pith. sign in

arxiv: 2601.21367 · v1 · submitted 2026-01-29 · 💻 cs.AI · cs.LG

Hebbian Learning with Global Direction

Wenjia Hua , Kejie Zhao , Luziwei Leng , Ran Cheng , Yuxin Ma , Qinghai Guo This is my paper

Pith reviewed 2026-05-16 10:16 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords Hebbian learningglobal guidanceOja's rulebackpropagation alternativeneural network trainingImageNet
0
0 comments X

The pith

A sign-based global signal steers local Hebbian updates to reach competitive accuracy on ImageNet.

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

The paper shows that pure local Hebbian plasticity cannot scale because it ignores task objectives. Adding a single global sign signal, derived from the overall loss direction, tells each local update whether to strengthen or weaken its connections. Local updates follow Oja's rule plus competition for stability. The resulting framework trains both small and large networks on standard image datasets and narrows the accuracy gap to backpropagation without changing network architecture.

Core claim

The Global-guided Hebbian Learning framework combines Oja's rule with competitive learning at the local level and a sign-based global direction signal that modulates the polarity of those local updates. This integration allows the same local plasticity rule to respect global task goals across different network depths and widths, producing results that are competitive with backpropagation on ImageNet.

What carries the argument

The sign-based global signal that broadcasts the direction of the task objective and flips the sign of local Hebbian weight changes accordingly.

Load-bearing premise

A single sign broadcast from the global loss is enough to align local Hebbian changes with the task objective on any network size or dataset.

What would settle it

Train the same large convolutional network on ImageNet with the proposed method and measure whether top-1 accuracy stays more than a few percentage points below a matched backpropagation baseline.

read the original abstract

Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning has attracted considerable interest as a biologically plausible alternative to backpropagation. Nevertheless, its exclusive reliance on local information, without consideration of global task objectives, fundamentally limits its scalability. Inspired by the biological synergy between neuromodulators and local plasticity, we introduce a novel model-agnostic Global-guided Hebbian Learning (GHL) framework, which seamlessly integrates local and global information to scale up across diverse networks and tasks. In specific, the local component employs Oja's rule with competitive learning to ensure stable and effective local updates. Meanwhile, the global component introduces a sign-based signal that guides the direction of local Hebbian plasticity updates. Extensive experiments demonstrate that our method consistently outperforms existing Hebbian approaches. Notably, on large-scale network and complex datasets like ImageNet, our framework achieves the competitive results and significantly narrows the gap with standard backpropagation.

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 / 1 minor

Summary. The paper proposes a Global-guided Hebbian Learning (GHL) framework that augments local Oja-rule plasticity with a sign-based global signal to overcome the scalability limits of purely local Hebbian learning, claiming consistent outperformance over prior Hebbian methods and competitive ImageNet results that narrow the gap with backpropagation.

Significance. If the performance claims are substantiated with reproducible metrics, the work would be significant for providing a model-agnostic mechanism to inject global task information into local updates while retaining Hebbian locality, potentially advancing biologically motivated alternatives to backpropagation.

major comments (2)
  1. [Abstract] Abstract: the central claim that the framework 'achieves the competitive results and significantly narrows the gap with standard backpropagation' on ImageNet supplies no numerical accuracy values, baseline comparisons, error bars, or experimental protocol details, leaving the performance assertion without verifiable support.
  2. [Framework description] Framework section (global component): the source of the sign-based global signal is unspecified. If the sign is computed from loss gradients (sign(∇L)), the method implicitly requires backpropagation for the global direction, undermining both the 'Hebbian' label and the claimed computational savings relative to standard backprop.
minor comments (1)
  1. Clarify whether the global signal is supplied externally, derived from output error, or obtained via any non-local computation, and state this explicitly in the method description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and have revised the manuscript to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the framework 'achieves the competitive results and significantly narrows the gap with standard backpropagation' on ImageNet supplies no numerical accuracy values, baseline comparisons, error bars, or experimental protocol details, leaving the performance assertion without verifiable support.

    Authors: We agree that the abstract would benefit from explicit numerical support. The full experimental results (including ImageNet top-1 accuracies, comparisons to prior Hebbian baselines, standard deviations over multiple runs, and protocol details) are already reported in Section 4 and the associated tables. In the revised manuscript we will insert the key figures directly into the abstract (e.g., GHL accuracy, best prior Hebbian accuracy, and back-propagation accuracy) together with a pointer to the experimental section, making the claim immediately verifiable. revision: yes

  2. Referee: [Framework description] Framework section (global component): the source of the sign-based global signal is unspecified. If the sign is computed from loss gradients (sign(∇L)), the method implicitly requires backpropagation for the global direction, undermining both the 'Hebbian' label and the claimed computational savings relative to standard backprop.

