arxiv: 2604.13546 · v1 · submitted 2026-04-15 · 💻 cs.LG

Recognition: unknown

Learning Inference Concurrency in DynamicGate MLP Structural and Mathematical Justification

Yongil Choi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:14 UTC · model grok-4.3

classification 💻 cs.LG

keywords DynamicGate MLPinference concurrencyparameter separationonline learningasynchronous updatesmodel snapshotsadaptive neural networkspartial updates

0 comments

The pith

DynamicGate MLP permits concurrent learning and inference by separating routing parameters from representation parameters.

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

Conventional networks cannot update parameters during inference without making outputs unstable and the inference function undefined. This paper shows that DynamicGate MLP structurally permits learning and inference to run at the same time. The separation of routing parameters from representation parameters lets the gate adapt online or allows selective updates only in inactive subspaces. Even with asynchronous or partial updates, each inference output remains equivalent to a forward pass through some valid, fixed model snapshot. A reader would care because this structure could support continuous online adaptation without pausing inference.

Core claim

By separating routing (gating) parameters from representation (prediction) parameters, DynamicGate MLP allows the gate to be adapted online while inference stability is preserved, or weights to be selectively updated only within the inactive subspace. Sufficient conditions for concurrency are mathematically formalized, and the inference output at each time step can always be interpreted as a forward computation of a valid model snapshot even under asynchronous or partial updates.

What carries the argument

Separation of routing (gating) parameters from representation (prediction) parameters, which keeps partial or asynchronous updates equivalent to a forward pass on a complete fixed snapshot.

If this is right

DynamicGate MLP can serve as a foundation for online adaptive and on-device learning systems.
The gate can be adapted online while inference stability is preserved.
Weights can be selectively updated only within the inactive subspace without affecting current outputs.
Inference remains well-defined and stable even when parameters change during the process.

Where Pith is reading between the lines

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

Architectures using similar routing-representation splits could support concurrent operations in other neural network families.
Real-time on-device adaptation becomes feasible if the snapshot equivalence holds under hardware-level update delays.
Empirical tests with controlled partial-update schedules could confirm the sufficient conditions derived in the paper.

Load-bearing premise

Separating routing parameters from representation parameters is sufficient to guarantee that any partial or asynchronous update still produces an output identical to some complete fixed model.

What would settle it

A concrete sequence of partial asynchronous updates where the observed inference output differs from the output of every possible fixed snapshot of the model at that moment.

Figures

Figures reproduced from arXiv: 2604.13546 by Yongil Choi.

**Figure 2.** Figure 2: (1) Online Adaptation Loss (𝜃-only) A graph showing the loss change during online adaptation steps for each gating/MoE model. The Dense model has no trainable gate/router parameters, so it has no loss curve [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Figure 3: (2) Accuracy under Drift Before vs After 𝜃-only Online Adaptation: A bar chart comparing how each model’s accuracy changes before and after online adaptation in a drift environment. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Figure 4: (3) Compute Proxy (FLOPs~) under Drift (lower is cheaper) [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: (4) Routing Flip Rate under Drift (higher = less stable) [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Correlation graph between Flip ratio and AdaptAcc [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

read the original abstract

Conventional neural networks strictly separate learning and inference because if parameters are updated during inference, outputs become unstable and even the inference function itself is not well defined [1, 2, 3]. This paper shows that DynamicGate MLP structurally permits learning inference concurrency [4, 5]. The key idea is to separate routing (gating) parameters from representation (prediction) parameters, so that the gate can be adapted online while inference stability is preserved, or weights can be selectively updated only within the inactive subspace [4, 5, 6, 7]. We mathematically formalize sufficient conditions for concurrency and show that even under asynchronous or partial updates, the inference output at each time step can always be interpreted as a forward computation of a valid model snapshot [8, 9, 10]. This suggests that DynamicGate MLP can serve as a practical foundation for online adaptive and on device learning systems [11, 12].

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.

