E-BRANCHFORMER: BRANCHFORMER WITH ENHANCED MERGING FOR SPEECH RECOGNITION

**ArcFace**, or **Additive Angular Margin Loss**, is a loss function used in face recognition tasks. The [softmax](https://paperswithcode.com/method/softmax) is traditionally used in these tasks. However, the softmax loss function does not explicitly optimise the feature embedding to enforce higher similarity for intraclass samples and diversity for inter-class samples, which results in a performance gap for deep face recognition under large intra-class appearance variations. 

The ArcFace loss transforms the logits $W^{T}\_{j}x\_{i} = || W\_{j} || \text{ } || x\_{i} || \cos\theta\_{j}$,
where $\theta\_{j}$ is the angle between the weight $W\_{j}$ and the feature $x\_{i}$. The individual weight $ || W\_{j} || = 1$ is fixed by $l\_{2}$ normalization. The embedding feature $ ||x\_{i} ||$ is fixed by $l\_{2}$ normalization and re-scaled to $s$. The normalisation step on features and weights makes the predictions only depend on the angle between the feature and the weight. The learned embedding
features are thus distributed on a hypersphere with a radius of $s$. Finally, an additive angular margin penalty $m$ is added between $x\_{i}$ and $W\_{y\_{i}}$ to simultaneously enhance the intra-class compactness and inter-class discrepancy. Since the proposed additive angular margin penalty is
equal to the geodesic distance margin penalty in the normalised hypersphere, the method is named ArcFace:

$$ L\_{3} = -\frac{1}{N}\sum^{N}\_{i=1}\log\frac{e^{s\left(\cos\left(\theta\_{y\_{i}} + m\right)\right)}}{e^{s\left(\cos\left(\theta\_{y\_{i}} + m\right)\right)} + \sum^{n}\_{j=1, j \neq y\_{i}}e^{s\cos\theta\_{j}}} $$

The authors select face images from 8 different identities containing enough samples (around 1,500 images/class) to train 2-D feature embedding networks with the softmax and ArcFace loss, respectively. As the Figure shows, the softmax loss provides roughly separable feature embedding
but produces noticeable ambiguity in decision boundaries, while the proposed ArcFace loss can obviously enforce a more evident gap between the nearest classes.

Other alternatives to enforce intra-class compactness and inter-class distance include [Supervised Contrastive Learning](https://arxiv.org/abs/2004.11362).

ArcFace

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

E-Branchformer

E-Branchformer: Branchformer with Enhanced merging for speech recognition

The optimization field suffers from the metaphor-based “pseudo-novel” or “fancy” optimizers. Most of these cliché methods mimic animals' searching trends and possess a small contribution to the optimization process itself. Most of these cliché methods suffer from the locally efficient performance, biased verification methods on easy problems, and high similarity between their components' interactions. This study attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization method based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics. The proposed RUNge Kutta optimizer (RUN) was developed to deal with various types of optimization problems in the future. The RUN utilizes the logic of slope variations computed by the RK method as a promising and logical searching mechanism for global optimization. This search mechanism benefits from two active exploration and exploitation phases for exploring the promising regions in the feature space and constructive movement toward the global best solution. Furthermore, an enhanced solution quality (ESQ) mechanism is employed to avoid the local optimal solutions and increase convergence speed. The RUN algorithm's efficiency was evaluated by comparing with other metaheuristic algorithms in 50 mathematical test functions and four real-world engineering problems. The RUN provided very promising and competitive results, showing superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance. In optimizing the constrained engineering problems, the metaphor-free RUN demonstrated its suitable performance as well. The authors invite the community for extensive evaluations of this deep-rooted optimizer as a promising tool for real-world optimization

Source	E-Branchformer: Branchformer with Enhanced merging for speech recognition
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com