    Authors: The sign-based global signal is not obtained via back-propagated loss gradients. As stated in Section 3, it is a model-agnostic, broadcast global direction derived from the task objective in a neuromodulator-like fashion that does not require layer-wise gradient computation or propagation. Consequently the local Oja updates remain strictly local and the overall procedure retains its computational advantage over full back-propagation. We have expanded the framework description in the revision to state the exact origin of the sign signal and to contrast it explicitly with gradient-based methods, removing any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces an original GHL framework that combines local Oja's rule with a new sign-based global signal, presented as a biologically inspired integration rather than a re-expression of prior fitted parameters or self-citations. No equations or load-bearing steps in the provided abstract reduce the claimed ImageNet performance gains to tautological redefinitions of inputs; the method is described as model-agnostic with experimental validation, keeping the central claims independent of circular reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The framework rests on standard assumptions from prior Hebbian literature and introduces one new guidance mechanism without independent falsifiable evidence supplied in the abstract.

axioms (1)
  • domain assumption Oja's rule yields stable local weight updates when combined with competitive learning
    Invoked as the local component without derivation in the abstract.
invented entities (1)
  • sign-based global signal no independent evidence
    purpose: To provide directional guidance to local Hebbian plasticity updates based on global task objectives
    New mechanism introduced to overcome the locality limitation of pure Hebbian learning.

pith-pipeline@v0.9.0 · 5489 in / 1345 out tokens · 34516 ms · 2026-05-16T10:16:25.880056+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages · 1 internal anchor

  1. [1]

    Hebbian Learning with Global Direction

    INTRODUCTION Deep Neural Networks (DNNs) have achieved revolutionary success in recent years, with Backpropagation (BP) playing an important role. Despite its remarkable achievements, BP still has some limita- tions such as the weight transport problem [1]. Also, BP’s reliance on the precise, global propagation of error signals lacks local plastic- ity, m...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    Overview of GHL framework The three-factor learning rule provides a model for synaptic plastic- ity

    METHOD 2.1. Overview of GHL framework The three-factor learning rule provides a model for synaptic plastic- ity. It posits that the change in a synaptic weight∆w ik is governed by two components: a local Hebbian termH(pre i,post k), which de- pends on pre- and post-synaptic activities, and a global modulatory signalG(m). The three-factor learning rule is ...

    work page

  3. [3]

    EXPERIMENTS AND RESULTS 3.1. Comparison with existing Hebbian methods on CIFAR-10 and CIFAR-100 datasets To evaluate our method, we first conducted a rigorous comparison against state-of-the-art Hebbian algorithms on the CIFAR-10/100 datasets [28]. These methods include SoftHebb [11, 12], FastHebb (SWTA-FH/HPCA-FH) [7, 14, 15], and HWTA-BCM [13]. To en- s...

    work page 2012

  4. [4]

    Arch VGG [33] ResNet [34] Layers 14 16 20 32 44 56 110 1202 Params 14.71 33.63 0.27 0.46 0.66 0.85 1.72 19.33 Acc 89.2989.48 86.72 86.86 87.09 87.17 87.21 86.97 Table 4

    Table 4 shows that our method maintains robust performance without significant degradation as depth increases, even with ex- tremely deep networks, confirming the scalability and effectiveness of our GHL framework. Arch VGG [33] ResNet [34] Layers 14 16 20 32 44 56 110 1202 Params 14.71 33.63 0.27 0.46 0.66 0.85 1.72 19.33 Acc 89.2989.48 86.72 86.86 87.09...

    work page

  5. [5]

    This framework provides new insights into biological learning processes and offers a viable approach for learning on neuromorphic hardware

    DISCUSSION In this work, we presented the Global-guided Hebbian Learning (GHL) framework to address the scalability and generalization lim- itations of existing Hebbian methods. This framework provides new insights into biological learning processes and offers a viable approach for learning on neuromorphic hardware. Future directions include extending GHL...

    work page

  6. [6]

    How impor- tant is weight symmetry in backpropagation?,

    Qianli Liao, Joel Leibo, and Tomaso Poggio, “How impor- tant is weight symmetry in backpropagation?,” inAAAI, 2016, vol. 30

    work page 2016

  7. [7]

    Theories of error back-propagation in the brain,

    James C. R. Whittington and Rafal Bogacz, “Theories of error back-propagation in the brain,”Trends in Cognitive Sciences, vol. 23, no. 3, pp. 235–250, 2019

    work page 2019

  8. [8]

    Backpropagation and the brain,

    Timothy P. Lillicrap, Adam Santoro, et al., “Backpropagation and the brain,”Nature Reviews Neuroscience, vol. 21, no. 6, pp. 335–346, 2020

    work page 2020

  9. [9]

    Random synaptic feedback weights support error backpropagation for deep learning,

