DeepNLP/ICLR-2023-Accepted-Papers huggingface dataset:
Subquadratic Algorithms for Kernel Matrices via Kernel Density Estimation
Authors: Ainesh Bakshi,Piotr Indyk,Praneeth Kacham,Sandeep Silwal,Samson Zhou

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is efficiency -- given $n$ input points, most kernel-based algorithms need to materialize the full $n \times n$ kernel matrix before performing any subsequent computation, thus incurring $\Omega(n^2)$ runtime. Breaking this quadratic barrier for various problems has therefore, been a subject of extensive research efforts. 

We break the quadratic barrier and obtain \emph{subquadratic} time  algorithms for several fundamental linear-algebraic and graph processing primitives, including approximating the top eigenvalue and eigenvector, spectral sparsification, solving linear systems, local clustering, low-rank approximation, arboricity estimation and counting weighted triangles. We build on the recently developed Kernel Density Estimation framework, which (after preprocessing in time subquadratic in $n$) can return estimates of row/column sums of the kernel matrix. In particular, we develop efficient reductions from \emph{weighted vertex} and \emph{weighted edge sampling} on kernel graphs, \emph{simulating random walks} on kernel graphs, and \emph{importance sampling} on matrices to Kernel Density Estimation and show that we can generate samples from these distributions in \emph{sublinear} (in the support of the distribution) time. Our reductions are the central ingredient in each of our applications and we believe they may be of independent interest. We empirically demonstrate the efficacy of our algorithms on low-rank approximation (LRA) and spectral sparsification, where we observe a $\textbf{9x}$ decrease in the number of kernel evaluations over baselines for LRA and a $\textbf{41x}$ reduction in the graph size for spectral sparsification.
A Higher Precision Algorithm for Computing the $1$-Wasserstein Distance
Authors: Pankaj K Agarwal,Sharath Raghvendra,Pouyan Shirzadian,Rachita Sowle

We consider the problem of computing the $1$-Wasserstein distance $\mathcal{W}(\mu,\nu)$ between two $d$-dimensional discrete distributions $\mu$ and $\nu$ whose support lie within the unit hypercube. There are several algorithms that estimate $\mathcal{W}(\mu,\nu)$ within an additive error of $\varepsilon$. However, when $\mathcal{W}(\mu,\nu)$ is small, the additive error $\varepsilon$ dominates, leading to noisy results. Consider any additive approximation algorithm with execution time $T(n,\varepsilon)$. We propose an algorithm that runs in $O(T(n,\varepsilon/d) \log n)$ time and boosts the accuracy of estimating $\mathcal{W}(\mu,\nu)$ from $\varepsilon$ to an expected additive error of $\min\{\varepsilon, (d\log_{\sqrt{d}/\varepsilon} n)\mathcal{W}(\mu,\nu)\}$. For the special case where every point in the support of $\mu$ and $\nu$ has a mass of $1/n$ (also called the Euclidean Bipartite Matching problem), we describe an algorithm to boost the accuracy of any additive approximation algorithm from $\varepsilon$ to an expected additive error of $\min\{\varepsilon, (d\log\log n)\mathcal{W}(\mu,\nu)\}$ in $O(T(n, \varepsilon/d)\log\log n)$ time.
Revisiting adapters with adversarial training
Authors: Sylvestre-Alvise Rebuffi,Francesco Croce,Sven Gowal

While adversarial training is generally used as a defense mechanism, recent works show that it can also act as a regularizer. By co-training a neural network on clean and adversarial inputs, it is possible to improve classification accuracy on the clean, non-adversarial inputs. We demonstrate that, contrary to previous findings, it is not necessary to separate batch statistics when co-training on clean and adversarial inputs, and that it is sufficient to use adapters with few domain-specific parameters for each type of input. We establish that using the classification token of a Vision Transformer (ViT) as an adapter is enough to match the classification performance of dual normalization layers, while using significantly less additional parameters. First, we improve upon the top-1 accuracy of a non-adversarially trained ViT-B16 model by +1.12% on ImageNet (reaching 83.76% top-1 accuracy). Second, and more importantly, we show that training with adapters enables model soups through linear combinations of the clean and adversarial tokens. These model soups, which we call adversarial model soups, allow us to trade-off between clean and robust accuracy without sacrificing efficiency. Finally, we show that we can easily adapt the resulting models in the face of distribution shifts. Our ViT-B16 obtains top-1 accuracies on ImageNet variants that are on average +4.00% better than those obtained with Masked Autoencoders.
UNICORN: A Unified Backdoor Trigger Inversion Framework
Authors: Zhenting Wang,Kai Mei,Juan Zhai,Shiqing Ma

