Reconstructing the connectivity of a neural network from spike train recordings normally requires observing all neurons simultaneously --- an experimental impossibility at scale. De Santis demonstrates that pairwise observation suffices. The Macro-Micro Extrapolation framework classifies synaptic connections --- excitatory, inhibitory, or absent --- from the spike trains of just two neurons at a time, without access to the rest of the network. The key innovation is a Spike-Triggered Estimator that exploits the local reset property of Galves-Locherbach neuron dynamics: after a spike, the neuron's state is known, decoupling the local synaptic effect from the network's higher-order contributions. This eliminates the confound that makes pairwise inference unreliable in recurrent networks --- the indirect correlations mediated by unobserved neurons. An adaptive hybrid algorithm switches between sample averaging and a Pyramid Extrapolation scheme depending on data density, achieving perfect classification accuracy across dense cliques and layered architectures even in low signal-to-noise regimes.
The structural achievement is the decoupling lemma. In any recurrent network, pairwise correlations reflect both direct connections and indirect paths through the rest of the network. Disentangling these requires either full network observation or a mathematical property that makes one of them vanish at a specific moment. The local reset is exactly that moment: immediately after a spike, the neuron's membrane potential is deterministic, and the only stochastic contribution at the next instant is the direct synaptic input from its partners. The reset creates a window in which the pairwise signal is clean. The Pyramid Extrapolation extends this to the continuum limit, extrapolating the synaptic effect as the time bin approaches zero without requiring infinite temporal resolution in the data.
Observability in networks is a sparsity problem disguised as a coverage problem. The instinct is always to observe more --- more neurons, more channels, more variables --- to capture the full state. The alternative is to find moments when the system's own dynamics compress the relevant information into a subspace that a limited observation can resolve. A spike followed by a reset is one such moment. The general principle: a dynamical system that periodically collapses to a known state hands the observer a series of clean initial conditions, each of which transforms an underdetermined inverse problem into a tractable one.
(arXiv:2603.16884)