nils-herrmann/clean_scirepeval huggingface dataset:
Prediction and generalisation over directed actions by grid cells
Authors: Changmin Yu, Timothy Behrens, Neil Burgess

Knowing how the effects of directed actions generalise to new situations (e.g. moving North, South, East and West, or turning left, right, etc.) is key to rapid generalisation across new situations. Markovian tasks can be characterised by a state space and a transition matrix and recent work has proposed that neural grid codes provide an efficient representation of the state space, as eigenvectors of a transition matrix reflecting diffusion across states, that allows efficient prediction of future state distributions. Here we extend the eigenbasis prediction model, utilising tools from Fourier analysis, to prediction over arbitrary translation-invariant directed transition structures (i.e. displacement and diffusion), showing that a single set of eigenvectors can support predictions over arbitrary directed actions via action-specific eigenvalues. We show how to define a "sense of direction" to combine actions to reach a target state (ignoring task-specific deviations from translation-invariance), and demonstrate that adding the Fourier representations to a deep Q network aids policy learning in continuous control tasks. We show the equivalence between the generalised prediction framework and traditional models of grid cell firing driven by self-motion to perform path integration, either using oscillatory interference (via Fourier components as velocity-controlled oscillators) or continuous attractor networks (via analysis of the update dynamics). We thus provide a unifying framework for the role of the grid system in predictive planning, sense of direction and path integration: supporting generalisable inference over directed actions across different tasks.
Characterizing Structural Regularities of Labeled Data in Overparameterized Models
Authors: Ziheng Jiang, Chiyuan Zhang, Kunal Talwar, Michael Curtis Mozer

Humans are accustomed to environments that contain both regularities and exceptions. For example, at most gas stations, one pays prior to pumping, but the occasional rural station does not accept payment in advance.
Likewise, deep neural networks can generalize across instances that share common patterns or structures yet have the capacity to memorize rare or irregular forms. We analyze how individual instances are treated by a model via  a consistency score. The score characterizes the expected accuracy for a held-out instance given training sets of varying size sampled from the data distribution. We obtain empirical estimates of this score for individual instances in multiple data-sets, and we show that the score identifies out-of-distribution and mislabeled examples at one end of the continuum and strongly regular examples at the other end. We identify computationally inexpensive proxies to the consistency score using statistics collected during training. We apply the score toward understanding the dynamics of representation learning and to filter outliers during training, and we discuss other potential applications including curriculum learning and active data collection.
AutoNF: Automated Architecture Optimization of Normalizing Flows Using a Mixture Distribution Formulation
Authors: Yu Wang, Jan Drgona, Jiaxin Zhang, Karthik Somayaji NS, Frank Y Liu, Malachi Schram, Peng Li

Although various flow models based on different transformations have been proposed, there still lacks a quantitative analysis of performance-cost trade-offs between different flows as well as a systematic way of constructing the best flow architecture. To tackle this challenge, we present an automated normalizing flow (NF) architecture search method. Our method aims to find the optimal sequence of transformation layers from a given set of unique transformations with three folds. First, a mixed distribution is formulated to enable efficient architecture optimization originally on the discrete space without violating the invertibility of the resulting NF architecture. Second, the mixture NF is optimized with an approximate upper bound which has a more preferable global minimum. Third, a block-wise alternating optimization algorithm is proposed to ensure efficient architecture optimization of deep flow models.
Autoregressive Latent Video Prediction with High-Fidelity Image Generator
Authors: Younggyo Seo, Kimin Lee, Fangchen Liu, Stephen James, Pieter Abbeel

Video prediction is an important yet challenging problem; burdened with the tasks of generating future frames and learning environment dynamics. Recently, autoregressive latent video models have proved to be a powerful video prediction tool, by separating the video prediction into two sub-problems: pre-training an image generator model, followed by learning an autoregressive prediction model in the latent space of the image generator. However, successfully generating high-fidelity and high-resolution videos has yet to be seen. In this work, we investigate how to train an autoregressive latent video prediction model capable of predicting high-fidelity future frames with minimal modification to existing models, and produce high-resolution (256x256) videos. Specifically, we scale up prior models by employing a high-fidelity image generator (VQ-GAN) with a causal transformer model, and introduce additional techniques of top-$k$ sampling and data augmentation to further improve video prediction quality. Despite the simplicity, the proposed method achieves competitive performance to state-of-the-art approaches on standard video prediction benchmarks with fewer parameters, and enables high-resolution video prediction on complex and large-scale datasets. Videos are available at the anonymized website https://sites.google.com/view/harp-anonymous
A Stochastic Trust Region Method for Non-convex Minimization
Authors: Zebang Shen, Pan Zhou, Cong Fang, Jiahao Xie, Alejandro Ribeiro

