Discovering heterogeneous synaptic plasticity rules via large-scale neural evolution
Authors: Ziyuan Ye
Beichen Huang
Yujie Wu
Guozhang Chen
Jibin Wu
Venue: ICLR 2026 Poster (2026)
Keywords: Synaptic plasticity
Evolutionary computation
Computational neuroscience
Primary area: applications to neuroscience & cognitive science
TL;DR: We introduce a Darwinian evolution-like process to discover biologically plausible heterogeneous synaptic plasticity rules in a mouse V1 model, uncovering several functionally equivalent rules, offering insights into memory and innate abilities.

Abstract: Synaptic plasticity is a fundamental substrate for learning and memory, where different synapse types exhibit distinct plasticity mechanisms. However, how functional behaviors emerge from heterogeneous synaptic plasticity mechanisms remains poorly understood. Here, we introduce a computational framework that harnesses Darwinian evolutionary principles to discover biologically plausible, heterogeneous synaptic plasticity rules within a biologically realistic model of the mouse primary visual cortex. Specifically, we parameterize several key factors related to synaptic plasticity, including presynaptic and postsynaptic spikes, their associated eligibility traces, and neuromodulatory signals. By integrating these factors via a truncated Taylor expansion, we construct a large-scale search space of candidate plasticity rules, with each rule containing over 2.6k optimizable parameters. Each rule is subsequently evaluated on both cross-domain visual task performance and biological validity. Leveraging a multi-objective evolutionary algorithm, we effectively navigate this high-dimensional search space to identify plasticity rules that are both biologically plausible and yield high task performance. We uncover diverse families of high-performing plasticity rules that achieve similar behavioral outcomes despite markedly different mathematical formulations, suggesting that real-world synaptic learning mechanisms may exhibit computational degeneracy. We further show that these biologically plausible rules are not only robust across network scales but also enable few-shot learning, offering a computational explanation for the emergence of innate ability.

Published as conference paper ICLR 2026
DISCOVERING HETEROGENEOUS SYNAPTIC PLASTICITY RULES VIA LARGE-SCALE NEURAL EVOLUTION
Ziyuan Ye Beichen Huang' Yujie Wu²i, Guozhang Chen Jibin Wu
Depparmeent of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University
2 *Department of Computing, The Hong Kong Polytechnic University
National Key Lab. for Multimedia Information Processing, School of Computer Science, Peking University {z iziyuan. ye, beichen. huang, ju-jie.wu, jibin, Sibin.wuj@polyyeee edu.hk, guozhang. chen@pku.edu. edu.hk
ABSTRACT
Synaptic plasticity is a fundamental substrate for learning and memory, where different synapse types exhibit distinct plasticity mechanisms. However, how functional behav- iors emerge from heterogeneous synaptic plasticity mechanisms remains poorly under- stood. Here, introduce computational framework that harnesses Darwinian evo- lutionary principles to discover biologically plausible, heterogeneous synaptic plasticity rules within biologically realistic model of the mouse primary visual cortex. Specifi- cally, we parameterize several key factors related to synaptic plasticity, including presy- naptic and postsynaptic spikes, their associated eligibility traces, and neuromodulatory signals. By integrating these factors via truncated Taylor expansion, we construct a large-scale search space of candidate plasticity rules, with each rule containing over 2.6k optimizable parameters. Each rule is subsequently evaluated on both cross-domain visual task performance and biological validity. Leveraging a multi-objective evolutionary al- gorithm, effectively navigate this high-dimensional search space to identify plasticity rules that are both biologically plausible and yield high task performance. We uncover di- verse families of high-pe tigh-performing plasticity rules that achieve similar behavioral outcomes despite markedly different mathematical formulations, suggesting that real-world synaptic learning mechanisms may exhibit computational degeneracy. We further show that these biologically plausible rules are not only robust across network scales but also enable few- shot learning, offering a computational explanation for the emergence of innate ability.
INTRODUCTION
A long-standing ambition in both neuroscience and artificial intelligence has been to uncover the mecha- nisms by which the brain learns to generate intelligent behavior. Synaptic plasticity, as one of the most
fundamental mechanisms underlying learning and memory (Bliss & Collingridge 1993 Markram al.)
2011 McFarlan et al., 2023). has been primarily characterized through experimental studies, revealing a rich repertoire of plasticity mechanisms associated with different types of synapses (Markram al.) [997]
Bi Poo 1998 2001] Woodin et al.) 2003) Froemke & Dan 2002) Kullmann & Lamsa 2007 Kullmann
ct al.
2012 D amour & Froemke 2015). Nevertheless, the technical challenges inherent in large-scale in
vivo experiments have limited our understanding of how these heterogeneous synaptic plasticity mechanisms cooperatively contribute the emergence of behaviors (McFarlan et al. 2023).
"Equal contribution
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In complement to experimental studies, theoretical modeling approaches aim to reveal the principles un-
derlying synaptic plasticity mechanisms by developing mathematical frameworks that explain how neural
activity patterns drive synaptic changes (Hebb) 1949] [Bienesttock et al. [982] Oja 1982 [Song et al. 2000)
Phister & Gerstner, [006] Clopath et al., 2010 Lagzi & Fairhall| 2024 Agnes [
& Vogels (024). Data- driven
inference approaches, on the other hand, seek to extract plasticity rules directly from neural recordings or
behavioral data using machine learning or statistical methods (Bengio et al.] 1991, Stevenson & Koerding
2011
Robinson et al. 2016; Confavreux et al. 2020; Chen et al. [023]] Mchta et al., 2024] [Bell et al.,
2024
Kaleb et al. 2024]] Contavreux et al. 2025a). However. none of these studies have explored the
tensive landscape of heterogeneous plasticity rules in biologically grounded networks, while simultaneously
accounting for biological constraints and functional objectives.
In this paper, we investigate the landscape of heterogeneous plasticity rules by asking:
What mathematical structure and computational principles allow heterogeneous plasticity rules to achieve functional efficacy in realistic cortical circuits?
Scientific Question:
Our approach leverages evolutionary algorithms to search a broad but interpretable candidate space of het- erogeneous plasticity rules on biologically realistic mouse primary visual cortex (V1) model, where each type of synapse is allowed to employ distinct learning mechanism. The exploration process evaluated under multiple objectives that balance task performance with biological plausibility. By simultancously eval- uating a diverse set of candidates within the population, our framework enables the study of not just single "optimal" rule, but a family of rules that span various trade-offs. This includes rules that are potentially very simple yet surprisingly effective, as well as more complex and highly performant ones. As a result, our approach offers way explore the rich diversity of plasticity rules that may exist in the brain. The key contributions are:
Methodological advances: (i) We construct an interpretable candidate space of plasticity rules through
truncated Taylor expansion, enabling comprehensive enumeration of plasticity rules ranging from sim- ple to complex forms, while maintaining biological interpretability (see Sec. 2.T.. (ii) We introduce an evolutionary framework that allows multi-objective optimization
the constructed candidate space for discovering diverse families of plasticity rules (see Sec. Sec.2.2). (iii) We develop several metrics cov- ering task performance and biological constraints, enabling the discovery and systematic evaluation of plasticity rules with varying trade-offs among simplicity, efficiency, task effectiveness, and biological plausibility (see Sec.
Neuroscientific insights: (i) Using the proposed framework, we uncovered families of
plasticity rules capable of producing similar memory behavioral outcomes, despite having significantly different mathematical forms (see Sec. 3.2 and 4.2). (ii) We show that the evolved plasticity rules discovered by our framework enable few-shot learning, suggesting potential mechanistic basis for innate abilities (see Sec. 3.3 and (iii) We further demonstrate that the explored plasticity rules generalize well beyond their evolutionary settings, maintaining their effectiveness across networks of varying scales (see Sec.
2
SYNAPTIC PLASTICITY RULE EXPLORRAIONN FRAMEWORK
In this section, we present the proposed multi-objective evolutionary optimization framework, which en- ables the discovery of biologically plausible synaptic plasticity rules by evolving large-scale population of candidate rules, illustrated in Fig.
2.1 CONSTRUCTION OF SYNAPTIC PLASTICITY RULE CANDIDATES
Studies have shown that cortical circuits comprise diverse synaptic connections between neuronal popula-
tions, which may be governed by distinct plasticity mechanisms (McFarlan al. 2023 To address this
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Heterogeneity of synapses
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mytomm syrapse
1 dy So
2009 rypees
ewtri
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Filtered Pareto onttollptimmll plasticit rules
Figure I: Overview of synaptic plasticity rule exploration framework. a. Our framework accounts for synap- tie heterogeneity by considering one excitatory (Exc) and three classes of inhibitory synapses (Pvalb, Sst, Htr3a), each highlighted with a distinct color. Light and dark variants further indicate layer-specine subtypes within these classes. b. Plasticity rules are constructed from fundamental neural signals, including pre- and postsynaptic spikes, their associated eligibility traces, and the reward prediction error. These signals are sys- tematically combined to generate candidate plasticity sub-rules for each synapse type. c. Plasticity rules are evolved through multi-objective optimization process that simultaneously considers both biological and task performance metrics in a manner that parallels Darwinian evolutionary processes. d. The evolutionary search produces Pareto-optimal subgroup of plasticity rules in the final generation, from which additional constraints are applied to select the filtered population and the overall best-performing rule.
complexity, we build the mouse V1 cortical model (Billeh al. 2020 Chen et al. 2022 biologically grounded spiking recurrent neural network comprising 17 neuron types: four excitatory subtypes from a single class (Exc) and 13 inhibitory subtypes across three classes (Pvalb, Sst, and Htr3a), distributed across six cortical layers (Fig. [a). Specifically, as shown in Fig. Tb, we consider 289 possible synaptic connection types, corresponding to all pairwise combinations of the 17 neuron types. For each of these synaptic types, we employ a set of commonly identified neural signals in constructing synaptic plasticity rules:
SSpre Spost Xpre, Xpost, R):
(1)
where Spee and Spost represent pre- and postsynaptic spikes, Xpre and Xposi denote pre- and postsynaptic eligibility traces that capture the history of neural activity, and R corresponds to the reward prediction error trace that encodes neuromodulatory signals. These signals serve as fundamental building blocks, enabling the systematic construction of diverse plasticity rules through their additive and multiplicative combinations. It is important to note that the diversity of neuron types can significantly influence the temporal dynamics of both reward prediction eтror traces (Mohebi et al. 2024h and eligibility traces (Kerlin et al.) 2010 He et al.] 2015). resulting in heterogeneous plasticity rules across the network. To capture this biological heterogene- ity, we use distinct trace decay parameters for different neuron types, as detailed below.
Reward prediction error trace model. Neuromodulators, such as dopaminergic signals, typically influence synaptic plasticity in the form of reward prediction errors (Steinberg et. 2013 Chang et al. 2016 Corkrum
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et al. 2020 Gershman al. 2024). Motivated by this finding, we model the neuromodulator signal a reward prediction error R in our plasticity formulation, with optimizable purronttype-peecee decay time constants Tn capture the potentially heterogeneous temporal profiles of neuromodulation across different neural populations.
each trial, the neuron population maintains and shares reward prediction signal, modeled as simple moving average of recent rewards: H [r,,-1, ",, - -.-..-.-... - where Nuii 20 is the window size. This approach reflects the fact that reward signals can persist and influence neuronal activity even after the immediate reward has been received (Hamid et al. 2016). Specifically, the population-shared reward prediction error 8R(14 (4.) for trial can be formulated as:
1
F(4) = N Nwin ==1
(2)
6R(4) = -
(3)
Eqs. 2 - drives OR close to when rewards become predictable. Given that neuromodulators signals exhibit distinct dynamics across different synaptic types (Huang et al. 2024b Mohebi et al. (2024) we model this biological heterogeneity by allowing different neuronal types to maintain distinct reward prediction error traces Rm
dRm dt
R
+ (R(()
at trial onset 4 +
R
(4)
Rm
during trial execution,
TR
where TR is the time constant for neuron type that controls the temporal dynamics of the reward signal. Note that the reward prediction error 8R(4) is only given the onset of the next trial.
Eligibility trace model. Similar to neuromodulatory signals, the eligibility traces of and postsynaptic activities also exhibit heterogeneous temporal dynamics across different neuron types (He et al. 2015). In model, each neuron type maintains cligibility trace that decays exponentially over time, with neuron- type-specific time constants to reflect this biological diversity. Specifically, the eligibility trace X' for neuron is denoted
( - At
x'(
where TE refers to the time constant of the eligibility trace for neuron type m, and (t) denotes spike occurrence at time L.