Desk Editor's Note private letter to a colleague

DynamicGate MLPs support concurrent learning and inference via gating-representation split, with formal conditions claimed but needing verification.

read the letter

The main point is that this paper argues DynamicGate MLPs can support learning during inference by separating the routing parameters from the representation ones. This separation means you can adapt the gates online or update only inactive weights, and the output at any time still counts as a forward pass on a complete model. What stands out is the attempt to formalize sufficient conditions for this concurrency property. It explains how asynchronous or partial updates don't invalidate the current inference because the active subspace stays well-defined. This could be useful for building systems that need to keep learning on the fly, like on-device models that adapt without stopping. The paper does well at connecting the dots from the architecture to practical stability. It cites the relevant prior results on the same model family and shows how the split avoids the usual problems where updates break the inference function. That said, the argument has a soft spot around independence. Since the concurrency is tied directly to the parameter separation defined in the authors' earlier papers, the claim that outputs are always valid snapshots comes close to being true by how the model is constructed. The abstract states that conditions have been formalized, but the lack of visible step-by-step derivations or tests against edge cases makes it hard to assess how general or strong those conditions are. The citation pattern stays mostly within the authors' sequence, which keeps things consistent but limits external grounding. This kind of work is for researchers focused on continual or online learning in neural nets, particularly those using gated or modular architectures. Someone looking for a concrete way to enable stable adaptation without full retraining would see value here. I think it deserves to go to peer review. A referee can examine the math in detail and decide if the formalization adds enough beyond the structural description.

Referee Report

2 major / 0 minor

Summary. The paper claims that DynamicGate MLP structurally permits concurrent learning and inference by separating routing (gating) parameters from representation (prediction) parameters. It mathematically formalizes sufficient conditions such that even under asynchronous or partial updates, each inference output can be interpreted as a forward pass on a valid, fixed model snapshot, enabling online adaptive and on-device learning systems.

Significance. If the formalization of sufficient conditions is rigorous and the parameter separation indeed ensures snapshot validity independent of update timing, the result would address a fundamental limitation of conventional networks and provide a practical basis for concurrent learning-inference pipelines in adaptive ML.

major comments (2)

Abstract: The central claim that 'sufficient conditions have been formalized' and that 'the inference output at each time step can always be interpreted as a forward computation of a valid model snapshot' lacks any visible derivations, proofs, or counter-example verification in the manuscript. This absence is load-bearing because the soundness of the concurrency guarantee rests entirely on the unshown formalization rather than on demonstrated properties of the architecture.
The weakest assumption—that separating gating parameters from prediction parameters is sufficient to guarantee that partial or asynchronous updates leave the output equivalent to a complete fixed snapshot—is presented as following directly from the architecture definition and prior works [4,5,6,7]. Without an independent argument or explicit theorem showing why this separation prevents ill-defined states, the claim risks circularity with the model's own structural definition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify that the manuscript's claims about formalized sufficient conditions require more explicit, visible derivations and an independent argument to avoid any perception of circularity. We have revised the manuscript to incorporate these elements.

read point-by-point responses

Referee: [—] Abstract: The central claim that 'sufficient conditions have been formalized' and that 'the inference output at each time step can always be interpreted as a forward computation of a valid model snapshot' lacks any visible derivations, proofs, or counter-example verification in the manuscript. This absence is load-bearing because the soundness of the concurrency guarantee rests entirely on the unshown formalization rather than on demonstrated properties of the architecture.

Authors: We agree that the abstract asserts the formalization without sufficient supporting detail visible to the reader. Although the full manuscript contains a mathematical formalization of the sufficient conditions (drawing on the parameter separation), the derivations, proofs, and verification steps are not presented with the required explicitness or counter-example checks. In the revised version we will add a dedicated subsection with theorem statements, step-by-step derivations showing snapshot equivalence under asynchronous updates, and concrete counter-example verifications that confirm the concurrency guarantee. revision: yes
Referee: [—] The weakest assumption—that separating gating parameters from prediction parameters is sufficient to guarantee that partial or asynchronous updates leave the output equivalent to a complete fixed snapshot—is presented as following directly from the architecture definition and prior works [4,5,6,7]. Without an independent argument or explicit theorem showing why this separation prevents ill-defined states, the claim risks circularity with the model's own structural definition.

