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Moving multimodal embeddings from the unit sphere to the probability simplex cut the modality gap by 97 to 99 percent

AspireAI community · arXiv (Mila and ServiceNow Research)
Multimodal contrastive models like CLIP and CLAP learn shared representations but leave a persistent gap between the two modalities' embeddings. The paper attacks it purely geometrically, changing the embedding domain from the unit sphere to the probability simplex, whose nonnegative, unit-mass constraints act as a structural prior forcing both modalities into the same coordinate system. With lightweight softmax adapters and Total Variation similarity in place of cosine distance, the authors report reducing the centroid l2 gap by 97 to 99 percent across five audio-text and image-text retrieval benchmarks while matching or exceeding the retrieval performance of standard unconstrained models. The paper also introduces RelGap, a geometry-adjusted gap measure that normalizes centroid separation by intra-modality spread. The limitation is that the adapters have to be trained, so this is a retrofit rather than a drop-in change, and the benchmarks are retrieval setups rather than generative ones.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.
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