Candidate rule set. We further generate candidate synaptic plasticity terms that act as fundamental building blocks for plasticity rules. Leveraging Taylor expansion's 's ability to enumerate possible neural signal inter- actions while preserving biological interpretability, we derive these plasticity terms by expanding the basic neural signals defined in Eq. (1) up to third order. Formally:
P
II j=1
Uj
Uj E (Spre, Spost, Xpre, Xpos, RJ, 333
(6)
In practice, redundant terms (c.g., Spe Spee since Spe is binary) and non-meaningful terms (e.g.. R²) are removed. This results in candidate term S (P* ppkkNN No jkm1 where Np 25, be used the subsequent construction of plasticity rules. Each plasticity rule is formulated as weighted combination of a subset of these candidate terms. Specifically, for a given pair of presynaptic neuronal type Mpre. and postsynaptic neuronal type Mpest, the candidate plasticity rules are defined as:
No
A W ( (Mire Mppce)
Σ 1=
k. (Vippe Mapoa) pk
(7)
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Physiology experimental data
Bio-information based model construction
Image
LGN model
LGN-V1 Model
v1 Model
Readout from excitatory neurons
Muttiplepaathh electrophysiooogy
Retina
LGN
V1
fixed module leernable module
Figure Overview the biologically realistic mouse V1 model (Billeh al. in this work.
2020 Chen et al.
2022 used
where (M(eeees) denotes the coefficient for the k-th candidate term specific to synapses connecting neu- ronal type mir to type Mpsst- The variable g" E {0, } is a binary selection gate that determines whether the k-th term is active, shared across all synaptic types. According to Eq. (7). the total number of optimiz- able parameters for each plasticity rule exceeds 2.6K, with the detailed calculation provided in Appendix D During the weight optimization, Dale's law (Strata al., 1999) is enforced and hard bounds on the maxi- mum and minimum weight (Gerstner et al. 2014) are implemented to maintain biological plausibility and numerical stability during the weight update. The implementation details are also provided in Appendix D
2.2 PLASTICITY RULE EXPLORATION VIA MULTI-OBJECTIVG EVOLUTIONARY OPTIMIZATION
All optimizable parameters of each synaptic plasticity rule are collected in a vector 0 {c, g, TE, TR). which comprises the plasticity coefficients binary gates g, and the time constants TÆ = {T } and TR {Tx) } that govern the temporal dynamics of eligibility and reward traces across distinct neuron populations, respectively. This parameterization allows us to formulate synaptic plasticity rule exploration as a multi- objective optimization problem:
Minimize F(O) E Y, 0 Qa.
(8)
where F(0) = (O)..... IN, (0)) represents No competing objective functions within the objective space Y, while S2 defines the feasible parameter search space. For each candidate synaptic plasticity rule defined by the parameter vector 0, we evaluate its performance by applying it to update the synaptic weights of the VI model across different cognitive tasks.
As shown in Fig. the input pathway to the VI model is constructed based on biological data follow- ing Billeh et al. 2020p. Visual stimuli are first processed by the fixed lateral geniculate nucleus (LGNN and LGN-VI models before being passed to the learnable V1 model. Model performance is evaluated via readout from the layer 5 excitatory neurons in the VI model. Model implementation is detailed in Appendix C
Each plasticity rule undergoes multi-objective evaluation based its performance across different cogni- tive tasks. The evaluation framework incorporates biological plausibility metrics to assess whether both the VI model's connectivity patterns and neural dynamics align with experimental observations after applying the plasticity rule. The evaluation framework also employs task performance metrics to quantify the plas- ticity rule's ability solve the presented cognitive tasks. To explore this complex optimization landscape, we introduce a custom multi-objective evolutionary algorithm, whose design is described Appendix [H] During the evolutionary process, following principles analogous Darwinian evolution, gerfpeerformin plasticity rules are retained and given opportunities to undergo crossover and mutation with other successful plasticity rules, thereby generating novel plasticity rules. Conversely, plasticity rules that exhibit poor per- formance on cognitive tasks or low biological plausibility are progressively eliminated from the population.
2.3 METRICS
To effectively evaluate each plasticity rule across the population, a comprehensive assessment comprising both task performance and biological metrics is employed, as illustrated in Fig. [T.. To maintain compu-
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Time (ms)
MAGEEET
Grating image
Natural image
30 ms
Inittaal trial
1-st trial
2-nd trial
--Stimulus
Response window
Grey image
V1
1GN
eetina
4raii trials
Lyal trials
Time
Training
Validation
Figure 3: Overview of the multitask experimental setting. a. In each evaluation, stimuli are drawn either from gratings or from natural images in ImageNet (not mixed), and are presented to the VI model. b. Each evaluation consists of training trials in the first half, with plasticity rules enabled, followed immediately by validation trials in the second half, with rules disabled.
b
Noraaizzdd fitness value
1.0
Whole plasticlyy rule populatio
Normalizee fitness value
Fltorrdd
Best- pess-ppefforiing plasticky rule
0.6
1.00)
1LS 199
0.2
LO CD DET
ACC (16)
Perni Max rate Aoyne proper rate dift
distn dif
ADC (N3
Turms Max cate Royne pro rate dift disut dif
(6)
(1)
Figure 4: Performance of the filtered plasticity rules after convergence of the population. a. Normalized fitness value of 6 objectives for the whole plasticity rule population (N=4000). b. Normalized fitness value for the filtered Pareto- careto-optimal population (N=70). The fitness values are normalized to [0, 1], with original value ranges provided for reference.
tational tractability and ensure balanced evaluation, the following six objectives are considered in the experiments. We leave the implementation details in the Appendix
1. Cross-domain task performance, measured by cross-domain task average accuracy, assesses whether the plasticity rule generalizes across different stimulus types rather than specializing to a particular type.
2. Rule complexity assesses the number of terms within each plasticity rule, with preference given to simple formulations when comparable performance achieved.
3. Maximum firing rate monitors peak neuronal firing rates during the cognitive task after the plasticity rule optimization has been done, with rules maintaining firing rates below 30 Hz considered biologically optimal Niell & Stryker 2008).
4. Asynchronous firing proportion evaluates population-level synchronous firing, requiring that simulta- neously active neurons constitute less than 1% of the total population at any time point (Lennie 2003).
5. Firing rate difference measures the discrepancy between the network's population firing dynamics during cognitive tasks, after the plasticity rule optimization has been done, and the mean firing rate data observed in mice performing analogous cognitive tasks (Siegle et al. 1 de Vries al. 2023).
6. Firing rate distribution difference quantifies the distributional differences between the network's pop- ulation firing dynamics during cognitive tasks, after the plasticity rule optimization has been done, and the firing rate distributions recorded from mice performing analogous cognitive tasks (Siegle et al. 202T de Vries et al. 2023
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Obj-1 (1)
Obj-2 (
Ohj-3 (U)
Ob)-4
Obj-5 (1)
Obj-6 (4)
Mathematical formulation of plasticity rules filtered population
Avg
JAng
Avg
Avg
Best
Avg
Best
JAn
Best
A W Spee
48.57%
66.18
70.29
|0.04 0.04
|,57.22
127.83
|0.00 0.00
|.225 0.86
|..8 0.71
A W Spre Xpost
7.14%
664.54
68.43
10.04
0.04
1665.0
125.96
|0.00 0.00
1.16
0.87
1..11 0.86
A w Spost Xpre
5.71%
62.50
63.21
0.04
170.62
137.43
0.00
1.04
0.84
0.91
A X pont Spre X
S Post Xpre
X
post
Xpost
1.43%
71.86
71.86
0.20
0.20
115.63
115.63
0.00
0.00
1.76
1.76 0.98
0.98
Table I: Mathematical formulations of plasticity rules ranked by ratio of occurrence the filtered population and their average performance on two visual change detection tasks. Each formulation may contain multiple rules with identical mathematical form but varying parameters. Arg: average fitness across individuals within each formulation; Best: optimal fitness within each formulation.
3 EXPERIMENTS AND RESULTS
3.1 EXPERIMENTAL SETTINGS
Cross-domain task setting. Based on the mouse behavioral studies in two visual change detection exper- iments (Garrett et al. 2020: Siegle et al. 2021), we designed cross-domain generalization learning (see Fig. 3a). For the natural image change detection, all stimuli are selected from set of 8 randomly cho- sen images from the ImageNet dataset (Deng et al. 2009). For the grating image change detection, static grating images generated with orientations uniformly sampled from the range [60", 120%] at 0.19 pre- cision. The probability of stimulus change between consecutive presentations in two tasks is maintained 50%. Change detection is signalled when the mean firing rate of the readout excitatory neurons during the response window exceeds a learnable, task-shared threshold şp. This experiment requires plasticity rules endow the VI model with working memory capabilities analogous to those required in 1-back working memory tasks (Owen et al. 2005).
Evaluation setting. Each plasticity rule is evaluated independently on each task using a two-phase proto- col: 100 training trials (plasticity enabled) followed by 100 validation trials (plasticity disabled). After the population converges, rules undergo a final evaluation using 100 training and 200 testing trials per task to assess average performance across both tasks, with additional testing trials employed to reduce overfitting bias performance assessment. Our evolution maintained population of 4,000 plasticity rules across 150 generations, with each individual evaluated by applying its plasticity rule to VI model of 3,000 neurons, sampled following the strategy proposed in Chen al. (2022). Details about the experimental setting and the search space 22g can be found in Appendix
3.2 DISCOVERED PLASTICITY RULES
As shown in Fig. we identified and filtered 70 candidate plasticity rules from the Pareto-optimal popula- tion from the last generation based on overall task performance and biological validity criteria. The prevalent mathematical formulations, as demonstrated in Table [ were ranked and selected according to their ratio of occurrence within the filtered population. We found that most plasticity rules exhibited performance consis- tent with biological observation. Specifically, the V1 model optimized using these plasticity rules achieves task accuracies comparable those observed in mice (~600 for grating change detection (Gllickfeld et al.) 2013) and 737 for natural image change detection (Garrett et al.) 2020)). Results were consistent across seeds; representative seed is shown. The full mathematical formulation table is provided in Appendix F
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Stiuulss change
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no change
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M0Get
ISPaato:
ISCeet
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IoPvalo
100
200
300
400
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Figure 5: Visualization of spike raster plot and firing distribution of the V1 model optimized by the overall best best-performing plasticity rule.
80%
Noralizedd fitness value
0.7-
performing rule
Gradient-Adam
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Test ACC (%)
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ACC (N)
Terms
(+) Max rate Async fr propy rate diff
diarst diff (4)
40%
(4) (6)
N training samples
Figure 6: Comparison of performance on visual change detection of grating images between the best individ- ual of three representative rules highlighted in Table and the widely used gradient-based Adam optimizer. Performance overview. b. Mean test accuracy and standard deviation over 5 seeds (200 test trials each).
In Table the simple presynaptic dependent plasticity rule (i.e., Aw = Spre) emerged as the most prevalent formulation, comprising nearly half of the filtered rules. Several reward-free plasticity rules (e.g. Aw Spee Xposs) also succeeded in our reward-require, task settings. To further analyze the explored plasticity rules, we selected the overall best pert-rerfonning plasticity rule from the filtered population, which takes the mathematical form Aw Xpos + Spre Xpre + Spod Xpe + X2 post, Xpes R (highlighted in red in Fig. Pb and Table The spike raster plot generated by this plasticity rule, as presented in Fig. 5p, illustrates the temporal dynamics of neural activity across cortical layers during both stimulus change and no-change conditions. Fig. 5p demonstrates the comparison of firing rate distributions between biological data (Garreti jet al. 2020) and the optimized VI model, both obtained during the grating change detection task. The analysis reveals that, consistent with the biological data, the optimized VI model also demonstrates a heavy- tailed firing rate distribution during the grating change detection task.