Authors: The separation of gating and representation parameters is an architectural primitive, and prior works supply supporting intuition. However, we accept that presenting this as following directly risks appearing circular. The revised manuscript will contain a new, standalone theorem that derives the snapshot-validity property solely from the separation of parameter classes and the update semantics, without presupposing the overall model definition. The proof will be self-contained and will explicitly show why partial or asynchronous updates cannot produce ill-defined states. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's core argument rests on introducing a parameter separation (routing vs. representation) as the structural mechanism enabling concurrency, then claiming to mathematically formalize sufficient conditions under which partial/asynchronous updates still yield valid model snapshots. No equations or derivations are exhibited in the provided text that reduce the claimed result to a tautological restatement of the input definition or to a fitted parameter. Self-citations to prior works [4,5,6,7,8,9,10] support the architecture's introduction but do not carry the load-bearing formalization step itself; the current manuscript positions its contribution as the independent formalization. The derivation chain therefore remains self-contained against external benchmarks rather than internally forced.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, new entities, or non-standard axioms are enumerated. The argument rests on the domain assumption that parameter separation preserves snapshot validity and on standard neural-network forward-pass definitions.

axioms (1)

domain assumption Separation of gating parameters from representation parameters guarantees that partial updates leave the current output identical to a forward pass of a complete fixed model.
Invoked when the abstract states that inference stability is preserved and outputs remain valid snapshots.

pith-pipeline@v0.9.0 · 5449 in / 1323 out tokens · 59194 ms · 2026-05-10T14:14:42.087407+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

40 extracted references · 13 canonical work pages

[1]

Large-scale machine learning with stochastic gradient descent

Léon Bottou. Large-scale machine learning with stochastic gradient descent. In Proceedings of COMPSTAT’2010. Springer, 2010

2010
[2]

Online learning and online convex optimization

Shai Shalev-Shwartz. Online learning and online convex optimization. Foundations and Trends in Machine Learning , 4(2):107–194, 2012

2012
[3]

Online convex programming and generalized infinitesimal gradient as- cent

Martin Zinkevich. Online convex programming and generalized infinitesimal gradient as- cent. Technical Report CMU-CS-03-110, Carnegie Mellon University, 2003

2003
[4]

Bengio, P.-L

Emmanuel Bengio, Pierre-Luc Bacon, Joelle Pineau, and Doina Precup. Conditional com- putation in neural networks for faster models. arXiv preprint arXiv:1511.06297 , 2015. 17

work page arXiv 2015
[5]

Outrageously large neural networks: The sparsely-gated mixture- of-experts layer

Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, and Jeff Dean. Outrageously large neural networks: The sparsely-gated mixture- of-experts layer. In International Conference on Learning Representations (ICLR) , 2017

2017
[6]

Castro, and Erich Elsen

Utku Evci, Trevor Gale, Jacob Menick, Pablo S. Castro, and Erich Elsen. Rigging the lottery: Making all tickets winners. In International Conference on Machine Learning (ICML), volume 119 of Proceedings of Machine Learning Research , 2020

2020
[7]

Song Han, Jeff Pool, John Tran, and William J. Dally. Learning both weights and connec- tions for eﬀicient neural networks. In Advances in Neural Information Processing Systems (NeurIPS), 2015

2015
[8]

Feng Niu, Benjamin Recht, Christopher Ré, and Stephen J. Wright. Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. In Advances in Neural Information Processing Systems (NeurIPS) , 2011

2011
[9]

Andersen, Jun Woo Park, Alexander J

Mu Li, David G. Andersen, Jun Woo Park, Alexander J. Smola, Amr Ahmed, Vanja Josifovski, James Long, Eugene J. Shekita, and Bor-Yiing Su. Scaling distributed machine learning with the parameter server. In USENIX Symposium on Operating Systems Design and Implementation (OSDI) , 2014

2014
[10]

Large scale distributed deep networks

Jeffrey Dean, Greg Corrado, Rajat Monga, et al. Large scale distributed deep networks. In Advances in Neural Information Processing Systems (NeurIPS) , 2012

2012
[11]

A survey on concept drift adaptation

João Gama, Indrė Žliobaitė, Albert Bifet, Mykola Pechenizkiy, and Abdelhamid Bouchachia. A survey on concept drift adaptation. ACM Computing Surveys , 46(4), 2014

2014
[12]

Tent: Fully test-time adaptation by entropy minimization

Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. In International Conference on Learn- ing Representations (ICLR) , 2021

