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This work focuses on the decentralized deep learning optimization framework. We propose Adjacent Leader Decentralized Gradient Descent (AL-DSGD), for improving final model performance, accelerating convergence, and reducing the communication overhead of decentralized deep learning optimizers. AL-DSGD relies on two main ideas. Firstly, to increase the influence of the strongest learners on the learning system it assigns weights to different neighbor workers according to both their performance and the degree when averaging among them, and it applies a corrective force on the workers dictated by both the currently best-performing neighbor and the neighbor with the maximal degree. Secondly, to alleviate the problem of the deterioration of the convergence speed and performance of the nodes with lower degrees, AL-DSGD relies on dynamic communication graphs, which effectively allows the workers to communicate with more nodes while keeping the degrees of the nodes low. Experiments demonstrate that AL-DSGD accelerates the convergence of the decentralized state-of-the-art techniques and improves their test performance especially in the communication constrained environments. We also theoretically prove the convergence of the proposed scheme. Finally, we release to the community a highly general and concise PyTorch-based library for distributed training of deep learning models that supports easy implementation of any distributed deep learning approach ((a)synchronous, (de)centralized)., Comment: 9 pages of main paper, and 12 pages of appendix

We study distributed training of deep learning models in time-constrained environments. We propose a new algorithm that periodically pulls workers towards the center variable computed as a weighted average of workers, where the weights are inversely proportional to the gradient norms of the workers such that recovering the flat regions in the optimization landscape is prioritized. We develop two asynchronous variants of the proposed algorithm that we call Model-level and Layer-level Gradient-based Weighted Averaging (resp. MGRAWA and LGRAWA), which differ in terms of the weighting scheme that is either done with respect to the entire model or is applied layer-wise. On the theoretical front, we prove the convergence guarantee for the proposed approach in both convex and non-convex settings. We then experimentally demonstrate that our algorithms outperform the competitor methods by achieving faster convergence and recovering better quality and flatter local optima. We also carry out an ablation study to analyze the scalability of the proposed algorithms in more crowded distributed training environments. Finally, we report that our approach requires less frequent communication and fewer distributed updates compared to the state-of-the-art baselines., Comment: 9 pages main of main text, in total 24

The goal of lifelong learning is to continuously learn from non-stationary distributions, where the non-stationarity is typically imposed by a sequence of distinct tasks. Prior works have mostly considered idealistic settings, where the identity of tasks is known at least at training. In this paper we focus on a fundamentally harder, so-called task-agnostic setting where the task identities are not known and the learning machine needs to infer them from the observations. Our algorithm, which we call TAME (Task-Agnostic continual learning using Multiple Experts), automatically detects the shift in data distributions and switches between task expert networks in an online manner. At training, the strategy for switching between tasks hinges on an extremely simple observation that for each new coming task there occurs a statistically-significant deviation in the value of the loss function that marks the onset of this new task. At inference, the switching between experts is governed by the selector network that forwards the test sample to its relevant expert network. The selector network is trained on a small subset of data drawn uniformly at random. We control the growth of the task expert networks as well as selector network by employing online pruning. Our experimental results show the efficacy of our approach on benchmark continual learning data sets, outperforming the previous task-agnostic methods and even the techniques that admit task identities at both training and testing, while at the same time using a comparable model size., Comment: accepted by CVPR 2024 Workshop on Continual Learning in Computer Vision

Among various sensors for assisted and autonomous driving systems, automotive radar has been considered as a robust and low-cost solution even in adverse weather or lighting conditions. With the recent development of radar technologies and open-sourced annotated data sets, semantic segmentation with radar signals has become very promising. However, existing methods are either computationally expensive or discard significant amounts of valuable information from raw 3D radar signals by reducing them to 2D planes via averaging. In this work, we introduce ERASE-Net, an Efficient RAdar SEgmentation Network to segment the raw radar signals semantically. The core of our approach is the novel detect-then-segment method for raw radar signals. It first detects the center point of each object, then extracts a compact radar signal representation, and finally performs semantic segmentation. We show that our method can achieve superior performance on radar semantic segmentation task compared to the state-of-the-art (SOTA) technique. Furthermore, our approach requires up to 20x less computational resources. Finally, we show that the proposed ERASE-Net can be compressed by 40% without significant loss in performance, significantly more than the SOTA network, which makes it a more promising candidate for practical automotive applications., Comment: accepted by ICRA 2023