3.3 DATA EFFICIENCY ANALYSIS
To evaluate the efficiency of the discovered plasticity rules, we compared their performance against a con- ventional gradient descent (GD) baseline. Specifically, trained the VI model on the same visual change detection tasks using the Adam optimizer (Kingma & Bal 2014) with a surrogate gradient function (Neftci) baseline that utilizes global error signals but learns without evolutionary pri-
et al. 2019a), serving ors. To ensure fair comparison, the biological validity metrics described in Sec. [.3 were incorporated as regularization terms in the loss function. A detailed training setup is provided in Appendix G
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b
Visual change detection of grating Image
Visual change detection of natural image
80
71.7%
Average accuracy (%)
75.7%
75.5%
Average accuracy (%)
75
70.3%
68.6%
71.0%
70.8%
73.2%
73.3%
75-
70.2%
70
65.8%
66.0%
70
65
65
60
60
55
55
50
50
1000
3000 Network size
5000
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3000
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Figure 7: Evaluation of the scalability of the overall best-performing plasticity rule across network sizes. Red bars indicate test accuracy on the V1 model size used during the evolutionary search, while blue bars show test performance on different VI model sizes. Results represent mean accuracy across independent random seeds, with each evaluated with 200 testing trials. Error bars denote standard deviation across seeds.
For benchmarking, we selected three representative rules from our discovered population: the best- performing rules from the top two prevalent formulations (shown in yellow and green in Table [.. and the overall best-performing rule (shown in red). As illustrated in Fig. dp, we observed substantial disparity in data efficiency. All three plasticity rules achieved superior detection accuracy within the first 100 training trials, whereas the Adam baseline required nearly 5000 more samples to attain comparable performance levels. In practice, the wall-clock training time for the Adam optimizer is even greater than this factor sug- similar phenomenon
gests, due to the additional computational overhead introduced by backpropagation. is also observed in visual change detection natural images (see Fig. 313). The detailed hyperparameter analysis of both Adam and Stochastic Gradient Descent (SGD) is provided in Appendix G.2.
3.4 SCALABILITY OF DISCOVERED PLASTICITY RULES
To evaluate the robustness and scalability of discovered plasticity rules, tested the overall best- performing plasticity rule across different network scales. Specifically, we varied the VI model size from 1,000 5,000 neurons using the sampling strategy described in Chen al. (2022). As shown in Fig. 7 the overall best- best-performing plasticity rule maintained strong performance across different network sizes. This scalability suggests that the discovered plasticity rule captures ccale-invariant principles underlying memory formation and retrieval, rather than being overfit to the 3,000-neuron V1 architecture used during the evolu- tionary optimization. This overall peesstterfrminggg rule also demonstrates remarkable homeostatic properties under a significantly long time horizon modulation beyond its evolutionary setting (see Appendix
4 DISCUSSION
4.1 FUNCTIONALLY EQUIVALENT PLASTICITY RULES
Table demonstrates that high task performance is not restricted to a single plasticity rule. other words, multiple structurally different computational strategies generate identical functional behavior, implying
a degree of computational degeneracy similar to the recent findings in Confavreux et al.) (2025b). This
observation sheds light why experimental synaptic plasticity studies focusing the same type of synapse
the visual cortex sometimes report contradictory mechanisms (Lu et al.) 2007] (aarhi et al.) 2008 Huang
et al. 2013 complementing previous explanations based neuromodulation (McFarlan
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4.2 EXPLORED PLASTICITY RULES SUPPORT MEMORY EMERGENCE
Fig. and Fig. STO reveal that sustained neural firing during delay periods between stimulus windows emerges naturally within the optimized V1 model, which is a canonical signature of working memory (Fuster & Alexander 1971 Miyashita 1988) from a neural activity aspect. Notably, reward-free plasticity rules relying exclusively on presynaptic activity constitute a significant proportion of the high-performing pop- ulation (see Table I and also result in stable firing dynamies as the reward-requires rule (see Fig. (ST) This computational efficacy challenges the exclusivity of classical Hebbian coincidence detection and aligns with recent computational modeling in episode memory (Pang & Recanatesi 2025) It also echoes experi- mental evidence from hippocampal mossy fiber synapses, where presynaptic activity has been identified as
sufficient to support robust memory storage and recall (Vandael al. 2020 Pelkey et al. 2023 Vandael
Jonas 2024
4.3
EVOLUTIONARY PRIORS AND THE SYNAPTIC PLASTICITY VIEW OF INNATE ABILITIES
As illustrated in Fig. 6 our comparison with GD is not intended to establish algorithmic superiority, but to provide a possible explanation of the origins of biological learning efficiency. While GD operates as a general-purpose solver requiring extensive data to learn from scratch, evolution can embed task-related inductive biases into the structure and parameters of the plasticity rules. Consequently, this may enable the plasticity rules, even in reward- seward-free formulation, achieve few-shot adaptation. This may explain why the sucking behavior of newborn mice requires maternal pheromone signals to be expressed (Logan et al. 2012 This perspective advances 'synaptic plasticity view' of innate behaviors beyond hardwired neural circuitry (Wilmer et al.) 2010 Haimson & Mizrahi 2025): innate capabilities may depend on pre-configured plasticity mechanisms that render specific behaviors accessible with minimal experience, thus bypassing the extensive trial-and-error learning required by acquired capabilities.
4.4 LIMITATIONS AND FUTURE WORK
Building on these findings, our framework has several limitations that motivate future extensions. First, while several neural signals are used as building blocks of plasticity rules, incorporating additional variables such as synaptic weights or membrane voltages would allow capturing a broader range of possible mech- anisms. Second, by grounding our plasticity rules in mouse V1 data and visual processing pathways, we ensure biological fidelity to some extent but limit conclusions about generalization to non-visual sensory modalities, such as auditory data. Third, our framework captures only millisecond-seat spike timing, without incorporating second-scale mechanisms such as behavioral timescale synaptic plas- ticity (BTSP) found in hippocampal CA1 BBittner et al.) 2017 Milstein et al., 202T). Fourth, the similarity between the optimized VI model and biological data is evaluated from a neural representation-bant
plasticity driven by
as- pect. Future work could incorporate recent advances in dynamics-basee similarity metrics (Zhang et al., 2025 to constrain and accelerate the exploration. Addressing these limitations through expanded signal sets, cross- modall validation, multi-timescale integration, and advanced biological constraints represents im- portant future directions.
5 CONCLUSION
In this paper, we present computational framework that employs multi-objective evolutionary algorithm to discover biologically plausible, heterogeneous plasticity rules within an experimentally grounded mouse VI model. Our approach uncovers structurally distinct yet functionally equivalent rules, highlighting the role of computational degeneracy in neural robustness. Furthermore, our findings offer potential explanations for the origins of memory and innate abilities, suggesting that efficient learning emerge from local synaptic dynamics. This work bridges the gap between evolutionary constraints and synaptic diversity, suggesting that the key to biological intelligence may lie in the degenerate yet robust landscape of learning rules.
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ACKNOWLEDGEMENT
This work was partially supported by the National Natural Science Foundation of China (Grant No. 62306259), the Research Grants Council of the Hong Kong SAR (Grant No. C5052-23G, PolyU25216422 and P01YU152174244) The Hong Kong Polytechnic University (P0058445). This work was also supported by the National Natural Science Foundation of China (NSFC) under Grant No. 62576011.
ETHICS STATEMENT
This work adheres to the ICLR Code of Ethics and addresses several ethical considerations relevant to computational neuroscience and artificial intelligence research:
Biological data usage. Our research builds upon publicly available mouse V1 cortical data from the Allen Brain Atlas (Billeh et al. 2020p, which was collected under appropriate institutional ethical approvals. We do not conduct new animal experiments and rely exclusively established, ethically-soureed datasets.
Computational resource considerations. While our evolutionary framework requires substantial compu- tational resources (8xA6000 GPUs), we have designed efficient algorithms based EvoX (Huang al.) 2024a) to minimize environmental impact through batched evaluation and gradient-free optimization. The computational efficiency gained enables broader scientific exploration while reducing overall resource sumption compared to conventional approaches.
Potential applications and dual use. The discovered plasticity rules could inform the development of more efficient neuromorphic computing systems and brain-inspired AI. While these advances may have benefi- cial upplications in assistive technologies and computational efficiency, learning algorithm could potentially be misused. However, our work focuses on fundamental scientific un- derstanding rather than specific applications, and the biological constraints inherent in our approach naturally limit potential for misuse.
acknowledge that any powerful
Research integrity. All experimental protocols, data processing steps, and evaluation metrics fully documented to ensure transparency and reproducibility. Our multi-objective evaluation framework explic- itly incorporates biological plausibility constraints prevent the discovery of biologically implausible but computationally expedient solutions.
REPRODUCIBILITY STATEMENT
We have made extensive efforts to ensure the reproducibility of our results:
Computational framework. Complete implementation details of our multi-objective evolutionary algo- rithm are provided in Appendix F, including the custom selection operators, reproduction mechanisms, and evaluation procedures. The framework is implemented using JAX and the EvoX library, with specific and hardware requirements detailed in Appendices and
Model specifications. The V1 model architecture, connectivity patterns, and neuronal parameters are fully specified in Appendix A building upon the publicly available Allen Brain Atlas data (Billeh et al.) 2020) and following the architecture modification in Chen et al. (2022). All modifications to the original GLIF3
model (Teeter et al. 2018) for plasticity compatibility are explicitly documented.
Experimental protocols. Detailed experimental settings, including stimulus generation, task protocols, evaluation metrics, and hyperparameter ranges, are provided in Appendices D and The visual change
detection paradigm follows established behavioral protocols (Garrett al. 2020 Siegle al. 2021
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Baseline comparisons. The gradient-based Adam optimizer bascline implementation, including surrogate gradient functions and training procedures, is fully described in Appendix G to enable direct replication of comparative results.
Statistical analysis. All reported results include appropriate statistical measures (means, standard devia- tions, sample sizes) across random seeds. The evolutionary search was conducted with a population of 4,000 rules over 150 generations, with final evaluations performed using 5 independent seeds and 200 test trials each.
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A SUMMARY OF NOTATIONS
This section provides summary of the important notations and variables that are frequently used throughout the paper in Table $2
Table S2: Summary of important notations
Notation
Description
General Indices
post
Indices denoting presynaptic and postsynaptic quantities, respectively. A pair of presynaptic and postsynaptic neuronal types uniquely identifies a certain synapse type.
(Mpre, Mpoa)
Plasticity Signals
S
Binary indicator for spike occurrence (e.g., Spres Spost). Eligibility trace capturing the history of neural activity (e.g.. Xpres Xpos).
R
Reward prediction errоr trace encoding neuromodulatory signals.
Plasticity Parameters
c
Learnable coefficient for a specific plasticity term (e.g., c²).
TE
Time constant for the eligibility trace of neuron type Time constant the reward trace of neuron type m.
TR
P
Set of candidate plasticity terms derived from Taylor expansion. Synaptic weight update value (plasticity rule).
AW
Network & Neuron Model
WGGN
Fixed synaptic weights from the LGN model the VI model. Synaptic time constant governing current decay.
Tsyn
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B RELATED WORK
B.1 MODELING PLASTICITY MECHANISM
Explaining the synaptic plasticity mechanism via mathematical formulation has been a main theme in com- putational neuroscience. Initial theoretical frameworks for synaptic plasticity, including BCM theory (Bi-
enenstock et al. 1982) and Oja's s rule (Oja 1982), were largely based on Hebbian assumptions (Hebb) 1949)
Later experimental evidence revealed that the precise timing of spikes is crucial for synaptic plasticity (Bi
& Poo 1998; Zhang et al. 1998 Debanne et al. 1998 Woodin et al. 2003). This led to the development
of rich body of spike deming-dependent plasticity (STDP) models (Song al. 2000 Kempter al.
1999
Phister & Gerstner 2006 Clopath et al. 2010). More recently. spike timing- based plasticity models have established connections with network properties, as well as network learning and memory characteristics,
offering an integrated view of how synaptic plasticity shapes neural computation (Zenke et al. 2015 illing
etal.
2021
Payeur et al.
2021
Eekmann et al. 2024 Brito
Gerstner
2024
Agnes & Vogels
2024).
Despite remarkable progress in understanding individual synaptic plasticity mechanisms in isolation, ex- perimental studies suggest that multiple types of synaptic plasticity often operate synergistically (D' d'amour & Froemke 2015; EI- El-Boustani et al.] 2018). These processes commonly involve various ncuromodula- tors (Seol et al. 2007] Huang et al. 3 et al. [0033] Park et al. 2025), which collectively shape network dynamics and functional behavior. However, technical limitations inherent to large-scale in vivo experiments have hindered a comprehensive understanding of how these heterogeneous synaptic plasticity mechanisms interact.
