Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers individual trained networks. However, different RNNs trained on the same task and achieving similar performance can exhibit strikingly different internal solutions, a phenomenon known as solution degeneracy. Here, we develop a unified framework to systematically quantify and control solution degeneracy across three levels: behavior, neural dynamics, and weight space. We apply this framework to 3,400 RNNs trained on four neuroscience-relevant tasks: flip-flop memory, sine wave generation, delayed discrimination, and path integration, while systematically varying task complexity, learning regime, network size, and regularization. We find that increased task complexity and stronger feature learning reduce degeneracy in neural dynamics but increase it in weight space, with mixed effects on behavior. In contrast, larger networks and structural regularization reduce degeneracy at all three levels. These findings empirically validate the Contravariance Principle and provide practical guidance for researchers seeking to tune the variability of RNN solutions, either to uncover shared neural mechanisms or to model the individual variability observed in biological systems. This work provides a principled framework for quantifying and controlling solution degeneracy in task-trained RNNs, offering new tools for building more interpretable and biologically grounded models of neural computation.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, $a_i$ and $a_j$, diverge to $\pm$infinity, and their input weight vectors, $\mathbf{w_i}$ and $\mathbf{w_j}$, become equal to each other. At convergence, the two neurons implement a gated linear unit: $a_i\sigma(\mathbf{w_i} \cdot \mathbf{x}) + a_j\sigma(\mathbf{w_j} \cdot \mathbf{x}) \rightarrow c \sigma(\mathbf{w} \cdot \mathbf{x}) + (\mathbf{v} \cdot \mathbf{x}) \sigma'(\mathbf{w} \cdot \mathbf{x})$. Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of this quasi-flat region in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show that the incoming weight vector of each neuron is identifiable up to sign or scaling, depending on the activation function. Our novel method ’Expand-and-Cluster’ can identify layer sizes and weights of a target network for all commonly used activation functions. Expand-and-Cluster consists of two phases: (i) to relax the non-convex optimisation problem, we train multiple overparameterised student networks to best imitate the target function; (ii) to reverse engineer the target network’s weights, we employ an ad-hoc clustering procedure that reveals the learnt weight vectors shared between students – these correspond to the target weight vectors. We demonstrate successful weights and size recovery of trained shallow and deep networks with less than 10% overhead in the layer size and describe an ’ease-of-identifiability’ axis by analysing 150 synthetic problems of variable difficulty.

Advances of deep learning for Artificial Neural Networks (ANNs) have led to significant improvements in the performance of digital signal processing systems implemented on digital chips. Although recent progress in low-power chips is remarkable, neuromorphic chips that run Spiking Neural Networks (SNNs) based applications offer an even lower power consumption, as a consequence of the ensuing sparse spikebased coding scheme. In this work, we develop a SNN-based Voice Activity Detection (VAD) system that belongs to the building blocks of any audio and speech processing system. We propose to use the bin encoding, a novel method to convert log mel filterbank bins of single-time frames into spike patterns. We integrate the proposed scheme in a bilayer spiking architecture which was evaluated on the QUT-NOISE-TIMIT corpus. Our approach shows that SNNs enable an ultra low-0power implementation of a VAD classifier that consumes only 3.8 μW, while achieving state-of-the-art performance. The code is freely available on Code Ocean [1].

Recent advances in Voice Activity Detection (VAD) are driven by artificial and Recurrent Neural Networks (RNNs), however, using a VAD system in battery-operated devices requires further power efficiency. This can be achieved by neuromorphic hardware, which enables Spiking Neural Networks (SNNs) to perform inference at very low energy consumption. Spiking networks are characterized by their ability to process information efficiently, in a sparse cascade of binary events in time called spikes. However, a big performance gap separates artificial from spiking networks, mostly due to a lack of powerful SNN training algorithms. To overcome this problem we exploit an SNN model that can be recast into a recurrent network and trained with known deep learning techniques. We describe a training procedure that achieves low spiking activity and apply pruning algorithms to remove up to 85% of the network connections with no performance loss. The model competes with state-of-the-art performance at a fraction of the power consumption comparing to other methods.