In this paper, we study the sharpness of a deep learning (DL) loss landscape around local minima in order to reveal systematic mechanisms underlying the generalization abilities of DL models. Our analysis is performed across varying network and optimizer hyper-parameters, and involves a rich family of different sharpness measures. We compare these measures and show that the low-pass filter-based measure exhibits the highest correlation with the generalization abilities of DL models, has high robustness to both data and label noise, and furthermore can track the double descent behavior for neural networks. We next derive the optimization algorithm, relying on the low-pass filter (LPF), that actively searches the flat regions in the DL optimization landscape using SGD-like procedure. The update of the proposed algorithm, that we call LPF-SGD, is determined by the gradient of the convolution of the filter kernel with the loss function and can be efficiently computed using MC sampling. We empirically show that our algorithm achieves superior generalization performance compared to the common DL training strategies. On the theoretical front, we prove that LPF-SGD converges to a better optimal point with smaller generalization error than SGD.

Modern deep learning (DL) architectures are trained using variants of the SGD algorithm that is run with a $\textit{manually}$ defined learning rate schedule, i.e., the learning rate is dropped at the pre-defined epochs, typically when the training loss is expected to saturate. In this paper we develop an algorithm that realizes the learning rate drop $\textit{automatically}$. The proposed method, that we refer to as AutoDrop, is motivated by the observation that the angular velocity of the model parameters, i.e., the velocity of the changes of the convergence direction, for a fixed learning rate initially increases rapidly and then progresses towards soft saturation. At saturation the optimizer slows down thus the angular velocity saturation is a good indicator for dropping the learning rate. After the drop, the angular velocity "resets" and follows the previously described pattern - it increases again until saturation. We show that our method improves over SOTA training approaches: it accelerates the training of DL models and leads to a better generalization. We also show that our method does not require any extra hyperparameter tuning. AutoDrop is furthermore extremely simple to implement and computationally cheap. Finally, we develop a theoretical framework for analyzing our algorithm and provide convergence guarantees., Comment: 12 figures, 23 pages

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC dimension, to provably bound this error. It is however unclear how to extend these measures to DNNs and therefore the existing analyses are applicable to simple neural networks, which are not used in practice, e.g., linear or shallow ones or otherwise multi-layer perceptrons. Moreover, many theoretical error bounds are not empirically verifiable. We derive estimates of the generalization error that hold for deep networks and do not rely on unattainable capacity measures. The enabling technique in our approach hinges on two major assumptions: i) the network achieves zero training error, ii) the probability of making an error on a test point is proportional to the distance between this point and its nearest training point in the feature space and at a certain maximal distance (that we call radius) it saturates. Based on these assumptions we estimate the generalization error of DNNs. The obtained estimate scales as O(1/(\delta N^{1/d})), where N is the size of the training data and is parameterized by two quantities, the effective dimensionality of the data as perceived by the network (d) and the aforementioned radius (\delta), both of which we find empirically. We show that our estimates match with the experimentally obtained behavior of the error on multiple learning tasks using benchmark data-sets and realistic models. Estimating training data requirements is essential for deployment of safety critical applications such as autonomous driving etc. Furthermore, collecting and annotating training data requires a huge amount of financial, computational and human resources. Our empirical estimates will help to efficiently allocate resources.

This paper studies a new design of the optimization algorithm for training deep learning models with a fixed architecture of the classification network in a continual learning framework. The training data is non-stationary and the non-stationarity is imposed by a sequence of distinct tasks. We first analyze a deep model trained on only one learning task in isolation and identify a region in network parameter space, where the model performance is close to the recovered optimum. We provide empirical evidence that this region resembles a cone that expands along the convergence direction. We study the principal directions of the trajectory of the optimizer after convergence and show that traveling along a few top principal directions can quickly bring the parameters outside the cone but this is not the case for the remaining directions. We argue that catastrophic forgetting in a continual learning setting can be alleviated when the parameters are constrained to stay within the intersection of the plausible cones of individual tasks that were so far encountered during training. Based on this observation we present our direction-constrained optimization (DCO) method, where for each task we introduce a linear autoencoder to approximate its corresponding top forbidden principal directions. They are then incorporated into the loss function in the form of a regularization term for the purpose of learning the coming tasks without forgetting. Furthermore, in order to control the memory growth as the number of tasks increases, we propose a memory-efficient version of our algorithm called compressed DCO (DCO-COMP) that allocates a memory of fixed size for storing all autoencoders. We empirically demonstrate that our algorithm performs favorably compared to other state-of-art regularization-based continual learning methods.