We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order $\mathcal{O}({1}/{k^{2/3}})$ as long as those differential estimations are sufficiently accurate.
Combining such result with a novel Hessian estimator, we propose a sample-efficient stochastic trust region (STR) algorithm which finds an $(\epsilon, \sqrt{\epsilon})$-approximate local minimum within $\tilde{\mathcal{O}}({\sqrt{n}}/{\epsilon^{1.5}})$ stochastic Hessian oracle queries. 
This improves the state-of-the-art result by a factor of $\mathcal{O}(n^{1/6})$. Finally,  we also develop Hessian-free STR algorithms which achieve the lowest runtime complexity. 
Experiments verify theoretical conclusions and the efficiency of the proposed algorithms.
Selective Brain Damage: Measuring the Disparate Impact of Model Pruning
Authors: Sara Hooker, Yann Dauphin, Aaron Courville, Andrea Frome

Neural network pruning techniques have demonstrated it is possible to remove the majority of weights in a network with surprisingly little degradation to top-1 test set accuracy. However, this measure of performance conceals significant differences in how different classes and images are impacted by pruning. We find that certain individual data points, which we term pruning identified exemplars (PIEs), and classes are systematically more impacted by the introduction of sparsity. Removing PIE images from the test-set greatly improves top-1 accuracy for both sparse and non-sparse models. These hard-to-generalize-to images tend to be of lower image quality, mislabelled, entail abstract representations, require fine-grained classification or depict atypical class examples.
ProxSGD: Training Structured Neural Networks under Regularization and Constraints
Authors: Yang Yang, Yaxiong Yuan, Avraam Chatzimichailidis, Ruud JG van Sloun, Lei Lei, Symeon Chatzinotas

In this paper, we consider the problem of training neural networks (NN). To promote a NN with specific structures, we explicitly take into consideration the nonsmooth regularization (such as L1-norm) and constraints (such as interval constraint). This is formulated as a constrained nonsmooth nonconvex optimization problem, and we propose a convergent proximal-type stochastic gradient descent (Prox-SGD) algorithm. We show that under properly selected learning rates, momentum eventually resembles the unknown real gradient and thus is crucial in analyzing the convergence. We establish that with probability 1, every limit point of the sequence generated by the proposed Prox-SGD is a stationary point. Then the Prox-SGD is tailored to train a sparse neural network and a binary neural network, and the theoretical analysis is also supported by extensive numerical tests.
Space-Time Graph Neural Networks
Authors: Samar Hadou, Charilaos I Kanatsoulis, Alejandro Ribeiro

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators.  We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.
GraphSAD: Learning Graph Representations with Structure-Attribute Disentanglement
Authors: Minghao Xu, Hang Wang, Bingbing Ni, Wenjun Zhang, Jian Tang

Graph Neural Networks (GNNs) learn effective node/graph representations by aggregating the attributes of neighboring nodes, which commonly derives a single representation mixing the information of graph structure and node attributes. However, these two kinds of information might be semantically inconsistent and could be useful for different tasks. In this paper, we aim at learning node/graph representations with Structure-Attribute Disentanglement (GraphSAD). We propose to disentangle graph structure and node attributes into two distinct sets of representations, and such disentanglement can be done in either the input or the embedding space. We further design a metric to quantify the extent of such a disentanglement. Extensive experiments on multiple datasets show that our approach can indeed disentangle the semantics of graph structure and node attributes, and it achieves superior performance on both node and graph classification tasks.
Shifting Mean Activation Towards Zero with Bipolar Activation Functions
Authors: Lars Hiller Eidnes, Arild Nøkland

