Alexander Gepperth

Eli Verwimp, Rahaf Aljundi, Shai Ben-David et al. · deepmind

Continual learning is a subfield of machine learning, which aims to allow machine learning models to continuously learn on new data, by accumulating knowledge without forgetting what was learned in the past. In this work, we take a step back, and ask: "Why should one care about continual learning in the first place?". We set the stage by examining recent continual learning papers published at four major machine learning conferences, and show that memory-constrained settings dominate the field. Then, we discuss five open problems in machine learning, and even though they might seem unrelated to continual learning at first sight, we show that continual learning will inevitably be part of their solution. These problems are model editing, personalization and specialization, on-device learning, faster (re-)training and reinforcement learning. Finally, by comparing the desiderata from these unsolved problems and the current assumptions in continual learning, we highlight and discuss four future directions for continual learning research. We hope that this work offers an interesting perspective on the future of continual learning, while displaying its potential value and the paths we have to pursue in order to make it successful. This work is the result of the many discussions the authors had at the Dagstuhl seminar on Deep Continual Learning, in March 2023.

Benedikt Bagus, Alexander Gepperth, Timothée Lesort

Continual Learning (CL, sometimes also termed incremental learning) is a flavor of machine learning where the usual assumption of stationary data distribution is relaxed or omitted. When naively applying, e.g., DNNs in CL problems, changes in the data distribution can cause the so-called catastrophic forgetting (CF) effect: an abrupt loss of previous knowledge. Although many significant contributions to enabling CL have been made in recent years, most works address supervised (classification) problems. This article reviews literature that study CL in other settings, such as learning with reduced supervision, fully unsupervised learning, and reinforcement learning. Besides proposing a simple schema for classifying CL approaches w.r.t. their level of autonomy and supervision, we discuss the specific challenges associated with each setting and the potential contributions to the field of CL in general.

Benedikt Bagus, Alexander Gepperth

We present an empirical study on the use of continual learning (CL) methods in a reinforcement learning (RL) scenario, which, to the best of our knowledge, has not been described before. CL is a very active recent research topic concerned with machine learning under non-stationary data distributions. Although this naturally applies to RL, the use of dedicated CL methods is still uncommon. This may be due to the fact that CL methods often assume a decomposition of CL problems into disjoint sub-tasks of stationary distribution, that the onset of these sub-tasks is known, and that sub-tasks are non-contradictory. In this study, we perform an empirical comparison of selected CL methods in a RL problem where a physically simulated robot must follow a racetrack by vision. In order to make CL methods applicable, we restrict the RL setting and introduce non-conflicting subtasks of known onset, which are however not disjoint and whose distribution, from the learner's point of view, is still non-stationary. Our results show that dedicated CL methods can significantly improve learning when compared to the baseline technique of "experience replay".

Alexander Krawczyk, Alexander Gepperth

Conventional replay-based approaches to continual learning (CL) require, for each learning phase with new data, the replay of samples representing all of the previously learned knowledge in order to avoid catastrophic forgetting. Since the amount of learned knowledge grows over time in CL problems, generative replay spends an increasing amount of time just re-learning what is already known. In this proof-of-concept study, we propose a replay-based CL strategy that we term adiabatic replay (AR), which derives its efficiency from the (reasonable) assumption that each new learning phase is adiabatic, i.e., represents only a small addition to existing knowledge. Each new learning phase triggers a sampling process that selectively replays, from the body of existing knowledge, just such samples that are similar to the new data, in contrast to replaying all of it. Complete replay is not required since AR represents the data distribution by GMMs, which are capable of selectively updating their internal representation only where data statistics have changed. As long as additions are adiabatic, the amount of to-be-replayed samples need not to depend on the amount of previously acquired knowledge at all. We verify experimentally that AR is superior to state-of-the-art deep generative replay using VAEs.

