Dual-Path Neuron Models

• Dual-path neurons are neural architectures with two integrated pathways that separately process forward activations and error signals to enhance learning and enable biological emulation.
• They are implemented in diverse models such as dyadic compartmental systems, dual-stream CNNs, and proton-coupled transistors that mimic dendritic processing and gain modulation.
• This dual function underpins efficient signal propagation, unsupervised parameter estimation, and dynamic oscillatory modes, promising improved learning dynamics and scalable neuromorphic systems.

A dual-path neuron is a neural architecture or device in which signal processing is partitioned into two distinct functional or physical pathways, typically enabling either biological plausibility, improved learning dynamics, robust processing, or hardware emulation of dendritic computations. Dual-path neuron concepts span energy-based artificial neuron models, knowledge-driven variational autoencoders, hardware implementations with ionic-electronic channels, and dynamical systems capable of switching between propagation and oscillation modes. This multifaceted idea draws on compartmental models, parallel sensory streams, and bifurcation dynamics to offer novel solutions for both learning and physical realization of neural computation.

1. Dyadic Compartmental Neuron Model

The dyadic compartmental architecture represents each neuron with two intrinsic real-valued states, $z^+_k \in \mathbb{R}^n$ and $z^-_k \in \mathbb{R}^n$ for layer $k$, allowing simultaneous encoding of forward activity and local error. The mean $\bar{z}_k = \frac{1}{2}(z^+_k + z^-_k)$ plays the role of traditional forward activation, while the half-difference $\delta_k = \frac{1}{2}(z^+_k - z^-_k)$ serves as the error or credit-assignment signal. The two states are evolved according to layer-wise closed-form updates derived from an energy-based min-max objective:

$$\mathcal{L}_{\alpha}(\theta) = \min_{z^+}\max_{z^-}\Big[\alpha\ell(z^+_L) + (1-\alpha)\ell(z^-_L) + \sum_{k=1}^L \frac{1}{\beta_k}\big(\bar{D}_{G_k}(z^+_k \| W_{k-1}\bar{z}_{k-1}) - \bar{D}_{G_k}(z^-_k \| W_{k-1}\bar{z}_{k-1})\big)\Big]$$

where $\ell(z_L)$ is a standard supervised loss and $G_k$ denotes a convex activation potential. Inference proceeds via block-coordinate updates in each layer, leading to efficient, single-pass learning comparable in accuracy and runtime to standard backpropagation. The Hebbian style weight update:

$$\frac{\partial\mathcal{L}_{1/2}}{\partial W_{k-1}} = -\frac{2}{\beta_k}\delta_k\bar{z}_{k-1}^T$$

localizes the gradient computation, facilitating analog or neuromorphic implementations. This dual-path construction alleviates the need for separate clamp/free phases of equilibrium propagation and enables asynchronous, layerwise relaxation (Høier et al., 2023).

2. Biological and Hardware Realizations

Physical realization of dual-path neurons is exemplified by proton-coupled oxide-based EDL transistors wherein two independent ionic-electronic pathways—multiple presynaptic gates and a modulatory gate—converge on a shared channel. Presynaptic gates control input summation through transient proton accumulation, emulating spatial and temporal integration, while the modulatory gate statically shifts proton concentration under the channel, providing multiplicative gain modulation. The resulting current can be analytically described as:

$$I_{DS}(V_{PSP},V_{mod}) = \mu\,C_{EDL}\,\frac{W}{L}\;V_{DS}\;\left[V_{PSP}-V_{th}^0+\alpha V_{mod}\right]$$

or in a subthreshold regime, as an exponential function of both presynaptic and modulatory voltages. Spatial summation and gain regulation are precisely tunable via the modulation voltage, achieving sublinear, linear, or superlinear integration. Temporal and rate coding arithmetic mirror biological dendritic functions, and multiplicative gain control is demonstrated empirically. Such hardware dual-path neurons offer scalable, low-energy neuromorphic substrates with potential for advanced dendritic function emulation (Wan et al., 2015).