B.2 INFERRING PLASTICITY MECHANISM
In addition to modeling plasticity rules, an alternative approach to understanding plasticity mechanisms in- volves inferring their mathematical formulations directly from neural or behavioral data using data-driven methods. Predicting plasticity rules from spike train data, in particular, represents an intuitive and powerful
means of uncovering the underlying synaptic mechanisms (Stevenson Koerding [00T]] Z0TT]Linden [Linderman et al.)
2014 Robinson al. 2016; Ghanbari et al. [017]] Wei & Stevenson [202]] Mehta et al.) 2024 Previ-
ous studies have also derived synaptic plasticity rules by examining changes in neuronal firing distributions
observed before and after learning (Lim et al. 2015 Chen et al. 2023). Alternatively, some studies
plore plasticity mechanisms by identifying how synaptic modifications enable networks to achieve desired network dynamics and computational functions (Confavreux al. [020 2023)). Complementarily, another
class of studies optimizes synaptic rules to endow networks with the capability for successful cognitive
task performance behavioral data fitting (Najarro Risi 2020 Ashwood al. 2020 Jordan al. 202T
Tyulmankov et al. 2022 Shervani- Tabar & Rosenbaum 2023 Miconi 2023 Mchta et al. 2024 Contavreux
ct al.
2025a
Although some of the aforementioned studies have employed evolutionary methods or meta-learning frame-
works to explore plasticity mechanisms (Najarro Risi 2020 Jordan et al. [021 Tyulmankov et al. 2022
Confavreux et al.) 2023 Miconi] [0233 Shervani- Tabar & Rosenbaum [023] Confavreux et al.) [025a
these approaches suffer from several limitations. First, they have largely been restricted to small artificial
networks or simplified biological models, which may limit their ability to incorporate biological constraints
and capture the full complexity of biological systems. Second, most current methods are restricted to a small, manually defined space of plasticity rules, typically spanning from uniform rule applied across all synapses to limited forms of heterogeneity that distinguish only between excitatory and inhibitory synapses. Third, prior studies have primarily been limited single-task settings have considered only a single biological objective. These limitations hinder comprehensive exploration of the broader landscape of het- erogeneous plasticity rules, as well the systematic identification of synaptic plasticity mechanisms that are both biologically plausible and functionally relevant.
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C MODEL CONSTRUCTIONS OF LGN AND V1
Our computational framework employs a hierarchical visual processing architecture comprising fixed LGN preprocessing stage and an adaptive VI cortical network. Specifically, the LGN model transforms visual stimuli through 17,400 spatiotemporal filters, while the VI network, built experimentally validated Allen Brain Atlas parameters (Billeh et al. 2020), serves as the substrate for plasticity rule discovery across 17 distinct cell types and cortical layers.
C.I LGN MODEL AND LGN-TO- VI MODEL
Visual stimuli undergo preprocessing through LGN model that qualitatively simulates the computational functions both retinal and LGN processing stages (Billch et al. 2020 The model architecture incorpo- rates 17,400 spatiotemporal filters designed to replicate the response characteristies of mouse LGN neurons to visual inputs (Durand et al. 2016). Each filter generates positive-value outputs representing the firing rates of individual LGN neurons.
The preprocessing pipeline begins with converting visual input pixels to grayscale, followed by normaliza- tion the interval of intensity [-Int, Int] where Int in our setting. The processed L.GN outputs subsequently transformed into external current injections for the VI model through fixed biological-data- based LGN-to-VI connection weight. The whole LGN to VI pathway can be represented as:
Ja WIGN LGG(
where Gint denotes the intensity eeeesity-normalizeer image inputs within the range [-2, following the settings in Chen et al. (2022). Note that the LGN model LGN(.) and LGN-to-VI model WLGN remain fixed during the whole optimization process, as we only focus on the plasticity within the V1 model.
C.2 VI MODEL
Neuron models. Our computational framework builds upon the point-neuron implementation of the biolog- ically realistic VI model developed by Billeh et al. (2020). To ensure compatibility with plasticity learning rules, we substituted the discrete membrane potential reset mechanism following spike generation with a continuous voltage reduction term 2j (1zs E,). where the spike indicator (t = during firing events of neuron j at time f, and (t) the resting membrane potential. This modification preserves the essential neural dynamics while enabling
otherwise. Here, Veh represents the spiking threshold and E, denotes
synaptic plasticity rule-based weight updates.
The temporal evolution of the spiking model follows the modified GLIF3 model can be represented as:
TTeter et al. 2018 which
By + = Buy(t) - (t)(( - -E)
=t)=
1 1-3 3
+ C
1)(++1++>X [ (t+
+ + +170m
(10)
m
2) H(v;(t)) vnn)
(11)
15(t) Σ (GN
(12)
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where C' rerereeeents neuron capacitance, 1 denotes external current input, 1 refers the post-spike current, 1 represents synaptic current, specifies membrane conductance, and væa indicates the spiking threshold. The LGN-to-V V1 connectivity is mediated by the weight matrix W WLGN- The decay factor 3 = e At/r incorporates the membrane time constant т, while At ms defines the resolution the simulation time step. The Heaviside step function (-) governs spike generation dynamics.
To model the neuronal refractory period, we implemented a simplified mechanism where 2,(1) remains fixed at 0 following each spike for brief refractory period determined by neuron type. Postsynaptic spike current dynamics are governed by:
rn (t + At) = f +(t) 772 ......,.ass. Nasc
(13)
where the multiplicative decay constant = exp(-k<m =xp= At) and additive term A characterize the after- spike current properties. Our implementation supports m 1 or 2 current types. Biophysical parameters are derived from experimental measurements of 111 neurons the Allen Brain Atlas database (Durand et al. 2016 Billeh et al. 2020), encompassing neuron capacitance C, conductance g. resting potential Er., refractory period duration, and the amplitudes A!T and decay constants hnd for both after-spike current types.
Synaptic connectivity and dynamics. The VI network architecture incorporates experimenttall--drrivee
connectivity patterns that define probabilistic synaptic connections between neuron populations. Connection probabilities for all pairwise combinations among the 17 characterized cell classes are specified according to experimental measurements (Billeh et al. 2020). with data organized in a comprehensive connectivity ma- trix. Grid entries indicating unknown values represent uncharacterized connection types in the experimental dataset.
The baseline connection probabilities reflect measured synaptic contact frequencies for neuron pairs po- sitioned within 75-um horizontal intersomatic distances. To incorporate spatial connectivity constraints, these probabilities are modulated by an exponentially decaying factor that scales with horizontal distance between neuronal somata following Chen et al. (2022) Fig. ID. This distance deppeddet scaling preserves the statistical properties observed in experimental connectivity data while accounting for spatial organization principles in cortical circuits.
Synaptic transmission delays are distributed uniformly within the interval [1,4] ms, derived from experimen- tal measurements presented in Fig. 4E of Billeh af.) (2020) and discretized to match the ms integration time step. The postsynaptic current dynamics for neuron follows first-order kinetics:
1, (t + At)
A Toun
1700 (1) AL.e Taun Crise
AL
(14)
Cj riic (t + At) TAym Ctise(t)
(t) + Σ WW (t)
1
(15)
Tayn
where Tsyn represents the synaptic time constant, W denotes the recurrent connection weight from presy- naptic neuron to postsynaptic neuron within V1, and (t) indicates spike occurrence in the presynaptic neuron. The synaptic time constants Teyn are cell-type specific, reflecting the diverse kinetic properties of synaptic transmission between different neuronal populations characterized in Billeh al. (2020).
Network initialization. All state variables, including spike indicators and membrane potentials, are initial- ized zero at simulation onset. The initial configurations of both feedforward weights W WLGN and recurrent connectivity weights Wvi are established according to the empirical values reported in Billeh et al. 22000) providing a biologically realistic starting point for network dynamics and subsequent plasticity-driven mod- ifications.
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D DETAILS ABOUT PLASTICITY RULES AND WEIGHT UPDATES
D.1 PLASTICITY RULE CANDIDATES TERMS
Here we present all the possible plasticity rule terms that may exist in Eq. plasticity rule candidate govemnd by binary selection indicator g and learnable coefficient c. This term set includes the first-order terms:
7 in the main manuscript. Each
g' c' Spre g² Spoat: cd. xpro g c
Xpost 9² cc.. R;
the second-order terms:
g c² Spre Spose, g² Spre Xpre gd c². Spre Xpust g0 d² Spee R,
g g0 0 Spoct Xpres meesggl clll Sport Xpoat g¹2 c22 Spost R.
g.و C23 X2 prey grh 220 Xpo X Xposs gb 625 Xpo R. gl 26 x²
post
g¹ c Xpoa Ri
and the third-order terms:
18 18. Xpre Spodl Rí g c. 19, Spre Xpos R, g20 20 x22 R
pre
21 22 X² post R, 92d 22 Spre Spos R. g2d 2 Xpee Xpost R.
24 24 Spoat Xpost R, 25 25 Spre Xpre R.
where serves as a binary indicator, and denotes the coefficient for candidate. Among the 25 candidate plasticity terms presented above, 16 terms depend only on neuron types, terms are yyapse-type specific, and term represents the global reward prediction eтror. Two additional decay factors govern the neuron- type-dependent eligibility trace and reward prediction error trace.
Optimizable parameter analysis. The total number of optimizable parameters for each of the plasticity rules our framework can be decomposed as follows:
Ropiimzzbbee 18 X nenuron types + 8 X Rsynaasee type + 7ggate + 2.
(16)
For VI model implementation following Billeh et (020), which contains 17 distinct neuron types and thus 172 = 289 possible synapse types, combined with our 25 candidate plasticity terms, the total number of optimizable parameters becomes:
Noppiiizabbee = 18 x 17 17 + 25 2 2645.
(17)
This formulation accounts for several parameter categories:
Neuron type specific coefficients. The first term (18 Racuron corresponds to 16 plasticity rule coefficients that depend only either presynaptic postsynaptic neuron type, encompassing most first-, second-, and third-order terms as well as the 2 heuroo-typeedepeeddem decay factors.
Synapse type specific coefficients. The second term (8 Tyysapse type) represents coefficients that depend on synapse types (i.e., both presynaptic and postsynaptic neuron types).
Binary selection gates. The term Ngae represents the number of binary indicators g for each can- didate term in the plasticity rule set.
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Additional parameters. The constant term accounts for: (i) the global coefficient for the reward prediction signal R in first-order terms, which is shared across all synaptic types; and (ii) the task- shared learnable readout threshold yp used in the
process.
Note that among the first-order terms, the reward prediction signal R has only single coefficient and gate parameter that can be optimized globally, rather than being specific to individual synaptic connections, reflecting its role a neuronal population-level learning signal.
D.2 WEIGHT UPDATE CONSTRAINTS
We enforce Dale's law Strata et 1999) during plasticity rule based weight updates to maintain biological plausibility and numerical stability. Dale's s law, which requires neurons to release identical neurotransmitters across synapses, ensures that synaptic polarity remains invariant throughout network optimization. More- over, due to physical constraints in biological synapses, we consider the synapse type-specific thresholds to prevent weights from becoming excessively large, which can treated as hard bounds during the network optimization /Gerstner et al. 2014). We set these bounds at 1.5 times the maximum biological values (Billeh
ct al. 2020) for each synapse type. We also implement an adaptive scaling mechanism to prevent excessive weight changes that could destabilize network dynamics. The weight updates are constrained by threshold proportional to the current weight magnitude, where the proportion is set to 0.01. This approach ensures that weight modifications remain proportional existing connection strengths, preventing dramatic changes that could disrupt established connectivity patterns.
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E EXPERIMENTAL DETAILS
E.I DETAILED IMPLEMENTATION OF THE EVALUATION METRICS
1. Cross-domain task performance, measured by cross-domain task average accuracy, assesses whether the plasticity rule generalizes across different stimulus types rather than specializing to a particular type. In this work, we measure it the average validation accuracy from independent training sessions using two distinct input domains (grating images and natural images). The accuracy is computed as the pro- portion of correct responses, including hits during change trials and correct rejections during no-change trials.
2. Rule complexity assesses the number of terms within each plasticity rule, with preference given to simple formulations when comparable performance is achieved. In our implementation, we quantify rule complexity by counting the number of active terms the plasticity rule, determined by the binary selection indicators of Eq. (7)
3. Maximum firing rate monitors peak neuronal firing rates during the cognitive task after the plasticity rule optimization has been done, with rules maintaining firing rates below 30 Hz considered biologically optimal (Niell Stryker] 2008 In our implementation, we record the maximum firing rate across all neurons in the network during the validation phases.
