or medical field where expert features are often available from domain experts, while transformations are generally elusive for time-series data. We start by proposing two properties that useful time-series representations should fulfill and show that current representation learning approaches do not ensure these properties. We therefore devise ExpCLR, a novel contrastive learning approach built on an objective that utilizes expert features to encourage both properties for the learned representation. Finally, we demonstrate on three real-world time-series datasets that ExpCLR surpasses several state-of-the-art methods for both unsupervised and semi-supervised representation learning.

Predictive coding networks (PCNs) are (un)supervised learning models, coming from neuroscience, that approximate how the brain works. One major open problem around PCNs is their convergence behavior.In this paper, we use dynamical systems theory to formally investigate the convergence of PCNs as they are used in machine learning. Doing so, we put their theory on a firm, rigorous basis, by developing a precise mathematical framework for PCN and show that for sufficiently small weights and initializations, PCNs converge for any input. Thereby, we provide the theoretical assurance that previous implementations, whose convergence was assessed solely by numerical experiments, can indeed capture the correct behavior of PCNs. Outside of the identified regime of small weights and small initializations, we show via a counterexample that PCNs can diverge, countering common beliefs held in the community. This is achieved by identifying a Neimark-Sacker bifurcation in a PCN of small size, which gives rise to an unstable fixed point and an invariant curve around it.

Comparison of data representations is a complex multi-aspect problem. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD) score measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The two data point clouds can lie in different ambient spaces. The RTD score is one of the few topological data analysis based practical methods applicable to real machine learning datasets. Experiments show the agreement of RTD with the intuitive assessment of data representation similarity. The proposed RTD score is sensitive to the data representation's fine topological structure. We use the RTD score to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment.

A major challenge in studying robustness in deep learning is defining the set of meaningless perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference human NN to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances, for which we propose a measure called STIR. STIR re-purposes existing representation similarity measures to make them suitable for measuring shared invariances. Using our measure, we are able to gain insights into how shared invariances vary with changes in weight initialization, architecture, loss functions, and training dataset. Our implementation is available at: https://github.com/nvedant07/STIR

Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the entire training experience. While this has been technically known since the 1960s, no prior work has effectively studied the operations of NNs in such a form, presumably due to prohibitive time and space complexities and impractical model sizes, all of them growing linearly with the number of training patterns which may get very large. However, this dual formulation offers a possibility of directly visualising how an NN makes use of training patterns at test time, by examining the corresponding attention weights. We conduct experiments on small scale supervised image classification tasks in single-task, multi-task, and continual learning settings, as well as language modelling, and discuss potentials and limits of this view for better understanding and interpreting how NNs exploit training patterns. Our code is public.

Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling up to bigger models. Previous methods mainly utilize the similarity decomposition and the associativity of matrix multiplication to devise linear-time attention mechanisms. They avoid degeneration of attention to a trivial distribution by reintroducing inductive biases such as the locality, thereby at the expense of model generality and expressiveness. In this paper, we linearize Transformers free from specific inductive biases based on the flow network theory. We cast attention as the information flow aggregated from the sources (values) to the sinks (results) through the learned flow capacities (attentions). Within this framework, we apply the property of flow conservation into attention and propose the Flow-Attention mechanism of linear complexity. By respectively conserving the incoming flow of sinks for source competition and the outgoing flow of sources for sink allocation, Flow-Attention inherently generates informative attentions without using specific inductive biases. Empowered by the Flow-Attention, Flowformer yields strong performance in linear time for wide areas, including long sequence, time series, vision, natural language, and reinforcement learning. The code and settings are available at this repository: https://github.com/thuml/Flowformer.

Recently, neural architectures with all Multi-layer Perceptrons (MLPs) have attracted great research interest from the computer vision community. However, the inefficient mixing of spatial-channel information causes MLP-like vision models to demand tremendous pre-training on large-scale datasets. This work solves the problem from a novel knowledge distillation perspective. We propose a novel Spatial-channel Token Distillation (STD) method, which improves the information mixing in the two dimensions by introducing distillation tokens to each of them. A mutual information regularization is further introduced to let distillation tokens focus on their specific dimensions and maximize the performance gain. Extensive experiments on ImageNet for several MLP-like architectures demonstrate that the proposed token distillation mechanism can efficiently improve the accuracy. For example, the proposed STD boosts the top-1 accuracy of Mixer-S16 on ImageNet from 73.8% to 75.7% without any costly pre-training on JFT-300M. When applied to stronger architectures, e.g. CycleMLP-B1 and CycleMLP-B2, STD can still harvest about 1.1% and 0.5% accuracy gains, respectively.