Alexander Gepperth

We present the Deep Convolutional Gaussian Mixture Model (DCGMM), a new probabilistic approach for image modeling capable of density estimation, sampling and tractable inference. DCGMM instances exhibit a CNN-like layered structure, in which the principal building blocks are convolutional Gaussian Mixture (cGMM) layers. A key innovation w.r.t. related models like sum-product networks (SPNs) and probabilistic circuits (PCs) is that each cGMM layer optimizes an independent loss function and therefore has an independent probabilistic interpretation. This modular approach permits intervening transformation layers to harness the full spectrum of (potentially non-invertible) mappings available to CNNs, e.g., max-pooling or half-convolutions. DCGMM sampling and inference are realized by a deep chain of hierarchical priors, where a sample generated by a given cGMM layer defines the parameters of sampling in the next-lower cGMM layer. For sampling through non-invertible transformation layers, we introduce a new gradient-based sharpening technique that exploits redundancy (overlap) in, e.g., half-convolutions. DCGMMs can be trained end-to-end by SGD from random initial conditions, much like CNNs. We show that DCGMMs compare favorably to several recent PC and SPN models in terms of inference, classification and sampling, the latter particularly for challenging datasets such as SVHN. We provide a public TF2 implementation.

Alexander Gepperth

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of diagonal or spherical CMs often imposes restrictions that are too severe. The Mixture of Factor analyzers (MFA) model is an important extension of GMMs, which allows to smoothly interpolate between diagonal and full CMs based on the number of \textit{factor loadings} $l$. MFA has successfully been applied for modeling high-dimensional image data. This article contributes both a theoretical analysis as well as a new method for efficient high-dimensional MFA training by stochastic gradient descent, starting from random centroid initializations. This greatly simplifies the training and initialization process, and avoids problems of batch-type algorithms such Expectation-Maximization (EM) when training with huge amounts of data. In addition, by exploiting the properties of the matrix determinant lemma, we prove that MFA training and inference/sampling can be performed based on precision matrices, which does not require matrix inversions after training is completed. At training time, the methods requires the inversion of $l\times l$ matrices only. Besides the theoretical analysis and proofs, we apply MFA to typical image datasets such as SVHN and MNIST, and demonstrate the ability to perform sample generation and outlier detection.

Andrea Cossu, Federico Giannini, Giacomo Ziffer et al.

Continual Learning (CL) and Streaming Machine Learning (SML) study the ability of agents to learn from a stream of non-stationary data. Despite sharing some similarities, they address different and complementary challenges. While SML focuses on rapid adaptation after changes (concept drifts), CL aims to retain past knowledge when learning new tasks. After a brief introduction to CL and SML, we discuss Streaming Continual Learning (SCL), an emerging paradigm providing a unifying solution to real-world problems, which may require both SML and CL abilities. We claim that SCL can i) connect the CL and SML communities, motivating their work towards the same goal, and ii) foster the design of hybrid approaches that can quickly adapt to new information (as in SML) without forgetting previous knowledge (as in CL). We conclude the paper with a motivating example and a set of experiments, highlighting the need for SCL by showing how CL and SML alone struggle in achieving rapid adaptation and knowledge retention.

Yannick Denker, Alexander Gepperth

Continual reinforcement learning (CRL) requires agents to learn from a sequence of tasks without forgetting previously acquired policies. In this work, we introduce a novel benchmark suite for CRL based on realistically simulated robots in the Gazebo simulator. Our Continual Robotic Simulation Suite (CRoSS) benchmarks rely on two robotic platforms: a two-wheeled differential-drive robot with lidar, camera and bumper sensor, and a robotic arm with seven joints. The former represent an agent in line-following and object-pushing scenarios, where variation of visual and structural parameters yields a large number of distinct tasks, whereas the latter is used in two goal-reaching scenarios with high-level cartesian hand position control (modeled after the Continual World benchmark), and low-level control based on joint angles. For the robotic arm benchmarks, we provide additional kinematics-only variants that bypass the need for physical simulation (as long as no sensor readings are required), and which can be run two orders of magnitude faster. CRoSS is designed to be easily extensible and enables controlled studies of continual reinforcement learning in robotic settings with high physical realism, and in particular allow the use of almost arbitrary simulated sensors. To ensure reproducibility and ease of use, we provide a containerized setup (Apptainer) that runs out-of-the-box, and report performances of standard RL algorithms, including Deep Q-Networks (DQN) and policy gradient methods. This highlights the suitability as a scalable and reproducible benchmark for CRL research.

