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How does SPLADE learn a sparse retrieval representation...
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See plansBM25 and every classical sparse scorer assign nonzero weight only to terms a document literally contains, so vocabulary mismatch — “laptop won’t charge” versus “AC adapter fails to supply power” — is structurally unfixable without a separate expansion step. SPLADE closes that gap by repurposing machinery already sitting in a BERT checkpoint: the masked-language-model head, which at every token position already predicts a score for every vocabulary entry, not just the token that’s actually there. SPLADE reuses that head unchanged as a per-position term-importance predictor, so a document can pick up nonzero weight on related terms it never mentions — implicit expansion, learned rather than generated as text.
The raw output is a dense matrix of positive and negative logits, which two transforms fix: ReLU zeroes negatives (a zero weight is what a posting list needs — no entry, no cost), and log(1+x) saturates large values before summing across positions into one sparse vector. Left alone, this would produce dense, unusably expensive posting lists. An L1 penalty controls only the count of nonzero weights, which doesn’t bound actual retrieval cost — a sum of products over the shared support. FLOPS regularization penalizes that cost directly, and because its gradient scales with how populated a dimension already is, it acts as a load balancer, spreading weight mass across the vocabulary instead of piling onto a few common terms — which is what keeps both index size and query latency predictable. Query and document sides get separate regularization strength because they have very different latency sensitivities.