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• DDCL is the first fully differentiable end-to-end framework for unsupervised prototype-based representation learning.method 95%
• DDCL replaces external k-means with an internal Dual Competitive Layer (DCL) that generates prototypes as native differentiable outputs.technical 90%
• The complete DDCL pipeline is trainable by backpropagation through a single unified loss with no external clustering steps.method 90%
• The soft quantisation loss decomposes exactly into a simplex-constrained reconstruction error and a non-negative weighted prototype variance term.technical 85%
• The variance term gradient acts as an implicit separation force that resists prototype collapse without auxiliary objectives.technical 80%
• DDCL with jointly trained backbone outperforms its non-differentiable ablation by 65% in clustering accuracy.result 95%
• DDCL outperforms DeepCluster end-to-end by 122% in clustering accuracy.result 95%
• The decomposition identity holds with zero violations across more than one hundred thousand training epochs.result 90%

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