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arxiv: 2606.01666 · v1 · pith:PY4CMPEHnew · submitted 2026-06-01 · 💻 cs.LG · cs.AI

DOT-MoE: Differentiable Optimal Transport for MoEfication

Udbhav Bamba , Arnav Chavan , Aryamaan Thakur , Steve Teig , Deepak Gupta This is my paper

Pith reviewed 2026-06-28 15:28 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords mixture of expertsoptimal transportmodel sparsificationmoeficationdifferentiable optimizationlarge language modelsinference efficiency
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The pith

DOT-MoE converts dense models to MoEs by framing neuron assignment as a differentiable optimal transport problem.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that modeling the split of feed-forward layers into experts as a balanced optimal transport problem, solved with differentiable Sinkhorn iterations, produces better MoE versions than heuristic clustering or random splits. A sympathetic reader would care because this supplies a stable route to sparsify already-trained dense models for cheaper inference instead of training MoEs from scratch. The method adds straight-through estimators so that discrete assignments and token routing can be learned together. If the claim holds, existing large models can be turned into sparse experts that keep most of their accuracy at half the active parameter count.

Core claim

DOT-MoE formulates the decomposition of dense layers as a balanced optimal transport problem and solves it with differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints, then uses straight-through estimators to jointly optimize the discrete neuron-to-expert assignments and the token-to-expert routing policy, yielding models that outperform structured pruning, heuristic clustering, and random-split baselines while retaining 90 percent of original performance at 50 percent active parameters.

What carries the argument

The balanced optimal transport formulation solved by differentiable Sinkhorn iterations that produces neuron-to-expert assignments under capacity constraints.

If this is right

  • Pre-trained dense models can be converted to MoEs without the instability of training sparse models from scratch.
  • Active parameter count can be halved while retaining 90 percent of the dense model's performance across tested architectures.
  • End-to-end learning of both the discrete assignments and the routing policy becomes feasible through straight-through estimators.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same transport framing might apply to partitioning weights in other layer types such as attention heads.
  • Automated conversion pipelines could become practical for deploying large models under tight memory or latency budgets.
  • The strict balance enforced by transport may produce different behavior when the number of experts grows very large.

Load-bearing premise

That the optimal transport solution for assigning neurons to experts preserves model capability better than simpler heuristic or random partitions.

What would settle it

A controlled test on a held-out architecture and benchmark set where DOT-MoE falls below the performance of heuristic clustering baselines.

Figures

Figures reproduced from arXiv: 2606.01666 by Arnav Chavan, Aryamaan Thakur, Deepak Gupta, Steve Teig, Udbhav Bamba.

Figure 1
Figure 1. Figure 1: Ablation results for DOT-MoE. (a) Increasing expert granularity improves performance until saturation. (b) Training with higher FFN sparsity yields robust expert representations that generalize better to extreme sparsity regimes at inference time. (c) Inference throughput remains stable across expert granularities when active parameters are held constant. adapt. This enables a stronger zero-shot transfer w… view at source ↗
Figure 2
Figure 2. Figure 2: Effect of initialization on training dynamics. DOT-MoE starts with substantially lower training loss and WikiText perplexity, maintaining this advantage throughout fine-tuning. This translates to consistently higher downstream accuracy on HellaSwag. tive neurons per token (k × s) remain constant, the GEMM sizes and thus throughput are largely unaffected by expert granularity. Observation 2: Fine-grained ex… view at source ↗
Figure 3
Figure 3. Figure 3: shows the resulting visualization for layer 9, where each color represents a different expert. The visualization reveals clear clustering structure, indicating that experts learn to specialize in processing distinct types of inputs. Activations from the same expert tend to cluster together in the embedding space, forming well-separated regions. The clear separation between expert clusters suggests that our… view at source ↗
Figure 4
Figure 4. Figure 4: Expert token allocation across transformer layers for Qwen2.5-7B with 50% sparsity on the WikiText-2 dataset. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
read the original abstract

