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Register a new userHASeparator: Hyperplane-Assisted Softmax
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Added by
Ioannis Kansizoglou
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Efficient feature learning with Convolutional Neural Networks (CNNs) constitutes an increasingly imperative property since several challenging tasks of computer vision tend to require cascade schemes and modalities fusion. Feature learning aims at CNN models capable of extracting embeddings, exhibiting high discrimination among the different classes, as well as intra-class compactness. In this paper, a novel approach is introduced that has separator, which focuses on an effective hyperplane-based segregation of the classes instead of the common class centers separation scheme. Accordingly, an innovatory separator, namely the Hyperplane-Assisted Softmax separator (HASeparator), is proposed that demonstrates superior discrimination capabilities, as evaluated on popular image classification benchmarks.
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Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used in attention mechanisms such as transformers, since the correlation scores between embeddings are often not normally distributed, the gradient vanishing problem appears, and we prove this point through experimental confirmation. In this work, we suggest that replacing the exponential function by periodic functions, and we delve into some potential periodic alternatives of Softmax from the view of value and gradient. Through experiments on a simply designed demo referenced to LeViT, our method is proved to be able to alleviate the gradient problem and yield substantial improvements compared to Softmax and its variants. Further, we analyze the impact of pre-normalization for Softmax and our methods through mathematics and experiments. Lastly, we increase the depth of the demo and prove the applicability of our method in deep structures.
The softmax loss and its variants are widely used as objectives for embedding learning, especially in applications like face recognition. However, the intra- and inter-class objectives in the softmax loss are entangled, therefore a well-optimized inter-class objective leads to relaxation on the intra-class objective, and vice versa. In this paper, we propose to dissect the softmax loss into independent intra- and inter-class objective (D-Softmax). With D-Softmax as objective, we can have a clear understanding of both the intra- and inter-class objective, therefore it is straightforward to tune each part to the best state. Furthermore, we find the computation of the inter-class objective is redundant and propose two sampling-based variants of D-Softmax to reduce the computation cost. Training with regular-scale data, experiments in face verification show D-Softmax is favorably comparable to existing losses such as SphereFace and ArcFace. Training with massive-scale data, experiments show the fast variants of D-Softmax significantly accelerates the training process (such as 64x) with only a minor sacrifice in performance, outperforming existing acceleration methods of softmax in terms of both performance and efficiency.
We propose an approximate strategy to efficiently train neural network based language models over very large vocabularies. Our approach, called adaptive softmax, circumvents the linear dependency on the vocabulary size by exploiting the unbalanced word distribution to form clusters that explicitly minimize the expectation of computation time. Our approach further reduces the computational time by exploiting the specificities of modern architectures and matrix-matrix vector operations, making it particularly suited for graphical processing units. Our experiments carried out on standard benchmarks, such as EuroParl and One Billion Word, show that our approach brings a large gain in efficiency over standard approximations while achieving an accuracy close to that of the full softmax. The code of our method is available at https://github.com/facebookresearch/adaptive-softmax.
Neural models for text generation require a softmax layer with proper token embeddings during the decoding phase. Most existing approaches adopt single point embedding for each token. However, a word may have multiple senses according to different context, some of which might be distinct. In this paper, we propose KerBS, a novel approach for learning better embeddings for text generation. KerBS embodies two advantages: (a) it employs a Bayesian composition of embeddings for words with multiple senses; (b) it is adaptive to semantic variances of words and robust to rare sentence context by imposing learned kernels to capture the closeness of words (senses) in the embedding space. Empirical studies show that KerBS significantly boosts the performance of several text generation tasks.
Training a classifier over a large number of classes, known as extreme classification, has become a topic of major interest with applications in technology, science, and e-commerce. Traditional softmax regression induces a gradient cost proportional to the number of classes $C$, which often is prohibitively expensive. A popular scalable softmax approximation relies on uniform negative sampling, which suffers from slow convergence due a poor signal-to-noise ratio. In this paper, we propose a simple training method for drastically enhancing the gradient signal by drawing negative samples from an adversarial model that mimics the data distribution. Our contributions are three-fold: (i) an adversarial sampling mechanism that produces negative samples at a cost only logarithmic in $C$, thus still resulting in cheap gradient updates; (ii) a mathematical proof that this adversarial sampling minimizes the gradient variance while any bias due to non-uniform sampling can be removed; (iii) experimental results on large scale data sets that show a reduction of the training time by an order of magnitude relative to several competitive baselines.
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