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In neuroscience and machine learning, three-factor learning is the combinaison of Hebbian plasticity with a third modulatory factor to stabilise and enhance synaptic learning.^[1] This third factor can represent various signals such as reward, punishment, error, surprise, or novelty, often implemented through neuromodulators.^[2]

Description

Three-factor learning introduces the concept of eligibility traces, which flag synapses for potential modification pending the arrival of the third factor, and helps temporal credit assignement by bridging the gap between rapid neuronal firing and slower behavioral timescales, from which learning can be done.^[3] Biological basis for Three-factor learning rules have been supported by experimental evidence.^[4]^[2] This approach addresses the instability of classical Hebbian learning by minimizing autocorrelation and maximizing cross-correlation between inputs.^[1]

References

^ ^a ^b Porr, Bernd; W?rg?tter, Florentin (October 2007). "Learning with "Relevance": Using a Third Factor to Stabilize Hebbian Learning". Neural Computation. 19 (10): 2694–2719. doi:10.1162/neco.2007.19.10.2694. ISSN 0899-7667. PMID 17716008.
^ ^a ^b Gerstner, Wulfram; Lehmann, Marco; Liakoni, Vasiliki; Corneil, Dane; Brea, Johanni (2025-08-06). "Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules". Frontiers in Neural Circuits. 12: 53. doi:10.3389/fncir.2018.00053. ISSN 1662-5110. PMC 6079224. PMID 30108488.
^ Frémaux, Nicolas; Gerstner, Wulfram (2025-08-06). "Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules". Frontiers in Neural Circuits. 9: 85. doi:10.3389/fncir.2015.00085. ISSN 1662-5110. PMC 4717313. PMID 26834568.
^ Ku?mierz, ?ukasz; Isomura, Takuya; Toyoizumi, Taro (2025-08-06). "Learning with three factors: modulating Hebbian plasticity with errors". Current Opinion in Neurobiology. Computational Neuroscience. 46: 170–177. doi:10.1016/j.conb.2017.08.020. ISSN 0959-4388. PMID 28918313.

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[:0-1] Porr, Bernd; W?rg?tter, Florentin (October 2007). "Learning with "Relevance": Using a Third Factor to Stabilize Hebbian Learning". Neural Computation. 19 (10): 2694–2719. doi:10.1162/neco.2007.19.10.2694. ISSN 0899-7667. PMID 17716008.

[Behavioral_Time_Scales_2018-2] Gerstner, Wulfram; Lehmann, Marco; Liakoni, Vasiliki; Corneil, Dane; Brea, Johanni (2025-08-06). "Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules". Frontiers in Neural Circuits. 12: 53. doi:10.3389/fncir.2018.00053. ISSN 1662-5110. PMC 6079224. PMID 30108488.

[3] Frémaux, Nicolas; Gerstner, Wulfram (2025-08-06). "Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules". Frontiers in Neural Circuits. 9: 85. doi:10.3389/fncir.2015.00085. ISSN 1662-5110. PMC 4717313. PMID 26834568.

[4] Ku?mierz, ?ukasz; Isomura, Takuya; Toyoizumi, Taro (2025-08-06). "Learning with three factors: modulating Hebbian plasticity with errors". Current Opinion in Neurobiology. Computational Neuroscience. 46: 170–177. doi:10.1016/j.conb.2017.08.020. ISSN 0959-4388. PMID 28918313.

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