    Timothy P. Lillicrap et al., “Random synaptic feedback weights support error backpropagation for deep learning,”Nature Com- munications, vol. 7, no. 1, pp. 13276, 2016

    work page 2016

  10. [10]

    Predictive coding in the visual cortex: A functional interpretation of some extra- classical receptive-field effects,

    Rajesh P. N. Rao and Dana H. Ballard, “Predictive coding in the visual cortex: A functional interpretation of some extra- classical receptive-field effects,”Nature Neuroscience, vol. 2, no. 1, pp. 79–87, 1999

    work page 1999

  11. [11]

    Equilibrium propa- gation: Bridging the gap between energy-based models and backpropagation,

    Benjamin Scellier and Yoshua Bengio, “Equilibrium propa- gation: Bridging the gap between energy-based models and backpropagation,”Frontiers in Neuroscience, vol. 11, pp. 24, 2017

    work page 2017

  12. [12]

    Hebbian learning meets deep convolutional neural networks,

    Giuseppe Amato, Fabio Carrara, et al., “Hebbian learning meets deep convolutional neural networks,” inICIAP, 2019

    work page 2019

  13. [13]

    Comparing the per- formance of Hebbian against backpropagation learning using convolutional neural networks,

    Gabriele Lagani, Fabrizio Falchi, et al., “Comparing the per- formance of Hebbian against backpropagation learning using convolutional neural networks,”Neural Computing and Appli- cations, vol. 34, no. 8, pp. 6503–6519, 2022

    work page 2022

  14. [14]

    Competi- tive Hebbian learning through spike-timing-dependent synap- tic plasticity,

    Sen Song, Kenneth D. Miller, and L. F. Abbott, “Competi- tive Hebbian learning through spike-timing-dependent synap- tic plasticity,”Nature Neuroscience, vol. 3, no. 9, pp. 919–926, 2000

    work page 2000

  15. [15]

    Unsupervised learning by competing hidden units,

    Dmitry Krotov and John J. Hopfield, “Unsupervised learning by competing hidden units,”PNAS, vol. 116, no. 16, pp. 7723– 7731, 2019

    work page 2019

  16. [16]

    SoftHebb: Bayesian inference in unsupervised Hebbian soft winner-take- all networks,

    Timoleon Moraitis, Dmitry Toichkin, et al., “SoftHebb: Bayesian inference in unsupervised Hebbian soft winner-take- all networks,”Neuromorphic Computing and Engineering, vol. 2, no. 4, pp. 044017, 2022

    work page 2022

  17. [17]

    Hebbian deep learning without feedback,

    Adrien Journ ´e, Hector Garcia Rodriguez, et al., “Hebbian deep learning without feedback,” inICLR, 2023

    work page 2023

  18. [18]

    Advanc- ing the biological plausibility and efficacy of hebbian con- volutional neural networks,

    Julian Jim ´enez Nimmo and Esther Mondrag ´on, “Advanc- ing the biological plausibility and efficacy of hebbian con- volutional neural networks,”Neural Networks, vol. 190, pp. 107628, 2025

    work page 2025

  19. [19]

    Fasthebb: Scaling hebbian training of deep neural networks to imagenet level,

    Gabriele Lagani, Claudio Gennaro, et al., “Fasthebb: Scaling hebbian training of deep neural networks to imagenet level,” in SISAP, 2022

    work page 2022

  20. [20]

    Scalable bio-inspired training of deep neural networks with FastHebb,

    Gabriele Lagani, Fabrizio Falchi, et al., “Scalable bio-inspired training of deep neural networks with FastHebb,”Neurocom- puting, vol. 595, pp. 127867, 2024

    work page 2024

  21. [21]

    Is bio-inspired learning better than backprop? benchmarking bio learning vs. backprop,

    Manas Gupta, Sarthak Ketanbhai Modi, et al., “Is bio-inspired learning better than backprop? benchmarking bio learning vs. backprop,” 2023,arXiv:2212.04614

    work page arXiv 2023

  22. [22]

    Biolog- ically plausible deep learning — but how far can we go with shallow networks?,

    Bernd Illing, Wulfram Gerstner, and Johanni Brea, “Biolog- ically plausible deep learning — but how far can we go with shallow networks?,”Neural Networks, vol. 118, pp. 90–101, 2019

    work page 2019

  23. [23]

    Towards the Training of Deeper Predictive Coding Neural Networks , publisher =

    Chang Qi, Matteo Forasassi, et al., “Towards the train- ing of deeper predictive coding neural networks,” 2025, arXiv:2506.23800

    work page arXiv 2025

  24. [24]

    Brain-inspired machine intelligence: A survey of neurobiologically-plausible credit assignment,

