🧠 neuroscience

Inhibitory budget matching constrains homeostatic plasticity in competitive spiking networks

This paper demonstrates that in competitive spiking networks, replacing fixed lateral inhibition with plastic homeostatic rules requires an "inhibitory budget matching" constraint to conserve total inhibitory drive, a principle that ensures network stability and preserves learning performance while allowing local inhibitory weights to adapt.

Original authors: Musacchio, F., Fuhrmann, M.

Published 2026-10-02

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CC BY 4.0

Original authors: Musacchio, F., Fuhrmann, M.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

In the brain, neurons do not work in isolation; they form vast, dynamic networks where excitation and inhibition must remain in a delicate balance. Excitatory neurons fire to carry information, while inhibitory neurons act as brakes, preventing the system from spiraling into chaos. For decades, computer scientists building artificial neural networks to mimic this biological intelligence have relied on a simplified model: they let the excitatory neurons learn and adapt, but they keep the inhibitory connections fixed and unchanging. This approach works well for teaching machines to recognize patterns, such as handwritten digits, but it ignores a fundamental truth of biology. In real brains, inhibitory connections are just as plastic as excitatory ones; they strengthen and weaken over time to maintain stability. The question researchers have long faced is whether an artificial network can survive if we replace those fixed, unchanging brakes with living, learning ones. If the brakes adjust themselves, will the car stay on the road, or will it crash?

A team of researchers at the German Center for Neurodegenerative Diseases set out to answer this by building a competitive spiking network, a type of artificial brain designed to learn without supervision. They trained this network on a standard set of 28-by-28 pixel images of handwritten digits, a task known as MNIST. In their setup, the network received these images as streams of electrical spikes, much like the brain processes visual data. The excitatory neurons competed to respond to specific patterns, strengthening their connections to the input when they fired first. To keep this competition fair and prevent a few neurons from dominating the entire network, the researchers introduced an inhibitory population. In the traditional version of this model, the connections from the inhibitory neurons to the excitatory ones were hard-coded and never changed. The researchers wanted to see what would happen if they allowed those inhibitory connections to change based on the network's activity, mimicking the plasticity found in the human cortex.

The team tested several different rules for how these inhibitory connections should change. One rule was based on the precise timing of spikes, a method previously shown to balance activity in other types of networks. Another rule was slower, adjusting inhibition based on the average firing rate over a longer period. They also tested a new approach that added a strict constraint: a "budget" that limited the total amount of inhibitory power any single excitatory neuron could receive. The results revealed that simply making the inhibition plastic was not enough to guarantee stability. When the researchers used the timing-based rule, the network often remained stable, but it was fragile; small changes in the starting conditions or the learning speed caused the system to fail, with neurons firing uncontrollably and the network collapsing. The slower, rate-based rule performed better, completing training in most of their test runs, but it still struggled when the total amount of inhibition drifted too far from the ideal level.

The breakthrough came when the researchers enforced the budget constraint. They found that for the network to remain stable while learning, the total inhibitory power delivered to each neuron had to stay within a specific range, matching the strength of the fixed connections used in the successful baseline models. When they set this budget to the correct value, the network learned just as well as the fixed version, achieving an accuracy of roughly 83.5 percent on the digit recognition task. The neurons developed clear preferences for different digits, and the network remained calm and organized throughout the training. However, when they doubled the budget, allowing twice as much inhibitory power, the network failed in every single attempt. The neurons fired so rapidly that the system crashed almost immediately. This showed that the stability of the network did not depend on the local learning rule alone, but on a global constraint that kept the total competitive pressure constant.

The study suggests that in competitive learning systems, you cannot simply swap fixed connections for plastic ones without managing the overall strength of the competition. The researchers demonstrated that inhibitory plasticity can replace fixed inhibition, but only if the system is guided by a rule that conserves the total inhibitory drive. This finding offers a practical design principle for building more biologically realistic artificial brains. It implies that for a network to learn effectively without falling apart, it needs a mechanism that allows individual connections to adapt while ensuring the total force of inhibition remains steady. Without this conservation, the network loses its balance, proving that in the complex dance of neural competition, the total strength of the brakes matters just as much as how they are applied.