We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with up to 144 layers, and show that bipolar activation functions help learning in this setting. On the Penn Treebank and Text8 language modeling tasks we obtain competitive results, improving on the best reported results for non-gated networks. In experiments with convolutional neural networks without batch normalization, we find that bipolar activations produce a faster drop in training error, and results in a lower test error on the CIFAR-10 classification task.
Toward Understanding Generalization of Over-parameterized Deep ReLU network trained with SGD in Student-teacher Setting
Authors: Yuandong Tian

To analyze deep ReLU network, we adopt a student-teacher setting in which an over-parameterized student network learns from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). Our contributions are two-fold. First, we prove that when the gradient is zero (or bounded above by a small constant) at every data point in training, a situation called  \emph{interpolation setting}, there exists many-to-one \emph{alignment} between student and teacher nodes in the lowest layer under mild conditions. This suggests that generalization in unseen dataset is achievable, even the same condition often leads to zero training error. Second, analysis of noisy recovery and training dynamics in 2-layer network shows that strong teacher nodes (with large fan-out weights) are learned first and subtle teacher nodes are left unlearned until late stage of training. As a result, it could take a long time to converge into these small-gradient critical points. Our analysis shows that over-parameterization plays two roles: (1) it is a necessary condition for alignment to happen at the critical points, and (2) in training dynamics, it helps student nodes cover more teacher nodes with fewer iterations. Both improve generalization. Experiments justify our finding.
Batch-shaping for learning conditional channel gated networks
Authors: Babak Ehteshami Bejnordi, Tijmen Blankevoort, Max Welling

We present a method that trains large capacity neural networks with significantly improved accuracy and lower dynamic computational cost. This is achieved by gating the deep-learning architecture on a fine-grained-level. Individual convolutional maps are turned on/off conditionally on features in the network. To achieve this, we introduce a new residual block architecture that gates convolutional channels in a fine-grained manner. We also introduce a generally applicable tool batch-shaping that matches the marginal aggregate posteriors of features in a neural network to a pre-specified prior distribution. We use this novel technique to force gates to be more conditional on the data. We present results on CIFAR-10 and ImageNet datasets for image classification, and Cityscapes for semantic segmentation. Our results show that our method can slim down large architectures conditionally, such that the average computational cost on the data is on par with a smaller architecture, but with higher accuracy. In particular, on ImageNet, our ResNet50 and ResNet34 gated networks obtain 74.60% and 72.55% top-1 accuracy compared to the 69.76% accuracy of the baseline ResNet18 model, for similar complexity. We also show that the resulting networks automatically learn to use more features for difficult examples and fewer features for simple examples.
Sqrt(d) Dimension Dependence of Langevin Monte Carlo
Authors: Ruilin Li, Hongyuan Zha, Molei Tao

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li et al. (2019), and this refined framework automates the analysis of a large class of sampling algorithms based on discretizations of contractive SDEs. Using this framework, we establish an $\tilde{O}(\sqrt{d}/\epsilon)$ mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known $\tilde{O}(d/\epsilon)$ result and is optimal (in terms of order) in both dimension $d$ and accuracy tolerance $\epsilon$ for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.
Automatically Discovering and Learning New Visual Categories with Ranking Statistics
Authors: Kai Han, Sylvestre-Alvise Rebuffi, Sebastien Ehrhardt, Andrea Vedaldi, Andrew Zisserman

We tackle the problem of discovering novel classes in an image collection given labelled examples of other classes. This setting is similar to semi-supervised learning, but significantly harder because there are no labelled examples for the new classes. The challenge, then, is to leverage the information contained in the labelled images in order to learn a general-purpose clustering model and use the latter to identify the new classes in the unlabelled data. In this work we address this problem by combining three ideas: (1) we suggest that the common approach of bootstrapping an image representation using the labeled data only introduces an unwanted bias, and that this can be avoided by using self-supervised learning to train the representation from scratch on the union of labelled and unlabelled data; (2) we use rank statistics to transfer the model's knowledge of the labelled classes to the problem of clustering the unlabelled images; and, (3) we train the data representation by optimizing a joint objective function on the labelled and unlabelled subsets of the data, improving both the supervised classification of the labelled data, and the clustering of the unlabelled data. We evaluate our approach on standard classification benchmarks and outperform current methods for novel category discovery by a significant margin.
Attention on Abstract Visual Reasoning
Authors: Lukas Hahne, Timo Lüddecke, Florentin Wörgötter, David Kappel