Benedikt Bagus, Alexander Gepperth

Continual learning (CL) is a major challenge of machine learning (ML) and describes the ability to learn several tasks sequentially without catastrophic forgetting (CF). Recent works indicate that CL is a complex topic, even more so when real-world scenarios with multiple constraints are involved. Several solution classes have been proposed, of which so-called replay-based approaches seem very promising due to their simplicity and robustness. Such approaches store a subset of past samples in a dedicated memory for later processing: while this does not solve all problems, good results have been obtained. In this article, we empirically investigate replay-based approaches of continual learning and assess their potential for applications. Selected recent approaches as well as own proposals are compared on a common set of benchmarks, with a particular focus on assessing the performance of different sample selection strategies. We find that the impact of sample selection increases when a smaller number of samples is stored. Nevertheless, performance varies strongly between different replay approaches. Surprisingly, we find that the most naive rehearsal-based approaches that we propose here can outperform recent state-of-the-art methods.

Benedikt Pfülb, Alexander Gepperth, Benedikt Bagus

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully probabilistic models aim at modeling the data distribution directly. Consequently, they provide functionalities that are highly relevant for continual learning, such as density estimation (outlier detection) and sample generation. As a concrete realization of generative continual learning, we propose Gaussian Mixture Replay (GMR). GMR is a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. Relying on the MNIST, FashionMNIST and Devanagari benchmarks, we first demonstrate unsupervised task boundary detection by GMM density estimation, which we also use to reject untypical generated samples. In addition, we show that GMR is capable of class-conditional sampling in the way of a cGAN. Lastly, we verify that GMR, despite its simple structure, achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.

Alexander Gepperth, Benedikt Pfülb

In this conceptual work, we present Deep Convolutional Gaussian Mixture Models (DCGMMs): a new formulation of deep hierarchical Gaussian Mixture Models (GMMs) that is particularly suitable for describing and generating images. Vanilla (i.e., flat) GMMs require a very large number of components to describe images well, leading to long training times and memory issues. DCGMMs avoid this by a stacked architecture of multiple GMM layers, linked by convolution and pooling operations. This allows to exploit the compositionality of images in a similar way as deep CNNs do. DCGMMs can be trained end-to-end by Stochastic Gradient Descent. This sets them apart from vanilla GMMs which are trained by Expectation-Maximization, requiring a prior k-means initialization which is infeasible in a layered structure. For generating sharp images with DCGMMs, we introduce a new gradient-based technique for sampling through non-invertible operations like convolution and pooling. Based on the MNIST and FashionMNIST datasets, we validate the DCGMMs model by demonstrating its superiority over flat GMMs for clustering, sampling and outlier detection.

Benedikt Pfülb, Alexander Gepperth

We present Gaussian Mixture Replay (GMR), a rehearsal-based approach for continual learning (CL) based on Gaussian Mixture Models (GMM). CL approaches are intended to tackle the problem of catastrophic forgetting (CF), which occurs for Deep Neural Networks (DNNs) when sequentially training them on successive sub-tasks. GMR mitigates CF by generating samples from previous tasks and merging them with current training data. GMMs serve several purposes here: sample generation, density estimation (e.g., for detecting outliers or recognizing task boundaries) and providing a high-level feature representation for classification. GMR has several conceptual advantages over existing replay-based CL approaches. First of all, GMR achieves sample generation, classification and density estimation in a single network structure with strongly reduced memory requirements. Secondly, it can be trained at constant time complexity w.r.t. the number of sub-tasks, making it particularly suitable for life-long learning. Furthermore, GMR minimizes a differentiable loss function and seems to avoid mode collapse. In addition, task boundaries can be detected by applying GMM density estimation. Lastly, GMR does not require access to sub-tasks lying in the future for hyper-parameter tuning, allowing CL under real-world constraints. We evaluate GMR on multiple image datasets, which are divided into class-disjoint sub-tasks.

Alexander Gepperth, Benedikt Pfülb

This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an approximation to the GMM log-likelihood that is particularly valid for high data dimensionalities. The SOM-like decrease of the neighborhood radius can be understood as an annealing procedure ensuring that gradient descent does not get stuck in undesirable local minima. This link allows to treat SOMs as generative probabilistic models, giving a formal justification for using SOMs, e.g., to detect outliers, or for sampling.