Technical Summary: Inhibitory Budget Matching Constrains Homeostatic Plasticity in Competitive Spiking Networks

Problem Statement
Competitive spiking neural networks (SNNs), such as the influential Diehl–Cook architecture, rely on local spike-timing-dependent plasticity (STDP) at feedforward excitatory synapses to form sensory representations. In these models, competition between excitatory neurons is typically enforced by a fixed lateral inhibitory circuit. While biologically plausible inhibitory synapses are plastic and contribute to excitation–inhibition (E-I) balance, most SNN implementations keep the competitive circuit fixed for computational convenience. It remains unclear whether biologically motivated inhibitory plasticity rules can replace fixed lateral inhibition in competitive STDP networks without disrupting representation learning or causing network instability (e.g., runaway activity or silent collapse). The core question is whether local homeostatic inhibitory updates alone are sufficient to stabilize competition, or if additional global constraints are required.

Methodology
The authors investigated this question using a competitive spiking network trained on the MNIST dataset. The network consisted of an input population (Poisson-encoded MNIST images), an excitatory population, and an inhibitory population.

Baseline: A standard Diehl–Cook setup with fixed inhibitory weights ( $W_{IE}$ ) and plastic feedforward weights ( $W_{XE}$ ) using STDP.
Plasticity Rules Tested: The study compared three inhibitory plasticity mechanisms against the fixed baseline:
1. Vogels-style iSTDP: A spike-timing-dependent rule adapted from Vogels et al. [10], which potentiates inhibition based on pre-post coincidence and depresses it based on a target offset.
2. Slow Homeostatic Inhibition: A rule that adjusts inhibitory weights based on stimulus-scale deviations from a target firing rate, removing fast spike-coincidence potentiation.
3. Budget-Constrained Slow Homeostasis: The slow homeostatic rule followed by a column-wise normalization step that enforces a fixed total inhibitory budget ( $B_I$ ) received by each excitatory neuron.
Experimental Design: The authors first mapped the stability of the fixed-inhibition regime across input gain ( $g$ ) and inhibitory strength ( $w_{IE}$ ) to identify a stable reference operating point ( $g=2.0, w_{IE}=10.0$ ). They then tested the plastic rules within this reference regime and across parameter grids (learning rates, target offsets, and budget values). Stability was defined by the ability to complete 30,000 training examples without triggering runaway activity (>5000 spikes/image) or silent collapse. Performance was measured via post-hoc classification accuracy and neuron usage entropy.

Key Results

Fixed-Inhibition Regime Sensitivity: Stability in the fixed-inhibition baseline was not guaranteed; it depended jointly on input gain and inhibitory strength. Stronger inhibition at high input gains led to runaway activity, while lower gains or strengths allowed for stable learning.
Vogels-style iSTDP: This rule was broadly but not uniformly stable. In the reference regime, it could preserve the operating point and achieve accuracy comparable to the fixed baseline (approx. 84%). However, stability was sensitive to parameter choices (specifically the target offset $\rho$ ) and replicate initializations, with some runs failing due to delayed runaway or silent collapse.
Slow Homeostatic Inhibition: Removing fast coincidence potentiation improved stability, with 96% of runs completing training. However, without a global constraint, the total inhibitory drive could drift, occasionally leading to weight saturation or instability under stress.
The Critical Role of the Inhibitory Budget: The most significant finding concerns the budget-constrained rule.
- Matched Budget: When the conserved inhibitory budget ( $B_I = 3990$ ) matched the total inhibitory drive of the stable fixed-inhibition reference, the rule was stable in all replicate runs. It achieved high accuracy (83.5%) and maintained firing rates and conductance statistics nearly identical to the fixed baseline.
- Mismatched Budget: When the budget was doubled ( $B_I = 7980$ ), the network failed in every replicate, exhibiting runaway activity.
- Mechanism: The budget constraint separates the local redistribution of inhibitory weights from changes in the total competitive drive. Matching the budget ensures the network remains in a viable dynamical regime, whereas mismatching it shifts the network into unstable high-gain or low-competition states.

Significance and Claims
The paper claims that inhibitory plasticity in competitive STDP networks is not governed by local homeostatic updates alone. Instead, stable plastic competition depends jointly on the operating regime and an inhibitory budget that fixes the total strength of competition while allowing local weights to adapt.

The authors argue that "inhibitory budget matching" is a practical design principle for replacing fixed inhibition with plastic, homeostatically regulated competition. Mechanistically, this constraint prevents plasticity from shifting the network away from a stable competitive state by decoupling local weight redistribution from global drive changes. The study concludes that for inhibitory plasticity to successfully replace fixed lateral inhibition in competitive learning architectures, the conserved total inhibitory input must be explicitly matched to a stable operating point established by the fixed circuit. This provides a concrete starting point for theories of inhibitory learning in competitive spiking networks, emphasizing that the stability of learning rules is context-dependent and requires global constraints to manage the total competitive drive.

Technical Summary: Inhibitory Budget Matching Constrains Homeostatic Plasticity in Competitive Spiking Networks

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