Artificial Neural Networks are functionally equivalent to special-purpose computers. Their inter-neuronal connection weights represent the learnt Neural Program that instructs the networks on how to compute the data. However, without storing Neural Programs, they are restricted to only one, overwriting learnt programs when trained on new data. Here we design Neurocoder, a new class of general-purpose neural networks in which the neural network “codes” itself in a data-responsive way by composing relevant programs from a set of shareable, modular programs stored in external memory. This time, a Neural Program is efficiently treated as data in memory. Integrating Neurocoder into current neural architectures, we demonstrate new capacity to learn modular programs, reuse simple programs to build complex ones, handle pattern shifts and remember old programs as new ones are learnt, and show substantial performance improvement in solving object recognition, playing video games and continual learning tasks.

Multi-head attention is a driving force behind state-of-the-art transformers, which achieve remarkable performance across a variety of natural language processing (NLP) and computer vision tasks. It has been observed that for many applications, those attention heads learn redundant embedding, and most of them can be removed without degrading the performance of the model. Inspired by this observation, we propose Transformer with a Mixture of Gaussian Keys (Transformer-MGK), a novel transformer architecture that replaces redundant heads in transformers with a mixture of keys at each head. These mixtures of keys follow a Gaussian mixture model and allow each attention head to focus on different parts of the input sequence efficiently. Compared to its conventional transformer counterpart, Transformer-MGK accelerates training and inference, has fewer parameters, and requires fewer FLOPs to compute while achieving comparable or better accuracy across tasks. Transformer-MGK can also be easily extended to use with linear attention. We empirically demonstrate the advantage of Transformer-MGK in a range of practical applications, including language modeling and tasks that involve very long sequences. On the Wikitext-103 and Long Range Arena benchmark, Transformer-MGKs with 4 heads attain comparable or better performance to the baseline transformers with 8 heads.

Attention mechanisms are dominating the explainability of deep models. They produce probability distributions over the input, which are widely deemed as feature-importance indicators. However, in this paper, we find one critical limitation in attention explanations: weakness in identifying the polarity of feature impact. This would be somehow misleading -- features with higher attention weights may not faithfully contribute to model predictions; instead, they can impose suppression effects. With this finding, we reflect on the explainability of current attention-based techniques, such as Attention ⨀ Gradient and LRP-based attention explanations. We first propose an actionable diagnostic methodology (henceforth faithfulness violation test) to measure the consistency between explanation weights and the impact polarity. Through the extensive experiments, we then show that most tested explanation methods are unexpectedly hindered by the faithfulness violation issue, especially the raw attention. Empirical analyses on the factors affecting violation issues further provide useful observations for adopting explanation methods in attention models.

Micro- and macro-architecture search have emerged as two popular NAS paradigms recently. Existing methods leverage different search strategies for searching micro- and macro- architectures. When using architecture parameters to search for micro-structure such as normal cell and reduction cell, the architecture parameters can not fully reflect the corresponding operation importance. When searching for the macro-structure chained by pre-defined blocks, many sub-networks need to be sampled for evaluation, which is very time-consuming. To address the two issues, we propose a new search paradigm, that is, leverage the attention mechanism to guide the micro- and macro-architecture search, namely AGNAS. Specifically, we introduce an attention module and plug it behind each candidate operation or each candidate block. We utilize the attention weights to represent the importance of the relevant operations for the micro search or the importance of the relevant blocks for the macro search. Experimental results show that AGNAS can achieve 2.46% test error on CIFAR-10 in the DARTS search space, and 23.4% test error when directly searching on ImageNet in the ProxylessNAS search space. AGNAS also achieves optimal performance on NAS-Bench-201, outperforming state-of-the-art approaches. The source code can be available at https://github.com/Sunzh1996/AGNAS.