Multimodal Physical Learning in Brain-Inspired Iontronic Networks

TL;DR

A physical alternative to traditional digital neural networks -- a microfluidic network in which nodes are connected by conical, electrolyte-filled channels acting as memristive iontronic synapses, which develops a training algorithm where learning is achieved by altering either the channel geometry or the applied stimuli.

Abstract

Inspired by the brain, we present a physical alternative to traditional digital neural networks -- a microfluidic network in which nodes are connected by conical, electrolyte-filled channels acting as memristive iontronic synapses. Their electrical conductance responds not only to electrical signals, but also to chemical, mechanical, and geometric changes. Leveraging this multimodal responsiveness, we develop a training algorithm where learning is achieved by altering either the channel geometry or the applied stimuli. The network performs forward passes physically via ionic relaxation, while learning combines this physical evolution with numerical gradient descent. We theoretically demonstrate that this system can perform tasks like input-output mapping and linear regression with bias, paving the way for soft, adaptive materials that compute and learn without conventional electronics.

Figures (3)

• Figure 1: (a) Illustration of a microfluidic memristor channel with applied external potential. (b) Schematic of a memristor-voltage divider. (c) Relative cost function $C(\boldsymbol{w}^s)/C(\boldsymbol{w}^0)$ as a function of the training steps, obtained by training with (d) lengths (pink), (e) concentrations (orange), (f) base radii (yellow), (g) pressures (green), with learning rates $\alpha = [3 \cdot 10^{-6}, 3 \cdot 10^{-6}, 5 \cdot 10^{-4}, 100]$, respectively, combined weight subsets: length and pressure (light blue), length and base radius (dark blue), as well as for the adaptive "best weight" choice (triangles, connected by a black dotted line). (h) Time evolution of $V_2(t)$ for the pressure-trained network, after switching on the input $V_1= 5 V$ at $t=0$. The evolution during the pressure-training step $s$ of (i) the steady-state output voltage $V_2({\bf w}^s)$ (symbols) towards three different consecutive desired voltages $V_2^D$ (horizontal dashed lines), with (j) the associated re-trained pressures, starting at $s=0$ from the default parameter set.
• Figure 2: (a) Generic network of $9$ nodes and $15$ edges. (b) Relative cost function for five subsets of weights indicated by colors, for learning rates $\alpha=[1\cdot 10^{-6}, 8\cdot 10^{-7}, 1\cdot 10^{-4}, 20]$. (c) Network geometry used for linear regression training. Among the three input nodes, one is used to ground the circuit ($V_2 = 0V$), one ($V_4$) provides a constant voltage source for bias, and the remaining one ($V_7$) is used to input the training data point. For the four weight types (channel length, base radius, ion concentration and pressure), we used as constant voltage input $V_4 = [11V,4V,4V,11V]$ and learning rates $[2\cdot 10^{-7}, 1\cdot 10^{-6}, 1\cdot 10^{-4}, 2\cdot 10^{2}]$. (c) Test cost function evaluated every $10$ training steps for four different weight choices. Figures (e), (f) and (g) show visual representations of the network’s output trained with varying channel lengths at three different training steps.
• Figure 3: The evolution of the weights during training (a)-(b) Voltage divider trained using different combinations of features: (a) length and base radius, $\boldsymbol{w} = \{L_1, L_2\} \cup \{R_{1}, R_{2}\}$; (b) length and pressure, $\boldsymbol{w} = \{L_1, L_2\} \cup \{P_{1}, P_{2}\}$. For a more complex network, weight evolution is shown for an allostery task using (c) length, (d) base radius, (g) ion concentration, and (h) pressure, and for a linear regression task using (e) length, (f) base radius, (i) ion concentration, and (j) pressure.