Attention mechanisms have been boosting the performance of deep learning models on a wide range of applications, ranging from speech understanding to program induction.  However, despite experiments from psychology which suggest that attention plays an essential role in visual reasoning, the full potential of attention mechanisms has so far not been explored to solve abstract cognitive tasks on image data. In this work, we propose a hybrid network architecture, grounded on self-attention and relational reasoning. We call this new model Attention Relation Network (ARNe). ARNe combines features from the recently introduced Transformer and the Wild Relation Network (WReN). We test ARNe on the Procedurally Generated Matrices (PGMs) datasets for abstract visual reasoning. ARNe excels the WReN model on this task by 11.28 ppt. Relational concepts between objects are efficiently learned demanding only 35% of the training samples to surpass reported accuracy of the base line model. Our proposed hybrid model, represents an alternative on learning abstract relations using self-attention and demonstrates that the Transformer network is also well suited for abstract visual reasoning.
Deterministic Policy Imitation Gradient Algorithm
Authors: Fumihiro Sasaki, Atsuo Kawaguchi

The goal of imitation learning (IL) is to enable a learner to imitate an expert’s behavior given the expert’s demonstrations. Recently, generative adversarial imitation learning (GAIL) has successfully achieved it even on complex continuous control tasks. However, GAIL requires a huge number of interactions with environment during training. We believe that IL algorithm could be more applicable to the real-world environments if the number of interactions could be reduced. To this end, we propose a model free, off-policy IL algorithm for continuous control. The keys of our algorithm are two folds: 1) adopting deterministic policy that allows us to derive a novel type of policy gradient which we call deterministic policy imitation gradient (DPIG), 2) introducing a function which we call state screening function (SSF) to avoid noisy policy updates with states that are not typical of those appeared on the expert’s demonstrations. Experimental results show that our algorithm can achieve the goal of IL with at least tens of times less interactions than GAIL on a variety of continuous control tasks.
Adaptive Label Smoothing with Self-Knowledge
Authors: Dongkyu Lee, Ka Chun Cheung, Nevin Zhang

Overconfidence has been shown to impair generalization and calibration of a neural network. Previous studies remedy this issue by adding a regularization term to a loss function, preventing a model from making a peaked distribution. Label smoothing smoothes target labels with a predefined prior label distribution; as a result, a model is learned to maximize the likelihood of predicting the soft label. Nonetheless, the amount of smoothing is the same in all samples and remains fixed in training. In other words, label smoothing does not reflect the change in probability distribution mapped by a model over the course of training. To address this issue, we propose a regularization scheme that brings dynamic nature into the smoothing parameter by taking model probability distribution into account, thereby varying the parameter per instance. A model in training self-regulates the extent of smoothing on the fly during forward propagation. Furthermore, inspired by recent work in bridging label smoothing and knowledge distillation, our work utilizes self-knowledge as a prior label distribution in softening target labels, and presents theoretical support for the regularization effect by knowledge distillation. Our regularizer is validated comprehensively on various datasets in machine translation and outperforms strong baselines not only in model performance but also in model calibration by a large margin.
Sobolev Training for the Neural Network Solutions of PDEs
Authors: Hwijae Son, Jin Woo Jang, Woo Jin Han, Hyung Ju Hwang

Approximating the numerical solutions of partial differential equations (PDEs) using neural networks is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be intuitively designed and guarantees the convergence for various kinds of PDEs. However, the rate of convergence has been considered as a weakness of this approach. This paper introduces a novel loss function for the training of neural networks to find the solutions of PDEs, making the training substantially efficient. Inspired by the recent studies that incorporate derivative information for the training of neural networks, we develop a loss function that guides a neural network to reduce the error in the corresponding Sobolev space. Surprisingly, a simple modification of the loss function can make the training process similar to Sobolev Training although solving PDEs with neural networks is not a fully supervised learning task. We provide several theoretical justifications for such an approach for the viscous Burgers equation and the kinetic Fokker--Planck equation. We also present several simulation results, which show that compared with the traditional $L^2$ loss function, the proposed loss function guides the neural network to a significantly faster convergence. Moreover, we provide the empirical evidence that shows that the proposed loss function, together with the iterative sampling techniques, performs better in solving high dimensional PDEs.