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Item cold-start is a pervasive challenge for collaborative filtering (CF) recommender systems. Existing methods often train cold-start models by mapping auxiliary item content, such as images or text descriptions, into the embedding space of a CF model. However, such approaches can be limited by the fundamental information gap between CF signals and content features. In this work, we propose to avoid this limitation with purely content-based modeling of cold items, i.e. without alignment with CF user or item embeddings. We instead frame cold-start prediction in terms of item-item similarity, training a content encoder to project into a latent space where similarity correlates with user preferences. We define our training objective as a sparse generalization of sampled softmax loss with the $α$-entmax family of activation functions, which allows for sharper estimation of item relevance by zeroing gradients for uninformative negatives. We then describe how this Sampled Entmax for Cold-start (SEMCo) training regime can be extended via knowledge distillation, and show that it outperforms existing cold-start methods and standard sampled softmax in ranking accuracy. We also discuss the advantages of purely content-based modeling, particularly in terms of equity of item outcomes.