Loss Functions in Deep Learning: A Comprehensive Review

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to minimize errors. Selecting the right loss function is critical, as it directly impacts model convergence, generalization, and overall performance across various applications, from computer vision to time series forecasting. This paper presents a comprehensive review of loss functions, covering fundamental metrics like Mean Squared Error and Cross-Entropy to advanced functions such as Adversarial and Diffusion losses. We explore their mathematical foundations, impact on model training, and strategic selection for various applications, including computer vision (Discriminative and generative), tabular data prediction, and time series forecasting. For each of these categories, we discuss the most used loss functions in the recent advancements of deep learning techniques. Also, this review explore the historical evolution, computational efficiency, and ongoing challenges in loss function design, underlining the need for more adaptive and robust solutions. Emphasis is placed on complex scenarios involving multi-modal data, class imbalances, and real-world constraints. Finally, we identify key future directions, advocating for loss functions that enhance interpretability, scalability, and generalization, leading to more effective and resilient deep learning models.

Rejection in Abstract Argumentation: Harder Than Acceptance?

Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.

Parameterized Complexity of Logic-Based Argumentation in Schaefer's Framework

Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this paper, we study the propositional variants of the following three computational tasks studied in argumentation: ARG (exists a support for a given claim with respect to a given set of formulas), ARG-Check (is a given set a support for a given claim), and ARG-Rel (similarly as ARG plus requiring an additionally given formula to be contained in the support). ARG-Check is complete for the complexity class DP, and the other two problems are known to be complete for the second level of the polynomial hierarchy (Parson et al., J. Log. Comput., 2003) and, accordingly, are highly intractable. Analyzing the reason for this intractability, we perform a two-dimensional classification: first, we consider all possible propositional fragments of the problem within Schaefer's framework (STOC 1978), and then study different parameterizations for each of the fragment. We identify a list of reasonable structural parameters (size of the claim, support, knowledge-base) that are connected to the aforementioned decision problems. Eventually, we thoroughly draw a fine border of parameterized intractability for each of the problems showing where the problems are fixed-parameter tractable and when this exactly stops. Surprisingly, several cases are of very high intractability (paraNP and beyond).