The A-not-B Error (2D Field Model): Object Permanence and Infant Working Memory

Search Setup

Infant age 8 months

Search delay 4.0 s

Prior reaches to A 3

Live Field Readouts

Field activation u(B)0%

Field activation u(A)0%

Memory trace m(A)

Memory trace m(B)

Trials run

A-not-B errors

0 (0%)

How it works

This is a two-node dynamic neural field (Amari-style activation-decay field, after Thelen, Schöner, Scheier & Smith, 2001, and Schöner & Dineva, 2007) with one reach-planning node for box A and one for box B. Both nodes are numerically integrated every animation frame with a real stochastic differential equation — nothing about the reach outcome is drawn from a lookup formula:

τ·du_i/dt = −u_i + h + S_i(t) + c_exc·f(u_i) − c_inh·f(u_j) + c_mem·m_i + noise
f(u) = 1 / (1 + exp(−β·(u − θ)))                 (sigmoid activation)
if f(u_i) > 0.5:  τ_bld·dm_i/dt = (1 − m_i) − m_i     (memory trace builds while node fires)
else:             τ_dec·dm_i/dt = −m_i                (memory trace decays slowly at rest)

Prior reaches to A — each one is a real short habituation sub-trial: the field is cued at A, integrated to threshold, and A's memory trace m(A) is built up exactly like the real dm/dt rule above. More trials → a stronger, more persistent habit trace.
Hiding at B — a brief external input S_B(t) drives u(B) up while the infant watches the toy hidden, seeding a fresh but weaker m(B).
Search delay — during the wait, both external inputs are off. u_A and u_B keep evolving under self-excitation, mutual inhibition, their own memory-trace input c_mem·m_i, and real Gaussian noise. The longer the delay, the more the fresh B-trace decays relative to the consolidated A-habit.
Reach decision — whichever node's activation u is higher at the end of the delay wins the competition and is where the simulated infant reaches; this is read directly off the integrated field, not sampled from a formula, so it can occasionally surprise you exactly as real infant data does.

Parameters (h, β, c_exc, c_inh, c_mem, noise σ) are fixed at literature-typical order-of-magnitude values for teaching the mechanism; this is not a fit to a specific published dataset.

Ready

Box A (trained location) Box B (new hiding location) Hidden object

The A-not-B Error: Object Permanence and Infant Working Memory (2D Field Model)