Interpretability is crucial to understand the inner workings of deep neural networks (DNNs) and many interpretation methods generate saliency maps that highlight parts of the input image that contribute the most to the prediction made by the DNN. In this paper we design a backdoor attack that alters the saliency map produced by the network for an input image only with injected trigger that is invisible to the naked eye while maintaining the prediction accuracy. The attack relies on injecting poisoned data with a trigger into the training data set. The saliency maps are incorporated in the penalty term of the objective function that is used to train a deep model and its influence on model training is conditioned upon the presence of a trigger. We design two types of attacks: targeted attack that enforces a specific modification of the saliency map and untargeted attack when the importance scores of the top pixels from the original saliency map are significantly reduced. We perform empirical evaluation of the proposed backdoor attacks on gradient-based and gradient-free interpretation methods for a variety of deep learning architectures. We show that our attacks constitute a serious security threat when deploying deep learning models developed by untrusty sources. Finally, in the Supplement we demonstrate that the proposed methodology can be used in an inverted setting, where the correct saliency map can be obtained only in the presence of a trigger (key), effectively making the interpretation system available only to selected users., Comment: Published at the 2022 AAAI Conference on Artificial Intelligence (AAAI), 2022

This paper addresses the problem of optimizing partition functions in a stochastic learning setting. We propose a stochastic variant of the bound majorization algorithm that relies on upper-bounding the partition function with a quadratic surrogate. The update of the proposed method, that we refer to as Stochastic Partition Function Bound (SPFB), resembles scaled stochastic gradient descent where the scaling factor relies on a second order term that is however different from the Hessian. Similarly to quasi-Newton schemes, this term is constructed using the stochastic approximation of the value of the function and its gradient. We prove sub-linear convergence rate of the proposed method and show the construction of its low-rank variant (LSPFB). Experiments on logistic regression demonstrate that the proposed schemes significantly outperform SGD. We also discuss how to use quadratic partition function bound for efficient training of deep learning models and in non-convex optimization.

End-to-end learning from sensory data has shown promising results in autonomous driving. While employing many sensors enhances world perception and should lead to more robust and reliable behavior of autonomous vehicles, it is challenging to train and deploy such network and at least two problems are encountered in the considered setting. The first one is the increase of computational complexity with the number of sensing devices. The other is the phenomena of network overfitting to the simplest and most informative input. We address both challenges with a novel, carefully tailored multi-modal experts network architecture and propose a multi-stage training procedure. The network contains a gating mechanism, which selects the most relevant input at each inference time step using a mixed discrete-continuous policy. We demonstrate the plausibility of the proposed approach on our 1/6 scale truck equipped with three cameras and one LiDAR., Comment: Published at the International Conference on Robotics and Automation (ICRA), 2020

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towards (or away from) (un)desired behaviors. Combined with smoothed WDs, the dual formulation allows us to devise efficient algorithms that take stochastic gradient descent steps through WD regularizers. We incorporate these regularizers into two novel on-policy algorithms, Behavior-Guided Policy Gradient and Behavior-Guided Evolution Strategies, which we demonstrate can outperform existing methods in a variety of challenging environments. We also provide an open source demo.

We consider multi-label classification where the goal is to annotate each data point with the most relevant $\textit{subset}$ of labels from an extremely large label set. Efficient annotation can be achieved with balanced tree predictors, i.e. trees with logarithmic-depth in the label complexity, whose leaves correspond to labels. Designing prediction mechanism with such trees for real data applications is non-trivial as it needs to accommodate sending examples to multiple leaves while at the same time sustain high prediction accuracy. In this paper we develop the LdSM algorithm for the construction and training of multi-label decision trees, where in every node of the tree we optimize a novel objective function that favors balanced splits, maintains high class purity of children nodes, and allows sending examples to multiple directions but with a penalty that prevents tree over-growth. Each node of the tree is trained once the previous node is completed leading to a streaming approach for training. We analyze the proposed objective theoretically and show that minimizing it leads to pure and balanced data splits. Furthermore, we show a boosting theorem that captures its connection to the multi-label classification error. Experimental results on benchmark data sets demonstrate that our approach achieves high prediction accuracy and low prediction time and position LdSM as a competitive tool among existing state-of-the-art approaches.

