Watch the local lens.
Same scene. Different medium. Follow a small patch into four branches, let the input stop, and see what is still there.
02Activity inside the lens
Input arrives03What reaches the soma
04The lens can adapt
Oja’s rule reshapes four input weights from repeated, slightly varied presentations of this patch. Adaptation is separate from playback.
Strengthen correlated inputs; restrain overall growth. This is synaptic normalization, not branch growth.
Try this: watch the waiting.
Replay the contour, then jump to waiting. The input has stopped, but the compartments have not instantly emptied. Change extent or leak and replay. Watch the spatial slope and remaining activity separately: longer persistence need not mean a stronger gradient.
Then change the lens.
Adapt to a contour patch, then move the box to a different patch. The weights stay learned. Switch to brightness samples to compare what the measurement preserves. Add distant context or a return pulse to see how timing changes an existing branch state.
What is computed, and what is only an analogy?
This is a deterministic, dimensionless toy cable with four branches of eight compartments and one soma. Adjacent voltage differences drive axial current. Each compartment leaks and stores activity; the soma integrates branch currents. Input is applied near branch tips from ticks 20–150, with different arrival times. The optional return is an externally scheduled somatic pulse at tick 260, not a spontaneous action potential. Optional context arrives locally at tick 100 plus the selected delay. Optional amplification adds a saturating, voltage-dependent current; it is not a calibrated ion-channel model.
The current lens and original lens receive the same patch and optional interventions. The original retains unit extent, unit leak, a 24-tick context delay, and uniform weights. Changing a control recomputes both complete trajectories from rest. The grey trace therefore isolates changes to lens properties; it is not an unpulsed control.
Extent scales axial conductance inversely and effective compartment capacitance directly. It is a coarse geometry proxy with fixed compartment count, not a model of dendritic growth. There is no molecular or lipid-zone simulation.
Oja update: y = w · x; Δw = η(yx − y²w), with η = 0.015 and deterministic, small input variations. It acts on weights; the electrical relaxation acts on voltages. Neither the input image differences nor cable currents have been shown here to equal an objective’s learning gradient. Learning uses the current four patch measurements, without labels.
¹ Branch activity is the sum of squared compartment voltages, an activity proxy, not a physical energy measurement. The spatial slope is the largest absolute adjacent voltage difference divided by compartment spacing. All values and time units are illustrative. No recognition, prediction, or biological validity benchmark is claimed.
References: Oja (1982) · Branch-specific calcium and plasticity (2015) · Mouse lipid atlas (2026) · Sihti patch-memory experiments.