The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition the Feed-Forward Network (FFN) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks demonstrate that DOT-MoE significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while reducing active parameters by 50%.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes DOT-MoE, a framework that converts pre-trained dense LLMs into sparse MoE models by casting FFN layer decomposition as a balanced differentiable optimal transport problem. Neuron-to-expert assignments are obtained via Sinkhorn-Knopp iterations with strict capacity constraints, and straight-through estimators enable joint end-to-end learning of the discrete assignments together with the token-to-expert routing policy. The central empirical claim is that this approach significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while halving the number of active parameters.

Significance. If the reported performance retention and outperformance hold under rigorous controls, the method would supply a more principled, capacity-constrained alternative to heuristic partitioning for post-hoc MoE conversion. This could reduce reliance on unstable from-scratch MoE training and improve inference efficiency for large models. The use of differentiable OT plus STE is a technically coherent way to enforce balance without post-hoc fixes, but the absence of concrete metrics, significance tests, or robustness data in the supplied material prevents a firm judgment of practical impact.

major comments (2)
  1. Abstract: the claim that DOT-MoE 'significantly outperforms' baselines and 'retains 90% of the original dense model's performance' is presented without any reported metrics (e.g., perplexity, accuracy deltas), statistical significance, hyperparameter sensitivity analysis, or checks for robustness across random seeds and model scales. This omission makes the central empirical claim impossible to evaluate from the given text.
  2. Abstract: the assumption that framing neuron assignment as a balanced OT problem solved by differentiable Sinkhorn iterations will yield partitions that preserve capability better than heuristics is stated but not accompanied by any derivation or ablation showing that the transport cost or capacity constraints are load-bearing for the reported gains; the experimental outcomes are the sole support.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments. We address each major point below and indicate where revisions to the manuscript will be made.

read point-by-point responses

  1. Referee: Abstract: the claim that DOT-MoE 'significantly outperforms' baselines and 'retains 90% of the original dense model's performance' is presented without any reported metrics (e.g., perplexity, accuracy deltas), statistical significance, hyperparameter sensitivity analysis, or checks for robustness across random seeds and model scales. This omission makes the central empirical claim impossible to evaluate from the given text.

    Authors: We agree that the abstract, due to length constraints, does not include specific numerical deltas, statistical tests, or robustness details. The full manuscript reports concrete perplexity and accuracy results across models and benchmarks, with baseline comparisons. To make the central claim more evaluable directly from the abstract, we will revise it to include example quantitative results (e.g., specific retention percentages and deltas on key tasks). revision: yes

  2. Referee: Abstract: the assumption that framing neuron assignment as a balanced OT problem solved by differentiable Sinkhorn iterations will yield partitions that preserve capability better than heuristics is stated but not accompanied by any derivation or ablation showing that the transport cost or capacity constraints are load-bearing for the reported gains; the experimental outcomes are the sole support.

    Authors: The method section motivates the balanced OT formulation by the need for strict, differentiable capacity constraints without post-hoc adjustments. No theoretical derivation of optimality is provided. The primary evidence is empirical comparison to heuristic baselines. We will add a targeted ablation isolating the transport cost and capacity terms in the revised manuscript to demonstrate their contribution to the observed gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper formulates neuron-to-expert assignment as a balanced optimal transport problem solved with differentiable Sinkhorn iterations and STE, then reports empirical gains over pruning, clustering, and random baselines. No equation or claim in the supplied abstract reduces the reported performance retention or parameter reduction to a quantity defined by the same fitted parameters or by a self-citation chain. The central claim rests on external experimental outcomes rather than on a definitional or fitted-input equivalence, making the derivation self-contained against the given material.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be extracted from derivations or experimental sections.

pith-pipeline@v0.9.1-grok · 5752 in / 1072 out tokens · 29366 ms · 2026-06-28T15:28:15.788950+00:00 · methodology

discussion (0)

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Reference graph

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