We agree that our discussion of Seung et al. was not1 sufficient and we will address this inafuture version. We kindly ask the reviewer to reconsider the following contributions. Thenotion ofbalanced networks isnot6 considered at all in Seung et al., but is an important phenomenon in neuroscience (Poo et al, 2009, Rupprecht et al,7 2018). Using ourframework,weconstructed balanced spiking neural networksforsolving various11 tasks (reconstruction, fixed point and manifold attractor dynamics) heavily studied in neuroscience. The attractors include specific inhibitory neurons and the network weights are pretrained20 giventhesespecific EandIneurons.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale's Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dale's Law is generally absent from RNNs because simply partitioning a standard network's units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale's ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale's Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale's Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dale's ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dale's ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The authors present a model of auto-associative memory in a rate-based neural network subject to a battery of biological plausible constraints. Previous models of auto-associative memory have failed to include several key features of real biological networks, namely an adherence to Dale's Law that neurons have a strictly excitatory or inhibitory effect on their projections and the observation that networks can encode memories without relying on units that simply respond at their saturation rate or respond in a binary manner. Memories are encoded in the network via synaptic modifications based on a gradient descent procedure, constrained using a recently published method for ensuring that the linearization of the dynamics around a dynamical system's fixed point is stable. The authors illustrate the effectiveness of their training procedure with simulations, noting that the trained fixed points exhibit slow network dynamics (i.e. they are close to being, but are not exactly, fixed points) and are stable, as desired.

We thank the reviewer for the thorough review. We agree that our discussion of Seung et al. was not However, our contributions go beyond Seung et al.'s work in We kindly ask the reviewer to reconsider the following contributions. Such applications were not available in Seung et al. We indeed applied the results in Seung et al. as a tool to provide necessary conditions of convergence of the dynamics, Reviewer 2: We thank the reviewer for the enthusiastic support! We will provide details in the appendix. Minimax objectives: We thank the author for the inspiring question.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale's Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dale's Law is generally absent from RNNs because simply partitioning a standard network's units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale's ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale's Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale's Law impair learning?

Eco Entrepreneur and Climate Campaigner, Dale Vince, OBE There's a saying that goes, 'don't meet your heroes as they may disappoint', well I pleased to say this wasn't the case when I spoke to green entrepreneur, Dale Vince, OBE for this episode for Irish Tech News Dale is one a what I would call a conscious CEO, where his work focuses on three key areas – energy, transport, and food. In 1995 he launched Ecotricity, the world's first green energy company, which today, powers around 200,000 homes and businesses across the UK with renewable energy from the wind and sun. Dale also owns Devil's Kitchen, which makes vegan school dinners, and his latest business, Skydiamond creates lab grown diamonds from the wind, rain and sun. If that wasn't enough, Dale is Chairman and owner of Forest Green Rovers recognised by FIFA as the "world's greenest football club" and became a United Nations Climate Champion in 2018. He launched his first book, Manifesto in 2020, and is Executive Producer of the Netflix Original documentary, Seaspiracy.