4. Asynchronous firing proportion evaluates population-level synchronous firing, requiring that simulta- neously active neurons constitute less than 1% of the total population at any time point (Lennie) 2003 In our implementation, we calculate the proportion of neurons firing simultaneously at each time step during the validation phase, and identify the maximum proportion.
5. Firing rate difference measures the discrepancy between the network's ' population firing dynamics during cognitive tasks, after the plasticity rule optimization has been done, and the mean firing rate data observed in mice performing analogous cognitive tasks (Siegle et al. 2021 de Vries et al. 2023). In our implementation, we compute the absolute difference between the average firing rate of the network during validation phase and the experimentally recorded mean firing rate from mice.
6. Firing rate distribution difference quantifies the distributional differences between the network's pop- ulation firing dynamics during cognitive tasks, after the plasticity rule optimization has been done, and the firing rate distributions recorded from mice performing analogous cognitive tasks (Siegle et al. [202T] de Vries et al. 2023). In our implementation, we compute the Wasserstein distance between the normal- ized firing rate distributions of the network during validation phase and the experimentally recorded firing rate distributions from mice.
E.2 CROSS-DOMAIN TASK SETTING
The original behavioral protocol (Siegle et al. 2021 de Vries et al. 2023 required mice to perform sequen- tial discrimination on static natural images or grating images (250 ms presentation duration) interspersed with inter-stimulus grey screen intervals (500 ms), determining whether consecutive stimuli are identical or different. To enable large-scale population search, we implemented 60 ms stimulus presentations and 90 ms stter-stimulus grey intervals (Fig. Pp. Each trial sequence initiated with a 30 ms pre-stimulus delay. Network responses are evaluated within a 30 ms response window beginning ms post-stimulus onset.
E.3 SEARCH SPACE SETTING
The search spaces of different parameters in each of the plasticity rules set follows:
Coefficient of plasticity candidate e E [-1,1], 1), binary selection indicator g E {0. 1), decay factor of eligibility trace
Te E (0, 150), and decay factor of reward prediction error TR (0, 150). The task-shared learnable readout
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Table S3: Statistics of 3,000 randomly sampled solutions across six objectives.
Metric
Mean
Std
Median
Best
Worst
Obj I: Cross-domain task performance (1)
0.503
0.016
0.500
0.685
0.440
Obj 2: Rule complexity (1)
0.501
0.097
0.520
0.200
0.840
Obj 3: Maximum firing rate (L)
437.21
122.96
500.00
99.33
500.00
Obj 4: Asynchronous firing proportion (L)
0.754
0.408
1,000
0.000
1,000
Obj 5: Firing rate difference (1)
139.13
93.66
144.87
0.62
271.71
Obj 6: Firing rate distribution difference (1)
0.612
0.201
0.610
0.144
1,253
threshold oo [0. 10) Hz, following mouse cortical pyramidal neuron firing rates where most neurons fire below 10 Hz (Buzsáki & Mizuseki 2014).
To gauge the complexity of this search space, we conducted preliminary analysis by evaluating 3, 000 randomly sampled solutions from the defined search space. The statistical distribution of the six objectives is summarized in Table S3 The results demonstrate that the search space highly non-trivial. Judging by the mean and median values, the vast majority of randomly sampled plasticity rules fail the task. While the best-observed values (Maximum for task performance, minimum for constraints) indicate that high- performing candidates exist within the theoretical bounds, these statistics are computed independently for each objective. Notably, a solution that achieves a good score on one metric (e.g., good accuracy) may perform poorly others (e.g., extremely high firing rate).
Our evolution framework and model implementation are built on Jax (Bradbury et al. 2018). All the experi- ments conducted 8 x A6000 GPUs The simulations conducted with ms temporal resolution.
E,4 BEHAVIOR DATA ESTIMATION FOR VISUAL CHANGE DETECTION
The behavioral accuracy of visual change detection natural images is estimated from Fig. 1I of Garrett et al. 2020) when familiar images were presented mice. The behavioral accuracy of visual change detec- tion on grating images is estimated from Fig. 3A of Glickfeld et al. (213) when the orientation difference was degrees.
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Proportion of Synapres Nfsccee
Date's Law Effect
Total Consiraints Active
Proportion of Synapess Affecied
0.012
Total Constralnts Active
Dale's Law
0.024
Dale Law Effect
lotal Constraints Active
Weight Effect
Weight Elfect
0.012
Weight Effect
0.15
Symapees
0.010
0 0.008
0.10
0.006
0.004
0.004
0.00
0.00
0.000
20
35
50
20
20
50
10
30
50
Trias
Trias
Figure S8: Analysis of constraint enforcement dynamics for the three selected rule sets from Fig. The rules were evaluated over 50 training trials; the curves show the proportion of synapses triggering Dale's s Law or hitting the maximum weight bound at each timestep. a. Overall best perforrerfnmigggg rule (form: Aw = X poss Spre pre + Spost Xpre + X22 Xpost R). b. Best rank I rule (form: Aw Spre). Best rank 2 rule. (form: Are Spre + Spre xpos)
F ADDITIONAL RESULTS OF PLASTICITY RULE
F.1 CONSTRAINT ENFORCEMENT DYNAMICS
To analyze the functionality of the constraints, we tracked the enforcement dynamics for the three represen- tative rules highlighted with color in Table [ and mentioned Fig. We observed significant differences
in how distinct plasticity rules interact with these boundaries. Fig. 58 shows that the best performing rule actively engages the constraints, with approximately 15% of synapses frequently hitting the hard bounds or Dale's law limits during training. In contrast, other rules (Fig. [S8p and (8p) remain almost entirely within the permissible range. Importantly, our evolutionary optimization process does not penalize boundary contact; rather, view these constraints integral components of the synaptic dynamics. From an evolutionary perspective, the existence of these hard bounds serves as a stabilizing scaffold, allowing the search algo- rithm explore more complex plasticity profiles that drive rapid learning. Without these bounds, such rules would very likely lead to catastrophic weight explosion or sign reversal, especially in the early stages when the parameters are not fully tuned.
F.2 DISTRIBUTION OF DISCOVERED PLASTICITY RULES
As shown in Table $4 we identified and filtered 70 candidate plasticity rules from the Pareto-optimal popula- tion from the last generation based on overall task performance and biological validity criteria. The prevalent mathematical formulations were ranked and selected according to their ratio of occurrence within the filtered population. Fig. 59 illustrates the visualization of tenapsettype-spelee
coefficients for representative plas- ticity rules from the filtered rule population in Table S54 Empty rows indicate that the corresponding term absent from all rules in the filtered population. Each polar plot shows the coefficient distribution of one plas- ticity candidate term. Panels (a-d) display coefficient distributions for manass--ypee-speiine plasticity terms that depend both presynaptic and postsynaptic neuron types (e.g.. Spre Spost Xpre Xppot), organized by connection class: (a) -ooitattry-t--exiittttryy (b) excitatory-to-inhiiie (d) -itittoot-t-ihbbbittry connections. Panel (e) shows coefficient distributions for terms that depend only on either presynaptic or postsynaptic activity (e.g., Spre or X Xpost), which are shared across all types of connections.
and (c) neuron-type-deeendee
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Excitatory to excitatory connections
b
Excitatory to inhibitory connections
Nar
3
Inhibitory to excitatory connections
Inhibitory to inhibitory connections
mone
made
caavas Dt
50
4
activity only
1.00
5.2
-.25
233vab
2.00
-8.9
Danck
Figure 89: Illustration of how different rules from the filtered population as shown in Table S4 distribute
their plasticity coefficients across the 25 plasticity candidate terms shown in Sec. D.I
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Stimulus change
Stimulus no change
Stimulus window
Response window
5
Firing Rate (122)
3
100
150
200
250
300
350
400
450
(ms)
L1 (59 neurons)
L4 (666 neurons)
L6 (873 neurons)
L2/3 (905 neurons)
L5 (497 neurons)
Figure S10: Visualization of cortical layer-specific firing rate dynamics during the test phase, optimized using the overall best perforeenor plasticity rule identified from the filtered rule population (form: Aw
xpstt Spre Xpm pre Spost X pre
X
post + X post Rt).
Stimulus change
Stimulus
Stimulus window
Response window
na change
I1Htr3a
E2/3
L2/3
12/3Pvalb
12/35st
12/3Htr3a
Cortical Layers
E4
I4Pvalb
L4
145st
IHHt33
L5
I5Pvalb
155st
15Htr3a
E6
I6Pvalb
165st
16Htr3a
100
200
300
400
Time (ms)
Figure S11: Spike raster plot during the test phase, optimized using reward-free plasticity rule with high performance identified from the filtered rule population (form: Aw = Spre).
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Weight change of E-E Types Synapse
Weight change of E-1 Types Synapse
Gre > 1yot
0.015
fore > Apett
0.000075
Feor Taee
feee Tpv
0.010
0.000050
0.000025
AW
0.000000
-0.00>
-0.000025
-0.010
0000000
-0.015
-0.020
00.000100
-150
-100
-50
0
50
100
150
-150
-100
-50
0
50
100
150
At (ms)
At (ms)
Weight change Types Synapse
Weight change Types Synapse
0.0015
Tye
0.004
Tee Tye
0.9010
0.002
0.5005
0.0000
AW
0.000
-0.002
-0.0010
-0.0015
-0,0020
-150
-150
At (ms)
At (ms)
Figure S12: Visualization of the overall best-performing plasticity rule.
b
Normalized lized fitness value
Best performing rule
Gradient-Adam
0.0-
rank 1 nule
80%
Baseline
70%
3000 x
0.4
03
02
0.1
50%
(36)
Temm num
Max fir cate (M2)
ih dift diart dif
20/00
(1)
(4)
training samples
Figure S13: Comparison of performance on visual change detection of natural images between three repre- sentative rules and the widely used gradient-basee Adam optimizer. Performance overview. b. Mean test accuracy over seeds (200 test trials each); shaded areas indicate standard deviation.
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Ohj-1 (1)
Ohj-2 (J)
Ohj-3
Obj-4 (L)
Obj-5 (J)
Ohj-6 (U)
Mathematical formulation of plasticity rules filtered population
Rank
Ratio
Avg
Avg
Avg
Avg
Best
|Avg
Best
JAvg
A Spm
46.67%
66511 70.29
0.04 0.04
156.99
127.83
00.00 0.00
1.25 0.86
0.83 0.71
Awe Sym Xpett
10.67%
63399
68.43
0.04 0.04
|66 88
125.96
|0.00 0.00
1114
0.87
|..92 0.86
Aw X R
5.33%
661.57
64.64 0.04 0.04
162.09
133.94
|..02 0.00
|,339
1.06
|0.87 0.78
Ave Spo Xpo
5.33%
(62.50
63.21 0.04 0.04
170.62
137.43
|0.00 0.00
1.04
0.84
10.91 0.85
Spos
4.00%
61195
63.57
191.33
|0.00
|0.85
0.75
|L.0
Aw Spc Xpre
4.00%
665.65
67.07 0.04
167.55
149.37
|0.00 0.00
1.06
0.76
1.85 0.84
Aw Spc Spm Xooet
2.67%
669.79
69.86 0.08 0.08
175.00
168.95
|0.00 0.00
|133
1.18
(073 0.62
Avn Spe + Spe X
2.67%
(65.89
67.36
0.08 0.08
1377004
133.72
|0.00 0.00
1.36
1.20
|..8 0.86
ww= = Syoe Xpot
2.67%
622.66
62.79
0.04 0.04
190.78
187.54
00.00 0.00
1..97
0.73
|.05 1.05
Xpos + Spre Xpro
Spon Xpro + Xpu + Xpso
1.33%
71,86
71.86
0.20 0.20
115.63
115.63
0.00 0.00
1.76 1.76
0.98 0.98
Aw Spee + Syz Neon +Spp Xpos + Space Xoas
1.33%
60.21
60.21
0.16 0.16
138.89
138.89
0.00 0.00
1.03 1.03
0.79 0.79
Au Spr Xprs + Syn Xyoni R 12
1.33%
661.07
61.07
0.08 0.08
119.51
119.51
10.00 0.00
1.22 1.21
1.99 0.92
Aw in Syaa + Spett pee R 1.33%
666.57
66.57
0.08 0.08
130.64
130.64
|0.00 0.00
1.36 1.36
0.90 0.90
A w = Spee + Sye Xoon + Spe Xyve"
14
1.33%
65.93 65.93
0,12 0.12
126.65 126.65
0.00 0.00
1.33
1.33
0.78 0.78
15
Amn Xpox
1.33%
(62.36
62.36
0.04 0.04
182.80
182,80
1..00
0.00
10.87
0.87
|.06 1.06
16
Aw Spee R.