We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by the currently best-performing worker (leader). Our method differs from the parameter-averaging scheme EASGD in a number of ways: (i) our objective formulation does not change the location of stationary points compared to the original optimization problem; (ii) we avoid convergence decelerations caused by pulling local workers descending to different local minima to each other (i.e. to the average of their parameters); (iii) our update by design breaks the curse of symmetry (the phenomenon of being trapped in poorly generalizing sub-optimal solutions in symmetric non-convex landscapes); and (iv) our approach is more communication efficient since it broadcasts only parameters of the leader rather than all workers. We provide theoretical analysis of the batch version of the proposed algorithm, which we call Leader Gradient Descent (LGD), and its stochastic variant (LSGD). Finally, we implement an asynchronous version of our algorithm and extend it to the multi-leader setting, where we form groups of workers, each represented by its own local leader (the best performer in a group), and update each worker with a corrective direction comprised of two attractive forces: one to the local, and one to the global leader (the best performer among all workers). The multi-leader setting is well-aligned with current hardware architecture, where local workers forming a group lie within a single computational node and different groups correspond to different nodes. For training convolutional neural networks, we empirically demonstrate that our approach compares favorably to state-of-the-art baselines. This work is a gentle extension of [2]., Comment: Extension of LSGD published in NeurIPS 2019. 24 pages

The paper proposes an on-line monitoring framework for continuous real-time safety/security in learning-based control systems (specifically application to a unmanned ground vehicle). We monitor validity of mappings from sensor inputs to actuator commands, controller-focused anomaly detection (CFAM), and from actuator commands to sensor inputs, system-focused anomaly detection (SFAM). CFAM is an image conditioned energy based generative adversarial network (EBGAN) in which the energy based discriminator distinguishes between proper and anomalous actuator commands. SFAM is based on an action condition video prediction framework to detect anomalies between predicted and observed temporal evolution of sensor data. We demonstrate the effectiveness of the approach on our autonomous ground vehicle for indoor environments and on Udacity dataset for outdoor environments., Comment: Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018)

Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several well-known issues, such as vanishing and exploding gradients, inability to handle non-differentiable nonlinearities and to parallelize weight-updates across layers, and biological implausibility. These limitations continue to motivate exploration of alternative training algorithms, including several recently proposed auxiliary-variable methods which break the complex nested objective function into local subproblems. However, those techniques are mainly offline (batch), which limits their applicability to extremely large datasets, as well as to online, continual or reinforcement learning. The main contribution of our work is a novel online (stochastic/mini-batch) alternating minimization (AM) approach for training deep neural networks, together with the first theoretical convergence guarantees for AM in stochastic settings and promising empirical results on a variety of architectures and datasets., Comment: First six authors contributed equally to this work: A.C. - theory, manuscript, B.C. - code, experiments, S.K. - code, experiments, R.L. - algorithm, experiments, M.R. - code, experiments, I.R. - algorithm, manuscript

We propose an efficient algorithm for the generalized sparse coding (SC) inference problem. The proposed framework applies to both the single dictionary setting, where each data point is represented as a sparse combination of the columns of one dictionary matrix, as well as the multiple dictionary setting as given in morphological component analysis (MCA), where the goal is to separate a signal into additive parts such that each part has distinct sparse representation within a corresponding dictionary. Both the SC task and its generalization via MCA have been cast as $\ell_1$-regularized least-squares optimization problems. To accelerate traditional acquisition of sparse codes, we propose a deep learning architecture that constitutes a trainable time-unfolded version of the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), a special case of the Alternating Direction Method of Multipliers (ADMM). We empirically validate both variants of the algorithm, that we refer to as LSALSA (learned-SALSA), on image vision tasks and demonstrate that at inference our networks achieve vast improvements in terms of the running time, the quality of estimated sparse codes, and visual clarity on both classic SC and MCA problems. Finally, we present a theoretical framework for analyzing LSALSA network: we show that the proposed approach exactly implements a truncated ADMM applied to a new, learned cost function with curvature modified by one of the learned parameterized matrices. We extend a very recent Stochastic Alternating Optimization analysis framework to show that a gradient descent step along this learned loss landscape is equivalent to a modified gradient descent step along the original loss landscape. In this framework, the acceleration achieved by LSALSA could potentially be explained by the network's ability to learn a correction to the gradient direction of steeper descent., Comment: ECML-PKDD 2019 via journal track; Special Issue Mach Learn (2019)