Despite being a key challenge, task confusion lacks a theoretical understanding.

In class-incremental learning (class-IL), models must classify all previously seen classes at test time without task-IDs, leading to task confusion. Despite being a key challenge, task confusion lacks a theoretical understanding. We present a novel mathematical framework for class-IL and prove the Infeasibility Theorem, showing optimal class-IL is impossible with discriminative modeling due to task confusion. However, we establish the Feasibility Theorem, demonstrating that generative modeling can achieve optimal class-IL by overcoming task confusion. We then assess popular class-IL strategies, including regularization, bias-correction, replay, and generative classifier, using our framework. Our analysis suggests that adopting generative modeling, either for generative replay or direct classification (generative classifier), is essential for optimal class-IL.

Learning a parametric model from a given dataset indeed enables to capture intrinsic dependencies between random variables via a parametric conditional probability distribution and in turn predict the value of a label variable given observed variables. In this paper, we undertake a comparative analysis of generative and discriminative approaches which differ in their construction and the structure of the underlying inference problem. Our objective is to compare the ability of both approaches to leverage information from various sources in an epistemic uncertainty aware inference via the posterior predictive distribution. We assess the role of a prior distribution, explicit in the generative case and implicit in the discriminative case, leading to a discussion about discriminative models suffering from imbalanced dataset. We next examine the double role played by the observed variables in the generative case, and discuss the compatibility of both approaches with semi-supervised learning. We also provide with practical insights and we examine how the modeling choice impacts the sampling from the posterior predictive distribution. With regard to this, we propose a general sampling scheme enabling supervised learning for both approaches, as well as semi-supervised learning when compatible with the considered modeling approach. Throughout this paper, we illustrate our arguments and conclusions using the example of affine regression, and validate our comparative analysis through classification simulations using neural network based models.

Energy-Based Models (EBMs) are an important class of probabilistic models, also known as random fields and undirected graphical models. EBMs are un-normalized and thus radically different from other popular self-normalized probabilistic models such as hidden Markov models (HMMs), autoregressive models, generative adversarial nets (GANs) and variational auto-encoders (VAEs). Over the past years, EBMs have attracted increasing interest not only from the core machine learning community, but also from application domains such as speech, vision, natural language processing (NLP) and so on, due to significant theoretical and algorithmic progress. The sequential nature of speech and language also presents special challenges and needs a different treatment from processing fix-dimensional data (e.g., images). Therefore, the purpose of this monograph is to present a systematic introduction to energy-based models, including both algorithmic progress and applications in speech and language processing. First, the basics of EBMs are introduced, including classic models, recent models parameterized by neural networks, sampling methods, and various learning methods from the classic learning algorithms to the most advanced ones. Then, the application of EBMs in three different scenarios is presented, i.e., for modeling marginal, conditional and joint distributions, respectively. 1) EBMs for sequential data with applications in language modeling, where the main focus is on the marginal distribution of a sequence itself; 2) EBMs for modeling conditional distributions of target sequences given observation sequences, with applications in speech recognition, sequence labeling and text generation; 3) EBMs for modeling joint distributions of both sequences of observations and targets, and their applications in semi-supervised learning and calibrated natural language understanding.