1.33%
660.71
60.71 0.04 0.04
132.30
132.30
|0.00
0.00
1.25
1.25
|0.83 0.83
Aw Spr + Spm. Xpont R
1.33%
666.99
66.29
0.08 0:08
162.30
162.30
|0.00 0.00
0.99
0.97
|0.80 0.80
Avl Sye Xpos + Spac yost
1.33%
663.58
131129
131.29
|0.00
|.35
6.94
Aw Syze + f2n
1.33%
667.29
150.14
10.00
|.115
1.15
6.85
Aw Spm Spoe Xpos R
1.33%
66621
66.21
0.08 0.08
155.119
156.19
|0.00 0.00
|1.09
1.09
6.82
0.82
Aw Syre Spre Xpre +Spra Xpre
1.33%
67.43 67.43
0.12
0.12
155.35 155.35
0.00
0.00
1.11
1.11
Table S4: Mathematical formulations of all plasticity rules ranked by ratio of occurrence in the filtered Pareto-optimal population and their average performance on six objectives. Each formulation may contain multiple rules with identical mathematical form but varying hyperparameters. Avg: average fitness across individuals within each formulation; Best: optimal fitness within each formulation.
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F.3 LAYER-WA WISE FIRING RATE DYNAMICS
Fig. STO complements Fig. P by visualizing the layer-specific average firing rate dynamics during the test phase, optimized using the overall best-perfore best-performing plasticity rule identified from the filtered rule population. The result demonstrates that the optimized V1 model effectively sustains persistent activity across all cortical layers during the delay period.
F.4 REWARD-FREE PLASTICITY RULE DYNAMICS
Fig. S11 also complements Fig. 5a by visualizing the spike raster plot of VI model optimized using a reward-free plasticity rule with high performance identified from the filtered rule population. The result demonstrates that even without reward modulation, the optimized V1 model can still maintain stable firing dynamics during the test phase. Especially, different types of neurons exhibit diverse firing patterns during the stimulus presentation, delay periods and response windows.
F.5 SYNAPTIC WEIGHT CHANGES OF THE OVERALL BEST- DEST-PERFORMING RULE
Fig. S12 illustrates the synaptic weight changes induced by the discovered overall best- pest-performing plasticity rule, Aw + Xpre + Spost Xpre - post + X Xpost Rt across coarser-grain categories of synap- cecitator-to-iniibiiin inhibitory-to-exciaatry and inhibitory-to-
tic connections:
inhibitory.
F.6 COMPARISON WITH GRADIENT-BASED OPTIMIZATION ON NATURAL IMAGES
Fig. $13 illustrates the performance comparison between three representative plasticity rules as defined in Sec.
in the main manuscript and the gradient-based Adam optimizer on visual change detection task with natural images. For clarity, we briefly restate the definitions of the three selected rules: (i) the overall best pest-performing rule with formulation Aw Xpost + Spre Xpre Spost Xpre + X post + Xpost R, (ii) the best rank-1 rule, defined as the optimal performer within the Aw = Spre class, and (iii) the best rank-2 rule, representing the top performer in the Aw Spre Xpost category.
F.7 LONG TIME HORIZON TRAINING AND HOMEOSTATIC PROPERTY
To further characterize the stability properties of the discovered plasticity mechanisms, we evaluated the overall best-performing rule, Aw Xpost Spre Xpre + Spost X pre + XXpostt + Xpost R. under extended training regimes beyond its evolutionary setting. As shown in [S although the overall best pest-perfonning rule evolved under 100 training trials' setting, it exhibits consistent performance stabilization when exposed to orders of more training samples. This sustained adaptability suggests that the discovered plas- ticity mechanism possesses intrinsic self-regulatory dynamics that prevent performance degradation during continued fine-tuning, analogous to homeostatic plasticity observed in biological neural circuits.
However, need acknowledge that this robustness is non-trivial and not representative of the entire filtered explored rule population. The majority of evolved rules exhibit performance degradation under prolonged exposure to stimuli. This fragility is especially evident in reward-free plasticity rules, where the lack of modulatory feedback renders the network prone to unbounded synaptic drift and functional collapse outside the evolutionary setting.
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Figure S14: Sensitivity analysis training V1 model on visual change detection on natural images via Adam and SGD with different learning rates. The best performance is achieved using Adam with learning rate 10-3, which is highlighted with marker. a. Adam optimizer. b. SGD optimizer.
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Figure $15: a. Task performance dynamics of the explored overall best-performing plasticity rule with sufficient training samples visual change detection natural images. b. Sensitivity analysis of the Adam optimizer's 'ss performance on visual change detection on natural images with respect to the 31 and 3n momentum hyperparameters. The learning rate is fixed at 10-3 Each data point shows the test accuracy averaged over its 50 nearest neighbors to mitigate sampling variability. The overall best-performing synaptic plasticity rule is also provided for reference, marked with *.
G GRADIENT DESCENT SETTINGS AND SENSITIVITY ANALYSIS
G.1 DETAILED GRADIENT BASED OPTIMIZATION SETTINGS
For the gradient- based results in the main manuscript, networks were trained using the Adam optimizer with a learning rate of 0.001 and default values for all other hyperparameters. This setting was chosen based on a sensitivity analysis in Sec. G.2
To enable gradient flow through spiking neurons, Gaussian surrogate gradient was implemented follow- ing Chen et al. (002)). The surrogate gradient was parameterized with a fixed standard deviation 0.5 and amplitude = 0.3, applied to the scaled membrane potential. These parameters were not updated during training. Backpropagation through time (BPTT) used for credit assignment across temporal sequences. This setup ensures a direct comparison between gradient-based optimization and the explored plasticity rules, while accounting for the additional computational cost introduced by surrogate gradients and BPTT.
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G.2 SENSITIVITY ANALYSIS IN HYPERPARAMETERS OF OPTIMIZERS
In Fig. S14a, we present the results of training the VI model on the visual change detection task with natural images using the Adam optimizer across range of learning rates: {10-5, 10-4 10 10-3). The analysis reveals that the VI model is highly sensitive to optimizer choice, where the model achieves peak performance with a learning rate of 10 while other rates degrade convergence. We also evaluated SGD with the same set of learning rates for comparison Fig. SS14p. However, SGD fails converge effectively across all tested learning rates within the same training budget.
We extended our analysis the sensitivity of Adam's momentum hyperparameters, 31 and 82, with the learning rate fixed at previously identified optimal value, 10-3, As shown in Fig. (155,, performance remains stable across 31 {0, 0.5, 0.9) and 33 E {0.99, 0.999). This relative insensitivity to parameters rein- forces our conclusion that evolved plasticity rules achieve behavioral performance with order-of-magninut greater efficiency than gradient- based methods.
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H DETAILS OF MULTI-OBJECTIVE EVOLUTIONARY FRAMEWORK
As outlined in Section 2 the discovery of plasticity mechanisms be cast multi- search problem. Each candidate corresponds to parameterized plasticity rule, and the goal is to identify rules that strike balance between predictive performance, biological plausibility, and computational efficiency. This search problem presents several key challenges:
Expensive evaluation. Evaluating the quality of a plasticity rule requires training VI network from scratch under the candidate rule. This involves long simulation times and limits the number of rules that can be explored within practical runtime.
Many objectives. The optimization multi-objective, combining quantitative performance (e.g., task ac- curacy, number of terms) with qualitative desiderata. Some objectives are seft-bounded: for instance, desirable for the learned plasticity rule to exhibit dynamics similar to biological systems, but perfect match- ing is neither required nor expected. This leaves room for approximate but functionally relevant behaviors.
High-dlmme diigenimnnsional search space. The plasticity rule is defined over multiple interacting components. This leads to large combinatorial search space with complex dependencies.
Noisy evaluation. Because a plasticity rule must be assessed by training a network from scratch on varying data, its measured performance inevitably exhibits a substantial degree of randomness. As result, eval- uations of the same rule can differ across runs. An effective search framework must therefore be robust this variability, avoiding misleading selections and favoring rules that demonstrate consistently strong performance.
Non-differentiable optimization. The objective functions not admit closed-form gradients with re- spect to the rule parameters. This rules out traditional gradient-based optimization and motivates the use of derivative-free search.
Taken together, these factors make the search for plasticity mechanisms especially demanding. To address them, we employ a evolutionary framework, which is well suited to handling non-differentiabiliyy, noise, and multiple objectives while naturally supporting parallel and scalable evaluation. The following section details the specific evolutionary algorithm used in our study.
H.1 PROPOSED EVOLUTIONARY FRAMEWORK
To address the challenges outlined above, we propose a tailored evolutionary framework for plasticity rule discovery. Our method builds on established multi-objective evolutionary algorithms (MOEAs) and is im- plemented within the EvoX framework (Huang et 2024a).
The algorithm is designed to be robust to noise, scalable to large populations, and efficient on modern GPU clusters through parallel evaluation. Its workflow follows four main phases: initialization, reproduction, evaluation (including re-evaluation), and selection, as summarized in Algorithm
During initialization, population of candidate rules is randomly sampled from the parameter space. In each generation, reproduction produces offspring via swarm-inspired updates followed by mutation. Eval- uation then proceeds on the offspring and on dynamically selected subset the current population for re-evaluation (i.c., individuals with few prior evaluations). This adaptive re-evaluation saves computational budget early while preserving the ability to reliably discriminate between similarly performing solutions in later stages through multiple rounds of evaluation. Finally, selection ranks all evaluated solutions ing a awire non-dominated sorting procedure and retains the most promising candidates for the next generation.
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Algorithm 1 Noise-Aware Multi-Ohjective Evolutionary Framework
1: Initialize population P with random candidates
2: Initialize evaluation statistics (counts, means, variances)
3: while termination criteria met do
4: Offisring + REPRODUCTION(P)
Sec.
H.I.J
5: R < select subset of P with lowest evaluation counts for re-evaluation
6: Evaluate Offspring U R in parallel
Sec.
H.1.3
7: Update evaluation statistics
8: P <- SELECTION((? (P, Offspring, R.)
Sec.
H.1.2
9: end while
10:
return Final non-dominated set from P
H.1.1 REPRODUCTION OPERATOR
The reproduction operator follows Competitive Swarm Optimizer (tyee mechanism adapted from TensorRVEA [Cengg & Jin 2015 Liang al. 2024 The population is randomly partitioned into N/2 disjoint pairs. For each pair, a teacher (winner) and a student (loser) are identified by comparing their performance randomly sampled objective, where the objective index is drawn according to predefined weight distribution. Only the student updates its velocity and position by combining directional cues from the teacher and the population center; the teacher remains stationary in this phase. To produce full set of N offspring per generation, both members of the pair then undergo mutation: one offspring is generated from the updated student, and a second offssring is generated from the teacher.
This CSO-style pairing and update are well suited to GPU acceleration: pair formation, pair-wise compar- ison, per-dimension velocity updates, and independent mutations can be executed in parallel without data dependencies (the population center is a single reduction).
H.1.2 SELECTION OPERATOR
The selection phase accounts for noisy evaluations by incorporating statistical confidence into the dominance relation used in non-dominated sorting (Deb al. 2002 while following the general principle of dealing with noisy data in evolutionary algorithm (Ui & Branke 2005 Fieldsend & Everson 2005). Each solution maintains online estimates the mean and variance its objectives, updated via Welford's 's method. Rather than applying deterministic dominance, solutions are compared probabilistically. the algorithm estimates the probability that one solution outperforms another using their means and variances.
Formally, for each objective, win-rate probability is computed between two solutions. A solution is said dominate another only if it achieves sufficiently high probability (e.g., > 55%) of being better on all objectives. This definition naturally adapts to noise: under high variance, dominance requires a clear margin of superiority, while under low variance, even small improvements can suffice. In this way, the selection pressure adjusts automatically to evaluation reliability.
