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abstract indexed · arXiv 2610.06677 · updated 2026-10-18

How Sparse Probability Maps Shape Mixture-of-Experts Routing

First page of How Sparse Probability Maps Shape Mixture-of-Experts Routing
From the original paper · arXiv 2610.06677Page 1. Select the image to read the PDF.

The technique replaces the standard softmax top-K MoE router with sparsity-inducing probability maps (sparsemax, entmax, normmax) that can assign exact zeros and adapt expert participation per token. It costs nothing at inference but requires pretraining the MoE from scratch, and the paper's central finding is that routers co-adapt their score distributions to the map, so adaptive sparsity often does not survive training and no map beats softmax validation loss. What can fail is the premise itself: entmax learns score spreads that keep gaps below its zeroing threshold, so the expected token-dependent participation may never materialize, making map choice alone an unreliable design lever.

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research area
efficient architectures
technical change
Sparse probability maps for MoE routing
published
2026-10-05

Adopting this requires training MoE models from scratch, which exceeds the reader's budget, and since there is no quality gain over softmax the only actionable lesson is conceptual: sparse routing behavior depends on learned score distributions, not the map alone.

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  1. claim 01Paperraft inference
    Read the brief interpretation

    The technique replaces the standard softmax top-K MoE router with sparsity-inducing probability maps (sparsemax, entmax, normmax) that can assign exact zeros and adapt expert participation per token. It costs nothing at inference but requires pretraining the MoE from scratch, and the paper's central finding is that routers co-adapt their score distributions to the map, so adaptive sparsity often does not survive training and no map beats softmax validation loss. What can fail is the premise itself: entmax learns score spreads that keep gaps below its zeroing threshold, so the expected token-dependent participation may never materialize, making map choice alone an unreliable design lever.

    This is a Paperraft inference. It is not pinned to a verified PDF passage.

    Inspect the source
  2. claim 02Paperraft inference

    Sparsemax trained with K=2 loses only 0.02 nats when run with K=8 experts at inference, versus 0.58 nats for softmax; no sparse map improves validation loss over softmax at matched 300M/1B scale.

    This is a Paperraft inference. It is not pinned to a verified PDF passage.

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