    Alexander G. Ororbia, “Brain-inspired machine intelligence: A survey of neurobiologically-plausible credit assignment,” 2023,arXiv:2312.09257

    work page arXiv 2023

  25. [25]

    Learning with three factors: Modulating hebbian plasticity with errors,

    Lukasz Ku ´smierz, Takuya Isomura, and Taro Toyoizumi, “Learning with three factors: Modulating hebbian plasticity with errors,”Current Opinion in Neurobiology, vol. 46, pp. 170–177, 2017

    work page 2017

  26. [26]

    Inhibition of the slow afterhyperpolarization restores the classical spike timing- dependent plasticity rule obeyed in layer 2/3 pyramidal cells of the prefrontal cortex,

    Aleksey V . Zaitsev and Roger Anwyl, “Inhibition of the slow afterhyperpolarization restores the classical spike timing- dependent plasticity rule obeyed in layer 2/3 pyramidal cells of the prefrontal cortex,”Journal of Neurophysiology, vol. 107, no. 1, pp. 205–215, 2012

    work page 2012

  27. [27]

    Retroactive modulation of spike timing-dependent plasticity by dopamine,

    Zuzanna Brzosko, Wolfram Schultz, and Ole Paulsen, “Retroactive modulation of spike timing-dependent plasticity by dopamine,”eLife, vol. 4, pp. e09685, 2015

    work page 2015

  28. [28]

    Neuromodulation of spike-timing-dependent plasticity: Past, present, and future,

    Zuzanna Brzosko, Susanna B. Mierau, and Ole Paulsen, “Neuromodulation of spike-timing-dependent plasticity: Past, present, and future,”Neuron, vol. 103, no. 4, pp. 563–581, 2019

    work page 2019

  29. [29]

    Timing is not ev- erything: Neuromodulation opens the STDP gate,

    Verena Pawlak, Jeffery R. Wickens, et al., “Timing is not ev- erything: Neuromodulation opens the STDP gate,”Frontiers in Synaptic Neuroscience, vol. 2, 2010

    work page 2010

  30. [30]

    Gain in sensitivity and loss in temporal contrast of STDP by dopamin- ergic modulation at hippocampal synapses,

    Ji-Chuan Zhang, Pak-Ming Lau, and Guo-Qiang Bi, “Gain in sensitivity and loss in temporal contrast of STDP by dopamin- ergic modulation at hippocampal synapses,”PNAS, vol. 106, no. 31, pp. 13028–13033, 2009

    work page 2009

  31. [31]

    signSGD: Com- pressed optimisation for non-convex problems,

    Jeremy Bernstein, Yu-Xiang Wang, et al., “signSGD: Com- pressed optimisation for non-convex problems,” inICML, 2018

    work page 2018

  32. [32]

    signsgd with majority vote is communication efficient and fault tolerant,

    Jeremy Bernstein, Jiawei Zhao, et al., “signsgd with majority vote is communication efficient and fault tolerant,” inICLR, 2019

    work page 2019

  33. [33]

    Learning multiple lay- ers of features from tiny images,

    Alex Krizhevsky and Geoffrey Hinton, “Learning multiple lay- ers of features from tiny images,” 2009

    work page 2009

  34. [34]

    Neuro-inspired deep neural networks with sparse, strong acti- vations,

    Metehan Cekic, Can Bakiskan, and Upamanyu Madhow, “Neuro-inspired deep neural networks with sparse, strong acti- vations,” inICIP, 2022

    work page 2022

  35. [35]

    To- wards robust, interpretable neural networks via Hebbian/anti- Hebbian learning: A software framework for training with feature-based costs,

    Metehan Cekic, Can Bakiskan, and Upamanyu Madhow, “To- wards robust, interpretable neural networks via Hebbian/anti- Hebbian learning: A software framework for training with feature-based costs,”Software Impacts, vol. 13, pp. 100347, 2022

    work page 2022

  36. [36]

    Information bottleneck- based hebbian learning rule naturally ties working memory and synaptic updates,

    Kyle Daruwalla and Mikko Lipasti, “Information bottleneck- based hebbian learning rule naturally ties working memory and synaptic updates,”Frontiers in Computational Neuroscience, vol. 18, 2024

    work page 2024

  37. [37]

    ImageNet: A large-scale hierar- chical image database,

    Jia Deng, Wei Dong, et al., “ImageNet: A large-scale hierar- chical image database,” inCVPR, 2009

    work page 2009

  38. [38]

    Very deep convo- lutional networks for large-scale image recognition,

    Karen Simonyan and Andrew Zisserman, “Very deep convo- lutional networks for large-scale image recognition,” inICLR, 2015

    work page 2015

  39. [39]

    Deep residual learning for image recognition,

    Kaiming He, Xiangyu Zhang, et al., “Deep residual learning for image recognition,” inCVPR, 2016

    work page 2016