These probabilistic dominance relations are used to construct dominance matrix, which forms the basis for confidence-awart non-dominated sorting procedure. After sorting, ties near the population cutoff are broken using a diversity measure (crowding distance) adjusted with an uncertainty penalty, favoring solutions that are both diverse and reliably evaluated.
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Algorithm 2 Reproduction( P. (v.).0)
1: Input: Population P {x Jim velocities {vi) ii convergence parameter 6, objective weights w
R.m
2: Output: Offisrrng set P' {x] IN and offssring velocities {vi)
3: Randomly shuffle indices and form N/2 disjoint pairs
4: Compute population center ct- Σ
(parallel reduction)
5: for each pair (i.j) parallel do
6: Sample objective l ~ Categorical(w)
7: Determine teacher/student by objective-wise comparison (assume minimization):
fx(x)) S fx(x)) tti, stj else t j, sti
8: Sample elementwise coefficients \ A2, A3 ~ U10
9: Student update (only):
A
x - x.) O
x x, + Vs
10:
Mutation (both members produce offspring):
x +- MUTATE(X.)
(continuous: polynomial; gating: discrete/bit--lj dimension-aware rates)
X + MUTATE(X;)
(teacher does not move before mutation)
11:
Set offspring velocities: v v. (updated), v/ v,, (unchanged)
12:
Add x,, x, (and v'. v/) to pl
13: end for
14: return P', (v/W
This procedure reduces bias from noisy evaluations, improving stability in stochastic environments and enabling reliable optimization when evaluations are expensive and uncertain. The overall process is summa- rized in Algorithm
H.1.3 EFFICIENT EVALUATION
Evaluating a candidate plasticity rule is computationally demanding, as each evaluation requires training a VI model from scratch. To make this feasible at scale, two key complementary strategies are explored: batched parallelism and an optimized forward pass enabled by the gradient-free setup. Together, these tech- niques substantially reduce computational and memory costs, making large-scale exploration of candidate rules tractable.
Batched evaluation. At each generation, P candidate rules are trained concurrently. State variables (mem- brane potentials, spikes, synaptic traces) are organized in a Afructureof-Arrayy (SoA) layout, rather than an -rayy-ffSStructurs (AoS). This design improves coalesced memory access and GPU bandwidth utilization, allowing all candidate rules to advance lockstep. Within a single device, data parallelism enables simul- taneous processing of multiple candidates and mini-batches. The same principle extends across multiple devices or nodes, achieving lear-linear scaling as computational resources increase.
Optimized forward pass (Gradient-free setup). Because the evolutionary search is gradient-free. no -thpggggttiotttuughhhho
required (Werbos] 1990). This removes the need to store long sequences of activations, memory usage depends only on the instantaneous network state rather than the simulation length. As result, models can be trained over long horizons by the plasticity rules without the prohibitive costs of differentiable approaches. The freee setup also aligns naturally with the event-driven nature
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Algorithm 3 Selection with Probabilistic Non-Dominated Sorting
1: Input: Candidate set C' (parents, offspring, re-evaluated), mean objectives f, variances s?, population
size N
2: Output: Survivor set
3: Update and s² for all C via online estimators
4: for each pair (i in C' do
for each objective do Compute win probability:
6:
WinRate (k)
1 + exx
214 +97 +e
V 4/
7: end for
8: i dominates j if WinRate, (k)
for all A
9: end for
10: Build dominance matrix and perform non-dominated sorting
11: Break ties at cutoff using adjusted crowding distance:
((k)
AdjDist, = Crowding,
2(k)
k= max, 8)
12: Select top N individuals as survivor set P
of spiking models. In contrast to surrogate-gradient methods (Huh & Sejnowski 2018 Zenke & Gan- guli 2018 Neftei al. 2019b), spikes treated directly as binary events, which be stored and pro- cessed compactly. This representation reduces both memory bandwidth demands and computation relative floating pointtoointtt operations. When combined with batched evaluation, these properties make forward-only simulation particularly efficient.
These efficiencies stem directly from the design of an evolutionary framework. Its gradient-free nature enables many techniques that avoid the heavy compute and memory demands of backpropagation, while its population-based structure inherently supports batching and large-scale parallelism. Taken together, these properties allow our system sustain evaluation throughput per GPU per day, with each rule applied to training VI model 3,000 neurons and approximately 400k parameters from scratch two distinct tasks. This level of scalability enables exploration of vast rule spaces that would otherwise computationally prohibitive.
the order of 10 candidate plasticity rules
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LARGE LANGUAGE MODEL USAGE DISCLOSURE
In accordance with the policy on LLM usage, we provide the following disclosure regarding how LLMs were employed during this work. LLMs were used only supportive roles, with all substantive research contributions, coding, and writing decisions made by the human authors.
Code base. LLMs were used strictly for short code cuto-completion, comparable to standard IDE assistance. All completions were reviewed and confirmed by the human authors. No unsupervised code generation, automatic project generation, or independent algorithm design was delegated to an LLM.
Paper writing. LLMs assisted only at the presentation level, e.g., suggesting alternative phrasings im- proving clarity of exposition. All scientific content, descriptions of methodology, results, and discussion written and verified by the authors. All language suggestions from the L.M were reviewed by the authors.
Research assistant. LLMs occasionally used research assistants in role analogous search engine. This included tasks such as quickly gathering related information or checking terminology. All final written content based on references and verified sources; scientific claims results were drawn solely from LLM outputs.
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Reviews:
[{"review_id": "LLU2b6n3ar", "reviewer": "Reviewer_N15c", "summary": "This paper proposes to find candidate plasticity rules that could be implemented in the brain using numerical optimisation (meta-learning, “learning the learning rule”). This is an important problem, as direct recordings of weights in vivo during learning are currently impossible, thus computational methods are the only option to integrate all the indirect evidence at our disposal (neural activity during learning, general circuit knowledge, task performance…). \n\nThe authors consider a biologically detailed model of mouse V1 cortex inspired by previous work with 289 synapse types, each evolving with their own, tunable plasticity rule. Plasticity rules are parameterised as Taylor expansions up to the third order on the presynaptic activity, postsynaptic activity and reward. To navigate this high-dimensional search space (~2.6k parameters in total), they use a multi-objective evolutionary strategy, refined from previous work that maintains and evolves a population of 4000 rules.\n\nThey apply this method to a working memory task (image change detection), for which there exists mouse recordings during learning. They select rules based on several objective: task performance, a bias towards simpler rules (fewer non-zero terms), matching of the in silicon and in vivo neural activity, and general biological plausibility (e.g. physiological weight values, individual firing rates). Each candidate plasticity rule (i.e. 289 individual rules) is evaluated by exposing the network to a 100 trials with plasticity on, while performance is evaluated on test trials with plasticity turned off. This means that task needs to be performed with a fixed connectivity learned by plasticity during training, and not via online weight changes during individual trials.\n\nThey find rules that solve the task with comparable performance to the animals. They show that the rules are scale-invariant via simulations in smaller and bigger networks of similar architecture. Their set of 70 best-performing rules display similar fit to data yet meaningfully different expressions (degeneracy). Notably, non-reward modulated rules, and simple, pre-only rules can solve the task, showing that the task at hand can be solved in an unsupervised way.  Finally, they show that their best rules learn the task faster than an implementation of gradient based optimization (Adam).", "questions": "(1) Fig 4, I would add a panel about the optimisation itself, not only after convergence (for instance the performance of the best rule at each step). I’m especially curious wrt how no plasticity performs on the task, as well as randomly drawn rules from the search space (step 0 of the optimisation). Right now, this is crucial evidence missing to show that your method efficiently navigates the space of rules. It would be a red flag that most rules in the search space are good at this task.\n\n(2) How reproducible is the optimization run shown in the study? I understand that within one run, you keep a population of rules (4000), but this is very small wrt to the dimensionality of the whole search space, so I would expect that you are “missing” many good candidate rules. For instance, starting from a different initialisation, does a run converge to a completely different population of rules? Or do you see regularities within the inferred rules? Apologies if I missed this experiment. And I understand this is a lot of compute to ask for. But at least this should be mentioned in limitations or in the discussion section. This method is not really fit to properly explore degeneracy (given the dimensionality of the space, probably no method can, but the claims in the paper (line 283) imply the opposite).\n\n(3) I would appreciate more work on analysing the solutions obtained by the optimisation. How come simple rules (pre-only or reward-free rules) are able to solve the task by themselves? How are the networks able to keep a memory of the previous stimulus? Since weights are frozen during testing, it has to be in the activity (or is there short term plasticity in the model?)? Can you decode the identity of previous stimulus from the activity? How does this change across time? Can you compare how a static network (without plasticity) behaves in this task, and what changes do a successful plasticity rule brings, especially the simplest ones you found in the optimization? If the evaluation trials are indeed a good metric of generalization performance, this would mean there is a connection between extremely simple, unsupervised rules and generic working memory abilities, which is exciting, and to my knowledge, novel. Can you analyse and compare the solutions that use/don’t use reward, and make predictions on how we could distinguish these two in future experiments. But as it stands, your results instead question the task choice, if reward is not necessary to learn. My worry is that the advantage of using such a complex search space is lost if simple, reward-free rules can solve the task. At least this warrants proper reverse engineering efforts to understand what these rules do to the network and how they solve the task. Nice insights for neuro could fall from this.\n\nSmaller points:\n\n- Why shut off plasticity during test trials? Presumably the candidate rules are restricted to be slow, or at least comparable to the brain. If you leave plasticity enabled during testing, do you learn radically different plasticity rules? Can the task be fairly recasted as novelty detection? In that case, it doesn’t have to be working memory and it would be a nice link between the working memory literature and the novelty detection literature.\n\n- Line 426: distributions of firing rates on the violin plots do look quite different to data still (mainly, a larger variance in exp data). Normally that wouldn’t be a concern for a network of identical neurons like are standard in the field, but given your much more refined model with many neuron types, how do you interpret the inability to better fit the distribution of firing rate (which is objective 6, so part of the fitting procedure if I understand correctly).\n\n- Define heterogenous: when reading initially I understood heterogenous as one rule per synapse, not one per synapse-type. Maybe co-active is better suited?\n\n- Fig 2: I would say from where the data was taken in the caption, not only in the main text.\n\n- I’m confused by the 2 timescales for reward: one is the window over which past rewards are averaged (20, not learned), and the other is the time constant in eq 4. Why not have a single timescale? And if 2, why not learn both?\n\n- Limitation section: besides the points raised above, I would acknowledge there that in experiments, people are moving away from pairwise rules with for instance btsp [4], which are not taken into account by your model.\n\n- Introduction has a whole paragraph on related work, followed by a section entirely dedicated to related work. Maybe merge the two for space, now it functions a bit like a repeat.\n\n- Line 55: “broad but interpretable candidate space of heterogeneous plasticity rules” Are Taylor expansions really a guarantee of interpretability? Especially when there are so many terms and so many co-active rules? By interpretable I mean that can give rise to theoretical insights or experimental predictions. This is a more general point, so does not affect my assessment of the paper.\n\n- Can you explain the choice for a single g for all synapses (which I understood to be tunable)? Wouldn’t the simplicity criterion introduced in the optimization already remove unnecessary terms, and the g could only be there to remove the non-sensical terms in the Taylor expansion once and for all (and potentially removed from the main text for clarity)?\n\n- Enforcing Dale’s law and maximum values: how often do your weights attempt to cross 0? I.e. how often is this condition not met by the rule itself but instead by your added bound. Same question for the upper bound. Ideally these bounds are not reached often.\n\n-  Given that one of the key conclusion is about degeneracy, a discussion of other work studying degeneracy should be added, for instance [2].\n\n- Please reformat the citations so that they are either in parenthesis or numbered (if ICLR allows this).\n\n- This is not really a question, but I found the scale-free result very nice and reassuring on the solutions that you find.\n\n[1] Jordan et al, Evolving interpretable plasticity for spiking networks, eLife, 2021.  \n[2] Confavreux et al, Memory by a thousand rules: Automated discovery of multi-type plasticity rules reveals variety & degeneracy at the heart of learning, bioRxiv, 2025.  \n[3] Bittner et al, Behavioral time scale synaptic plasticity underlies ca1 place fields, Science 2017", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The method presented has many strong points compared to existing work: (i) flexible, high dimensional search space with co-active rules across many synapse types, (ii) large scale, biologically detailed network model which enables (iii) direct comparison with experimental data (iv) multi-objective optimisation which allows to select meaningful candidate rules (v) some level of a population view: recovering several candidate rules, reporting that many different rules are equally consistent with data. Though there exists work with the ingredients mentioned above, this is, to my knowledge, the first study to put all of these together. The only work that comes close, [2], is 1/ very recent and 2/ trades off the flexibility of the search space for a more exhaustive survey of the space using numerical inference instead of local optimisation, and thus provides a complementary instead of redundant perspective. Thus this work is novel and interesting as it adresses many limitations of existing work, and worthy of being shared with the community.