The backdoor attack, where the adversary uses inputs stamped with triggers (e.g., a patch) to activate pre-planted malicious behaviors, is a severe threat to Deep Neural Network (DNN) models. Trigger inversion is an effective way of identifying backdoor models and understanding embedded adversarial behaviors. A challenge of trigger inversion is that there are many ways of constructing the trigger. Existing methods cannot generalize to various types of triggers by making certain assumptions or attack-specific constraints. The fundamental reason is that existing work does not formally define the trigger and the inversion problem. This work formally defines and analyzes the trigger and the inversion problem. Then, it proposes a unified framework to invert backdoor triggers based on the formalization of triggers and the identified inner behaviors of backdoor models from our analysis. Our prototype UNICORN is general and effective in inverting backdoor triggers in DNNs. The code can be found at https://github.com/RU-System-Software-and-Security/UNICORN.
ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion
Authors: Aleksandar Pavlović,Emanuel Sallinger

Knowledge graphs are inherently incomplete. Therefore substantial research has been directed toward knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). KG embedding models (KGEs) have yielded promising results for KGC, yet any current KGE is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent patterns jointly (e.g., hierarchy and composition), and (3) providing an intuitive interpretation of captured patterns. In this work, we propose ExpressivE, a fully expressive spatio-functional KGE that solves all these challenges simultaneously. ExpressivE embeds pairs of entities as points and relations as hyper-parallelograms in the virtual triple space $\mathbb{R}^{2d}$. This model design allows ExpressivE not only to capture a rich set of inference patterns jointly but additionally to display any supported inference pattern through the spatial relation of hyper-parallelograms, offering an intuitive and consistent geometric interpretation of ExpressivE embeddings and their captured patterns. Experimental results on standard KGC benchmarks reveal that ExpressivE is competitive with state-of-the-art KGEs and even significantly outperforms them on WN18RR.
Localized Randomized Smoothing for Collective Robustness Certification
Authors: Jan Schuchardt,Tom Wollschläger,Aleksandar Bojchevski,Stephan Günnemann

Models for image segmentation, node classification and many other tasks map a single input to multiple labels. By perturbing this single shared input (e.g. the image) an adversary can manipulate several predictions (e.g. misclassify several pixels). Collective robustness certification is the task of provably bounding the number of robust predictions under this threat model. The only dedicated method that goes beyond certifying each output independently is limited to strictly local models, where each prediction is associated with a small receptive field. We propose a more general collective robustness certificate for all types of models. We further show that this approach is beneficial for the larger class of softly local models, where each output is dependent on the entire input but assigns different levels of importance to different input regions (e.g. based on their proximity in the image). The certificate is based on our novel localized randomized smoothing approach, where the random perturbation strength for different input regions is proportional to their importance for the outputs. Localized smoothing Pareto-dominates existing certificates on both image segmentation and node classification tasks, simultaneously offering higher accuracy and stronger certificates.
Learning Probabilistic Topological Representations Using Discrete Morse Theory
Authors: Xiaoling Hu,Dimitris Samaras,Chao Chen

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose a novel deep learning based method to learn topological/structural. We use discrete Morse theory and persistent homology to construct a one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks. It also facilitates semi-automatic interactive annotation/proofreading via the sampling of structures and structure-aware uncertainty.
Model-based Causal Bayesian Optimization
Authors: Scott Sussex,Anastasia Makarova,Andreas Krause

How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the {\em model-based causal Bayesian optimization algorithm (MCBO)} that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.
Training language models to summarize narratives improves brain alignment
Authors: Khai Loong Aw,Mariya Toneva

Building systems that achieve a deeper understanding of language is one of the central goals of natural language processing (NLP). Towards this goal, recent works have begun to train language models on narrative datasets which require extracting the most critical information by integrating across long contexts. However, it is still an open question whether these models are learning a deeper understanding of the text, or if the models are simply learning a heuristic to complete the task. This work investigates this further by turning to the one language processing system that truly understands complex language: the human brain. We show that training language models for deeper narrative understanding results in richer representations that have improved alignment to human brain activity. We further find that the improvements in brain alignment are larger for character names than for other discourse features, which indicates that these models are learning important narrative elements. Taken together, these results suggest that this type of training can indeed lead to deeper language understanding. These findings have consequences both for cognitive neuroscience by revealing some of the significant factors behind brain-NLP alignment, and for NLP by highlighting that understanding of long-range context can be improved beyond language modeling.
Dual Algorithmic Reasoning
Authors: Danilo Numeroso,Davide Bacciu,Petar Veličković

Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much of the current work has focused on learning reachability and shortest path graph algorithms, showing that joint learning on similar algorithms is beneficial for generalisation. However, when targeting more complex problems, such "similar" algorithms become more difficult to find. Here, we propose to learn algorithms by exploiting duality of the underlying algorithmic problem. Many algorithms solve optimisation problems. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning and qualitatively better solutions. Specifically, we exploit the max-flow min-cut theorem to simultaneously learn these two algorithms over synthetically generated graphs, demonstrating the effectiveness of the proposed approach. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task, which likely depends on the vessels’ flow properties. We demonstrate a clear performance gain when using our model within such a context, and empirically show that learning the max-flow and min-cut algorithms together is critical for achieving such a result.
A Primal-Dual Framework for Transformers and Neural Networks
Authors: Tan Minh Nguyen,Tam Minh Nguyen,Nhat Ho,Andrea L. Bertozzi,Richard Baraniuk,Stanley Osher

Self-attention is key to the remarkable success of transformers in sequence modeling tasks including many applications in natural language processing and computer vision. Like neural network layers, these attention mechanisms are often developed by heuristics and experience. To provide a principled framework for constructing attention layers in transformers, we show that the self-attention corresponds to the support vector expansion derived from a support vector regression problem, whose primal formulation has the form of a neural network layer. Using our framework, we derive popular attention layers used in practice and propose two new attentions: 1) the Batch Normalized Attention (Attention-BN) derived from the batch normalization layer and 2)  the Attention with Scaled Head (Attention-SH) derived from using less training data to fit the SVR model. We empirically demonstrate the advantages of the Attention-BN and Attention-SH in reducing head redundancy, increasing the model's accuracy, and improving the model's efficiency in a variety of practical applications including image and time-series classification.
Fisher-Legendre (FishLeg) optimization of deep neural networks
Authors: Jezabel R Garcia,Federica Freddi,Stathi Fotiadis,Maolin Li,Sattar Vakili,Alberto Bernacchia,Guillaume Hennequin

Incorporating second-order gradient information (curvature) into optimization can dramatically reduce the number of iterations required to train machine learning models. In natural gradient descent, such information comes from the Fisher information matrix which yields a number of desirable properties. As exact natural gradient updates are intractable for large models, successful methods such as KFAC and sequels approximate the Fisher in a structured form that can easily be inverted. However, this requires model/layer-specific tensor algebra and certain approximations that are often difficult to justify. Here, we use ideas from Legendre-Fenchel duality to learn a direct and efficiently evaluated model for the product of the inverse Fisher with any vector, in an online manner, leading to natural gradient steps that get progressively more accurate over time despite noisy gradients. We prove that the resulting “Fisher-Legendre” (FishLeg) optimizer converges to a (global) minimum of non-convex functions satisfying the PL condition, which applies in particular to deep linear networks. On standard auto-encoder benchmarks, we show empirically that FishLeg outperforms standard first-order optimization methods, and performs on par with or better than other second-order methods, especially when using small batches. Thanks to its generality, we expect our approach to facilitate the handling of a variety  neural network layers in future work.
Capturing the Motion of Every Joint: 3D Human Pose and Shape Estimation with Independent Tokens
Authors: Sen Yang,Wen Heng,Gang Liu,GUOZHONG LUO,Wankou Yang,Gang YU