Alexander Gepperth, Benedikt Pfülb

We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter initialization (e.g., k-means) and can thus be trained based on a random initialization. Furthermore, the approach allows mini-batch sizes as low as 1, which are typical for streaming-data settings. Major problems in such settings are undesirable local optima during early training phases and numerical instabilities due to high data dimensionalities. We introduce an adaptive annealing procedure to address the first problem, whereas numerical instabilities are eliminated by using an exponential-free approximation to the standard GMM log-likelihood. Experiments on a variety of visual and non-visual benchmarks show that our SGD approach can be trained completely without, for instance, k-means based centroid initialization. It also compares favorably to an online variant of Expectation-Maximization (EM) - stochastic EM (sEM), which it outperforms by a large margin for very high-dimensional data.

Benedikt Pfülb, Christoph Hardegen, Alexander Gepperth et al.

We present a study of deep learning applied to the domain of network traffic data forecasting. This is a very important ingredient for network traffic engineering, e.g., intelligent routing, which can optimize network performance, especially in large networks. In a nutshell, we wish to predict, in advance, the bit rate for a transmission, based on low-dimensional connection metadata ("flows") that is available whenever a communication is initiated. Our study has several genuinely new points: First, it is performed on a large dataset (~50 million flows), which requires a new training scheme that operates on successive blocks of data since the whole dataset is too large for in-memory processing. Additionally, we are the first to propose and perform a more fine-grained prediction that distinguishes between low, medium and high bit rates instead of just "mice" and "elephant" flows. Lastly, we apply state-of-the-art visualization and clustering techniques to flow data and show that visualizations are insightful despite the heterogeneous and non-metric nature of the data. We developed a processing pipeline to handle the highly non-trivial acquisition process and allow for proper data preprocessing to be able to apply DNNs to network traffic data. We conduct DNN hyper-parameter optimization as well as feature selection experiments, which clearly show that fine-grained network traffic forecasting is feasible, and that domain-dependent data enrichment and augmentation strategies can improve results. An outlook about the fundamental challenges presented by network traffic analysis (high data throughput, unbalanced and dynamic classes, changing statistics, outlier detection) concludes the article.

Timothée Lesort, Alexander Gepperth, Andrei Stoian et al.

We present a new replay-based method of continual classification learning that we term "conditional replay" which generates samples and labels together by sampling from a distribution conditioned on the class. We compare conditional replay to another replay-based continual learning paradigm (which we term "marginal replay") that generates samples independently of their class and assigns labels in a separate step. The main improvement in conditional replay is that labels for generated samples need not be inferred, which reduces the margin for error in complex continual classification learning tasks. We demonstrate the effectiveness of this approach using novel and standard benchmarks constructed from MNIST and FashionMNIST data, and compare to the regularization-based \textit{elastic weight consolidation} (EWC) method.

Thomas Kopinski, Alexander Gepperth, Uwe Handmann

We present a novel method to perform multi-class pattern classification with neural networks and test it on a challenging 3D hand gesture recognition problem. Our method consists of a standard one-against-all (OAA) classification, followed by another network layer classifying the resulting class scores, possibly augmented by the original raw input vector. This allows the network to disambiguate hard-to-separate classes as the distribution of class scores carries considerable information as well, and is in fact often used for assessing the confidence of a decision. We show that by this approach we are able to significantly boost our results, overall as well as for particular difficult cases, on the hard 10-class gesture classification task.

Thomas Kopinski, Stéphane Magand, Uwe Handmann et al.

We present a novel hierarchical approach to multi-class classification which is generic in that it can be applied to different classification models (e.g., support vector machines, perceptrons), and makes no explicit assumptions about the probabilistic structure of the problem as it is usually done in multi-class classification. By adding a cascade of additional classifiers, each of which receives the previous classifier's output in addition to regular input data, the approach harnesses unused information that manifests itself in the form of, e.g., correlations between predicted classes. Using multilayer perceptrons as a classification model, we demonstrate the validity of this approach by testing it on a complex ten-class 3D gesture recognition task.