\n\n- This work is a technical tour de force, the sheer number of simulations of large-scale, biologically detailed models with so many co-active rules simulated in parallel on GPUs using modern ML libraries lays the groundwork for the field to embrace such large scale simulations more easily in the future. Navigating and optimising such a landscape is notoriously hard, with most previous work effectively failing to do so. The method presented here appears to work at a scale large enough for direct experimental comparison. Moreover, the biological model, search space and optimisation procedure are very well explained. This is remarkable, given the complexity of the method with nested loops of learning systems and evaluations. Overall, I see the methodological and technical side of this work as exceptionally strong, and the evidence that this method could be useful for neuroscience is convincing (provided a few clarifications and additional plots, see question 1).", "weaknesses": "However, despite the exciting aspects above (for which the authors should be commended), I found the results drawn from the method currently lackluster and underdeveloped, especially given how promising their setup is.\n\n1/ The paper lacks a discussion and limitations section, and at present is convincing only as a method paper, not as much as a work that attempts to make actual predictions on which plasticity rules are in the brain. I could still recommend this paper for acceptance for the methods alone, provided some clarifications and some claims to be adjusted accordingly. A much more exciting route would be to dig deeper on the current results and extract some new neuroscientific insights (more on this, with hopefully actionable items in question 3).\n\n2/ Position wrt prior work: though the section comparing this work to prior work is thorough, I think it needs more precision and nuance. Right now, many different papers are bunched together with general statements on limitations for which the reader needs to investigate applies to which reference mention all potential weakness. e.g. for the paragraph line 115: consider a small search space (….), or simple tasks (…). I also think 2 important papers are missing: [1] which is also evolutionary search in an effectively infinite dimension search space, though it is applied to ~single neuron spiking models and simple tasks, without direct comparison to experimental data. [2] which considers 4 co-active rules and a smaller search space, but also in large scale spiking models, with direct comparison to data and a multi-objective selection of rules. Importantly, this paper also finds degeneracy of rules, which is interesting to relate somewhere in discussion to the current paper’s claims. To summarise: 1/ the precise method used in the paper is novel 2/ there exists work that has each of the advantages ascribed by the method, but not all at once. 3/ the combination of the advantages allows for unique capabilities of the method presented (e.g. visualize the trade-offs between different objectives).\n\n3/ Overclaims and paper’s lack of a main message.\n- Line 53 (and similarly Line 58): “systematically”: I don’t think that the authors can claim that at present they are systematically exploring the 2.6K parameter space with an evolutionary strategy, almost by design given how big this space is. It’s both a strength (large, very flexible space) and a weakness (hard to survey systematically) of the paper. Despite this limitation that should be acknowledged somewhere, I think it’s very nice that this paper still makes a point about the observed degeneracy. I am pointing this out mainly in contrast to the SBI line of work [2] which infers posteriors over rules to be able to more systematically explore the search space and degeneracy. In their case, the search space has to be much smaller dimensional.\n- Can you really call this a “multitask setting”, when it’s 2 tasks, both image change detection? Why not simply image detection task with either natural images or gratings. Currently this makes the rules inferred look like they solve a wider range of tasks than they probably do, and makes especially the simple rules found seem suspicious.\n- The comparison with gradient descent. Line 24: “Experimental results demonstrate that the discovered plasticity rules can attain high task performance with orders of magnitude fewer training samples than the gradient-based rule”. I think this statement is vastly overinflated, and I’m not sure how useful this point is, given how underdeveloped the analysis of the results is otherwise. Is the claim destined to alert machine learning practicioners that this paper proposes rules more efficient better than gradient descent? Then many additional results are required to show the results generalises across different tasks and architectures. The gradient descent claim can be rephrased into a more fair sentence acknowledging this is probably heavily dependent (overfit?) on the task and network model considered here (and would require more results on the GD hyperparameter search). I’m not sure of the value of adding the gradient descent debate into this paper, and would rather see the space used to analyse and reverse engineer more thoroughly the rules found to make predictions for neuroscience (see questions). Overall, I think this GD point risks being a distractor on what your framework offers, and I would keep this paper “AI4neuro”, focused at understanding the rules in the brain, and not “Neuro4AI”, aiming to develop novel learning rules for ML inspired by neuro, at least in this submission.\n- The final section of the paper brushes too fast over the interpretation of the plasticity rules and implications for neuroscience (see questions).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XUKBtqorpg", "reviewer": "Reviewer_XrNa", "summary": "This paper presents a large-scale framework for evolving heterogeneous synaptic plasticity rules within a model of mouse V1. This work is ambitious, and seeks to unify many observed biological features of synaptic plasticity by using a multi-objective optimization across biological and task metrics and exploring a vast parameter space of rules. The approach is technically impressive and represents a major engineering effort. However, the biological and computational insights drawn from the discovered rules remain limited: the evolved rules are simple, the tasks are minimal, and there is little analysis of why heterogeneity helps.", "questions": "Questions\n\n1. The Adam baseline in Fig. 6 seems poorly tuned and underperforms due to a long period of no learning. Have the authors tested alternative optimiser settings, initialisations, and standard regularisations?\n2. Is the heterogenous nature of plasticity rules required? Have the authors tested reduced models with fewer cell types? It also appears like very simple rules are sufficient for the task - is that the correct interpretation?\n3. How important is the task choice for the conclusions? Have the authors tested this framework on other tasks?\n4. What insight is gained about why certain terms (pre/post, eligibility, reward) occur in the best rules? \n\nMinor questions: \n1. What is n in (2)? Also, l_i is a little odd for a trial index? \n2. Eq 7, g^k is learned by evolutionary search, correct?\n3. I don’t think the implementation of metrics in 3.3 is explained? They might also be suitable as regularisers for GD. \n4. Are the authors making an implicit assumption that plasticity rules are learning rules? I think a clear statement or discussion on the relationship between plasticity rules and learning rules could be valuable to the reader (but do not think this is a must). My perspective is that synaptic plasticity rules are often components of a larger learning rule or process. But I’d be interested in their perspective. The authors touch on this in paragraph 393 with the observation that reward free rules succeeded.   \n5. Dale’s law, maximum & minimum weights, adaptive scaling (appendix B.2) might be valuable aspects that sculpt which plasticity rules are found. It reads as a little odd that these features were chosen to be explicitly dealt with if the whole point is to discover rules that fit biology. Do the authors have a justification?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Ambitious attempt to systematically explore a large rule space under biological constraints.\n- Clear and reproducible description of the evolutionary framework.\n- A tour de force of synaptic plasticity modelling and related works.", "weaknesses": "The scientific hypothesis being tested isn’t clearly stated. Filling in gaps between existing approaches isn’t a hypothesis. I think stemming from this, the paper is somewhat unfocused in its choice of related literature and methods description throughout. For example I think much of section 2 could go in the appendix. As a result, there is no space for details of the V1 model in the main text. \n\nIt reads as if many of the modelling choices are included because they exist in the literature and field, rather than being focused behind testing a hypothesis.  For example, it is not clear why the network needs to be so large: if general principles are being discovered, a reduced network would likely be a more tractable and informative place to start than beginning with 17 neuron types. Also, to this point, it is not shown clearly that heterogeneous complexity is even needed. This is especially pertinent given the simplistic task nature, and simplicity of the rank1 and rank2 rules found. \n\nIn my opinion the primary weakness that needs to be addressed is the empirical results. These results, as currently presented, do not support the claims in the abstract. The single task (image change detection) is overly simple and does not support the general claim of “high task performance”. Moreover, I am not convinced by the comparison to Adam. From Figure 6, it looks as if there is an initialisation issue with Adam. At the very least there should be a hyperparameter search over Adam’s parameters. It may also be that without some regularisation (e.g. the metrics in 3.3) the network struggles to learn. Also, cutting off training when task accuracy is ~%70 is strange. Neither learning rule appears to have been run to convergence and again, this is important for the claims made.\n\nI would find the claims of superior performance over GD more convincing if the authors were to take an existing SANN task/dataset, for example Heidelberg Digits, and compare their framework to an optimized surrogate gradient benchmark. Ideal would be a small set of tasks that required the network to implement different computational strategies. \n\nFinally, there is minimal mechanistic insight or discussion into how the rules support learning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "GpeEa15xOI", "reviewer": "Reviewer_Txin", "summary": "This paper proposes a synaptic plasticity evolutionary method that achieves a balance between task performance and biological interpretability through heterogeneous plasticity. This method is trained by finding an interpretable search space. Also, the plasticity algorithm they discovered has better generalization and the ability to learn from few shot learning.", "questions": "See Weakness Section.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "**1.** It's a very interesting job with intriguing ideas. The ideas presented offer fresh perspectives and will likely stimulate further academic discussion.\n\n**2.** The thesis is well-written, logical, and clear. The manuscript demonstrates good academic writing standards.\n\n**3.** The research question is clearly defined.", "weaknesses": "**1.** The article is not very clear on how it assesses biological interpretability. Is it through the values related to firing rate in the metrics? Why would similar firing rates be more biologically similar? The methodology for evaluating biological interpretability requires clarification. \n\nFor example, How model units are aligned or matched with biological neurons, How the neural recordings from LGN were preprocessed?\n\n**2.** There is no paragraph explaining how the similarity with the LGN regions is calculated and how the neural data is utilized.\n\n**3.** Many formulas are presented without explaining the meanings of all the symbols. It is recommended to provide a complete explanation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XqddvL4XJR", "reviewer": "Reviewer_t465", "summary": "The paper presents a computational framework that uses Darwinian evolution to automatically discover biologically plausible, heterogeneous synaptic plasticity rules in a realistic model of mouse primary visual cortex (V1). By parameterizing plasticity as a Taylor expansion of pre- and postsynaptic spikes, eligibility traces, and neuromodulators, the authors create a compact space plasticity rules. A multi-objective evolutionary algorithm optimizes rules for both task performance and biological validity. The resulting rules achieve high performance on visual change-detection tasks with far fewer samples than gradient-based methods, generalize to networks of different sizes, and maintain biological constraints, offering insights into how the brain might implement efficient, heterogeneous plasticity.", "questions": "- The paper should explain the Evaluation Tasks (visual change detections) more clearly at least in the appendices, which is less clear for readers who are not familiar enough\n\n- Can you explain where did the $c^k$ in equation 7 go in Table 1? Are Table 1 cluster different plasticity rules by $g^k$ only? I think $c^k$ is real number and is non-homogeneous for different synapses. Why is it possible to collapse to 4000 unique rules?\n\n- Did the paper study the problem of generalization? What is the relation between training/testing and training/validation trials? Are those tasks unchanged? Or are the tasks different? How different they are?\n\n- It seems to me that evolution are done on a fixed V1 model, while the evolved plasticity rules can be applied to train different networks / networks of different size? Please clarify more on the experiment settings.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- First large-scale attempt to let evolution simultaneously optimize thousands of plasticity coefficients inside a biological cortical model.\nIntroduces a compact closed-form plasticity rules that keeps rules local and therefore biologically testable (Up to 25 terms, far surpassing existing plasticity rules containing 2 to 4 terms).\n- Multi-objective fitness to control both the task performance and biological plausibility.\n- If I understand it correctly, the exact same rules work after rescaling on networks from 1 k to 5k neurons without re-evolution.", "weaknesses": "- The work is an impressive proof-of-concept that evolutionary search can find local plasticity rules which learn quickly and remain biologically plausible, but it stops short of asking whether those rules generalize to new and practical tasks. My main concern after reading this paper is “what should the readers take away?” Sample efficiency of Hebbian plasticity has already been proved by many previous works. According to my knowledge, the real problem for Hebbian plasticity is “are there general plasticity rules that generalize any tasks & networks?” So far, the generalization of those local learning rules can not compare with that of gradient descent.\n- The paper contains no statistical comparison with other biologically plausible learning rules.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)