2021
[13]

Kingma and Jimmy Ba

Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR) , 2015

2015
[14]

Rumelhart, Geoffrey E

David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams. Learning representations by back-propagating errors. Nature, 323:533–536, 1986

1986
[15]

Parisi, Ronald Kemker, Jose L

German I. Parisi, Ronald Kemker, Jose L. Part, Christopher Kanan, and Stefan Wermter. Continual lifelong learning with neural networks: A review. Neural Networks , 113:54–71, 2019

2019
[16]

A continual learning survey: Defying forgetting in classification tasks

Matthias De Lange, Rahaf Aljundi, Marc Masana, Sarah Parisot, Xu Jia, Aleš Leonardis, Gregory Slabaugh, and Tinne Tuytelaars. A continual learning survey: Defying forgetting in classification tasks. arXiv preprint arXiv:1909.08383 , 2019

work page arXiv 1909
[17]

Overcoming catastrophic for- getting in neural networks

James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, et al. Overcoming catastrophic for- getting in neural networks. Proceedings of the National Academy of Sciences , 114(13):3521– 3526, 2017

2017
[18]

Switch transformers: Scaling to trillion parameter models with simple and eﬀicient sparsity

William Fedus, Barret Zoph, and Noam Shazeer. Switch transformers: Scaling to trillion parameter models with simple and eﬀicient sparsity. Journal of Machine Learning Research, 23(120):1–39, 2022

2022
[19]

Revisiting batch normalization for practical domain adaptation,

Yanghao Li, Naiyan Wang, Jianping Shi, Jiaying Liu, and Xiaodi Hou. Revisiting batch normalization for practical domain adaptation. arXiv preprint arXiv:1603.04779 , 2016. 18

work page arXiv 2016
[20]

Ttn: A domain-shift aware batch normalization in test-time adaptation

Hyesu Lim, Byeonggeun Kim, Jaegul Choo, and Sungha Choi. Ttn: A domain-shift aware batch normalization in test-time adaptation. In International Conference on Learning Representations (ICLR), 2023. arXiv:2302.05155

work page arXiv 2023
[21]

Eﬀicient test-time model adaptation without forgetting

Shuaicheng Niu, Jiaxiang Wu, Yifan Zhang, Yaofo Chen, Shijian Zheng, Peilin Zhao, and Mingkui Tan. Eﬀicient test-time model adaptation without forgetting. In Proceedings of the 39th International Conference on Machine Learning (ICML) , volume 162 of Proceedings of Machine Learning Research , pages 16888–16905. PMLR, 2022

2022
[22]

Towards stable test-time adap- tation in dynamic wild world

Shuaicheng Niu, Jiaxiang Wu, Yifan Zhang, Zhiquan Wen, Yaofo Chen, Peilin Zhao, and Mingkui Tan. Towards stable test-time adaptation in dynamic wild world. In International Conference on Learning Representations (ICLR) , 2023. arXiv:2302.12400

work page arXiv 2023
[23]

Continual test-time domain adaptation

Qin Wang, Olga Fink, Luc Van Gool, and Dengxin Dai. Continual test-time domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 7201–7211, June 2022

2022
[24]

Test- time training with self-supervision for generalization under distribution shifts

Yu Sun, Xiaolong Wang, Zhuang Liu, John Miller, Alexei Efros, and Moritz Hardt. Test- time training with self-supervision for generalization under distribution shifts. In Proceed- ings of the 37th International Conference on Machine Learning (ICML) , volume 119 of Pro- ceedings of Machine Learning Research , pages 9229–9248. PMLR, 2020. arXiv:1909.13231

work page arXiv 2020
[25]

Yossi Gandelsman, Yu Sun, Xinlei Chen, and Alexei A. Efros. Test-time training with masked autoencoders. In Advances in Neural Information Processing Systems (NeurIPS) , pages 29374–29385, 2022. arXiv:2209.07522

work page arXiv 2022
[26]

Memo: Test time robustness via adapta- tion and augmentation

Marvin Zhang, Sergey Levine, and Chelsea Finn. Memo: Test time robustness via adapta- tion and augmentation. In Advances in Neural Information Processing Systems (NeurIPS) , volume 35, pages 38629–38642, 2022. arXiv:2110.09506

work page arXiv 2022
[27]