In this paper we present a novel method to estimate 3D human pose and shape from monocular videos. This task requires directly recovering pixel-alignment 3D human pose and body shape from monocular images or videos, which is challenging due to its inherent ambiguity. To improve precision, existing methods highly rely on the initialized mean pose and shape as prior estimates and parameter regression with an iterative error feedback manner. In addition, video-based approaches model the overall change over the image-level features to temporally enhance the single-frame feature, but fail to capture the rotational motion at the joint level, and cannot guarantee local temporal consistency. To address these issues, we propose a novel Transformer-based model with a design of independent tokens. First, we introduce three types of tokens independent of the image feature: \textit{joint rotation tokens, shape token, and camera token}. 
By progressively interacting with image features through Transformer layers, these tokens learn to encode the prior knowledge of human 3D joint rotations, body shape, and position information from large-scale data, and are updated to estimate SMPL parameters conditioned on a given image. Second, benefiting from the proposed token-based representation, we further use a temporal model to focus on capturing the rotational temporal information of each joint, which is empirically conducive to preventing large jitters in local parts. Despite being conceptually simple, the proposed method attains superior performances on the 3DPW and Human3.6M datasets. Using ResNet-50 and Transformer architectures, it obtains 42.0 mm error on the PA-MPJPE metric of the challenging 3DPW, outperforming state-of-the-art counterparts by a large margin. Code will be publicly available\footnote{\url{https://github.com/yangsenius/INT_HMR_Model}}.
Efficient recurrent architectures through activity sparsity and sparse back-propagation through time
Authors: Anand Subramoney,Khaleelulla Khan Nazeer,Mark Schöne,Christian Mayr,David Kappel

Recurrent neural networks (RNNs) are well suited for solving sequence tasks in resource-constrained systems due to their expressivity and  low computational requirements. However, there is still a need to bridge the gap between what RNNs are capable of in terms of efficiency and performance and real-world application requirements. The memory and computational requirements arising from propagating the activations of all the neurons at every time step to every connected neuron, together with the sequential dependence of activations, contribute to the inefficiency of training and using RNNs. We propose a solution inspired by biological neuron dynamics that makes the communication between RNN units sparse and discrete. This makes the backward pass with backpropagation through time (BPTT) computationally sparse and efficient as well. We base our model on the gated recurrent unit (GRU), extending it with units that emit discrete events for communication triggered by a threshold so that no information is communicated to other units in the absence of events.  We show theoretically that the communication between units, and hence the computation required for both the forward and backward passes, scales with the number of events in the network. Our model achieves efficiency without compromising task performance, demonstrating competitive performance compared to state-of-the-art recurrent network models in real-world tasks, including language modeling. The dynamic activity sparsity mechanism also makes our model well suited for novel energy-efficient neuromorphic hardware. Code is available at https://github.com/KhaleelKhan/EvNN/.
Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
Authors: Xingchao Liu,Chengyue Gong,qiang liu

We present rectified flow, a simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions $\pi_0$ and $\pi_1$, hence providing a unified solution to generative modeling and domain transfer, among various other tasks involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight paths connecting the points drawn from $\pi_0$ and $\pi_1$ as much as possible. This is  achieved by solving a straightforward nonlinear least squares optimization problem, which can be easily scaled to large models without introducing extra parameters beyond standard supervised learning. The straight paths are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that, by learning a rectified flow from data, we effectively turn an arbitrary coupling of $\pi_0$ and $\pi_1$ to a  new deterministic coupling with provably non-increasing convex transport costs. In addition, with a ``reflow" procedure that iteratively learns a new rectified flow from the data bootstrapped from the previous one, we obtain a sequence of flows with increasingly straight paths, which can be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we show that rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation. In particular, on image generation and translation, our method yields nearly straight flows that give high quality results even with \emph{a single Euler discretization step}. Code is available at \url{https://github.com/gnobitab/RectifiedFlow}.
Inequality phenomenon in $l_{\infty}$-adversarial training, and its unrealized threats
Authors: Ranjie Duan,YueFeng Chen,Yao Zhu,Xiaojun Jia,Rong Zhang,Hui Xue'

The appearance of adversarial examples raises attention from both academia and industry. Along with the attack-defense arms race, adversarial training is the most effective against adversarial examples.
However, we find inequality phenomena occur during the $l_{\infty}$-adversarial training, that few features dominate the prediction made by the adversarially trained model. We systematically evaluate such inequality phenomena by extensive experiments and find such phenomena become more obvious when performing adversarial training with increasing adversarial strength (evaluated by $\epsilon$). We hypothesize such inequality phenomena make $l_{\infty}$-adversarially trained model less reliable than the standard trained model when few ``important features" are influenced. To validate our hypothesis, we proposed two simple attacks that either perturb or replace important features with noise or occlusion. Experiments show that $l_{\infty}$-adversarially trained model can be easily attacked when the few important features are influenced. 
Our work shed light on the limitation of the practicality of $l_{\infty}$-adversarial training.