3. Dual-Stream Computation and Mixed Selectivity

The dual-path paradigm generalizes beyond individual neurons to network-wide architectures, as seen in dual-stream models inspired by the dorsal (spatial/attention) and ventral (object/recognition) pathways of the primate visual cortex. Inputs are radially sampled into coarse (magnocellular) and fine (parvocellular) representations, processed by separate CNN branches (WhereCNN and WhatCNN) with shared backbone but distinct heads. Recurrent interaction via fixation point selection forms a functional loop:

• WhereCNN produces a spatial saliency map $S_t$, which determines the next fixation location.
• WhatCNN accumulates object representations over sequential fixations via a GRU.
• Both branches are jointly trained with loss terms for saliency and object recognition:

$$L_{total} = \lambda L_{where} + (1-\lambda)L_{what}$$

Mixed selectivity is observed in early visual layers, where convolutional units exhibit joint responsiveness to both input streams, effectively behaving as dual-path neurons at a network scale. The system’s robustness to variation and its correspondence to dorsal/ventral fMRI patterns are enhanced by task-driven segregation rather than anatomical biases alone (Choi et al., 2023).

4. Dual-Path in Knowledge-Aware Estimators

Dual-path neural designs are exploited in knowledge-aware autoencoder frameworks, specifically for unsupervised massive MIMO channel estimation. Here, the encoder splits into two ResNet branches:

• Channel-Gain Path: Processes raw signal to estimate path gains and path angles.
• AoA Path: Processes the empirical covariance matrix to estimate angles of arrival.

The decoder is fixed to the domain-specific signal propagation model; encoder outputs are therefore forced to be physical parameters. Alternating minimization is employed for encoder parameter updates, with initialization based on empirical AoA pseudo-labels. The procedure ensures convergence to globally optimal solutions for channel estimates when AoAs are correctly determined, while demonstrating the necessity of the two-path separation due to multiple optima in AoA estimation. The technique achieves performance parity with supervised learning and state-of-the-art unsupervised baselines without labels (Guo et al., 2023).

5. Dual Functionality in Symmetric Dynamical Neuron Models

A class of low-dimensional models based on symmetric differential equations manifests dual-path functionality by operating in either a stable propagator mode or switching into a Lyapunov-stable oscillator regime. The system is specified as:

$$\dot E = K_{1}P^{-1}E - K_{2}E - K_{3}(E \circ P^{-2}E)$$

where $E$ denotes the vector of neural states and cyclic permutation matrices implement structured generative, damping, and inhibitory loops. The system’s regime is dictated by parameter choices, notably the damping $K_2$ and structural offsets in inhibition. For sufficiently strong damping, all trajectories converge to a fixed point, emulating stable signal propagation; as damping is weakened, a Hopf bifurcation induces sustained oscillations akin to rhythm generation. The proposed “on-road energy” metric

$$\mathcal{R}(D) = \sum_{i=1}^5 k_{3,i}D_i(t) D_{i-2}(t)$$

monitors in real time the state of the system, providing a theoretical bridge to biological phenomena such as pacemaker cells and highlighting external control via targeted inhibitory input (Jiang, 20 Jul 2025).

6. Functional Significance and Neuromorphic Implications

Dual-path neurons unify several themes in neural computation:

• Decoupling forward inference and error propagation to enable efficient, hardware-friendly learning dynamics.
• Physical realization of dendritic arithmetic and gain modulation in neuromorphic substrates.
• Exploiting parallel processing for enhanced robustness and adaptation in vision models.
• Structurally partitioned estimation pathways for interpretable unsupervised learning.
• Dynamical flexibility in circuit function via parameter and structural modulation.

A plausible implication is that ongoing research integrating dual-path designs across learning algorithms, neuromorphic hardware, and biological modeling will continue to yield architectures that are both more efficient and more capable of emulating the multifaceted roles of biological neurons.

Table: Summary of Dual-Path Neuron Implementations

Implementation Type	Pathways	Key Mechanism / Functionality
Dyadic artificial neuron (Høier et al., 2023)	$z^+_k$, $z^-_k$	Bi-directional mean/error encoding; local Hebbian weight updates
Visual dual-stream CNN (Choi et al., 2023)	WhereCNN, WhatCNN	Parallel spatial + object pathways; mixed selectivity, recurrent interaction
MIMO dual-path VAE (Guo et al., 2023)	Channel-Gain, AoA	Knowledge-driven split for unsupervised channel/AoA estimation
Proton-coupled neuron transistor (Wan et al., 2015)	Presynaptic, Modulatory	Ionic-electronic spatial and gain pathways; hardware dendritic mimicry
Symmetric dynamical neuron (Jiang, 20 Jul 2025)	Propagator, Oscillator	Parameter/structure controlled signal transmission and oscillation

Further research into dual-path neuron architectures holds promise for advancing both computational neuroscience and scalable machine learning systems.