Test-time classifier adjustment module for model- agnostic domain generalization

Yusuke Iwasawa and Yutaka Matsuo. Test-time classifier adjustment module for model- agnostic domain generalization. In Advances in Neural Information Processing Systems (NeurIPS), volume 34, pages 2427–2440, 2021

2021
[28]

Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation

Jian Liang, Dapeng Hu, and Jiashi Feng. Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation. In Proceedings of the 37th International Conference on Machine Learning (ICML) , volume 119 of Proceedings of Machine Learning Research, pages 6028–6039. PMLR, 2020. arXiv:2002.08546

work page arXiv 2020
[29]

Dynamic evaluation of neural sequence models

Ben Krause, Emmanuel Kahembwe, Iain Murray, and Steve Renals. Dynamic evaluation of neural sequence models. In Proceedings of the 35th International Conference on Machine Learning (ICML) , volume 80 of Proceedings of Machine Learning Research , pages 2766–
[30]

arXiv:1709.07432

PMLR, 2018. arXiv:1709.07432

work page arXiv 2018
[31]

Efficient test-time prompt tuning for vision-language models.arXiv preprint arXiv:2408.05775, 2024

Yuhan Zhu, Guozhen Zhang, Chen Xu, Haocheng Shen, Xiaoxin Chen, Gangshan Wu, and Limin Wang. Eﬀicient test-time prompt tuning for vision-language models. arXiv preprint arXiv:2408.05775, 2024. Submitted to ICLR 2025 (OpenReview)

work page arXiv 2024
[32]

Hee Suk Yoon, Eunseop Yoon, Joshua Tian Jin Tee, Mark Hasegawa-Johnson, Yingzhen Li, and Chang D. Yoo. C-tpt: Calibrated test-time prompt tuning for vision-language models via text feature dispersion. In International Conference on Learning Representations (ICLR), 2024. arXiv:2403.14119

work page arXiv 2024
[33]

Test-time low rank adaptation via confidence maximization for zero-shot generalization of vision-language models

Raza Imam, Hanan Gani, Muhammad Huzaifa, and Karthik Nandakumar. Test-time low rank adaptation via confidence maximization for zero-shot generalization of vision-language models. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (W ACV), pages 5449–5459, February 2025. arXiv:2407.15913. 19

work page arXiv 2025
[34]

A stochastic approximation method

Herbert Robbins and Sutton Monro. A stochastic approximation method. The Annals of Mathematical Statistics , 22(3):400–407, 1951

1951
[35]

Nguyen, Madeleine Gibescu, and Antonio Liotta

Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H. Nguyen, Madeleine Gibescu, and Antonio Liotta. Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science. Nature Communications, 9(1), 2018

2018
[36]

Song Han, Huizi Mao, and William J. Dally. Deep compression: Compressing deep neu- ral networks with pruning, trained quantization and huffman coding. In International Conference on Learning Representations (ICLR) , 2016

2016
[37]

Lawrence, editors

Joaquin Quiñonero-Candela, Masashi Sugiyama, Anton Schwaighofer, and Neil D. Lawrence, editors. Dataset Shift in Machine Learning . MIT Press, 2009

2009
[38]

Efros, and Moritz Hardt

Yu Sun, Xiaolong Wang, Zhuang Liu, John Miller, Alexei A. Efros, and Moritz Hardt. Test-time training with self-supervision for generalization under distribution shifts. In International Conference on Machine Learning (ICML) , volume 119 of Proceedings of Machine Learning Research, pages 9229–9248, 2020

2020
[39]

Gshard: Scaling giant models with conditional computation and automatic sharding

Dmitry Lepikhin, HyoukJoong Lee, Yuanzhong Xu, et al. Gshard: Scaling giant models with conditional computation and automatic sharding. In International Conference on Learning Representations (ICLR) , 2021

2021
[40]

Dai, et al

Nan Du, Yanping Huang, Andrew M. Dai, et al. Glam: Eﬀicient scaling of language models with mixture-of-experts. In International Conference on Machine Learning (ICML), volume 162 of Proceedings of Machine Learning Research , 2022. 20

2022