# Input correlations impede suppression of chaos and learning in balanced rate networks

arXiv: https://arxiv.org/abs/2201.09916 · HTML: https://mlsanity.com/paper/2201.09916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [Lyapunov spectra of chaotic recurrent neural networks](https://mlsanity.com/paper/2006.02427/) (2020)
- [full-FORCE: A Target-Based Method for Training Recurrent Networks](https://mlsanity.com/paper/1710.03070/) (2017)
- [Transition to chaos in random neuronal networks](https://mlsanity.com/paper/1508.06486/) (2015)
- [Transition to chaos in random networks with cell-type-specific connectivity](https://mlsanity.com/paper/1407.2297/) (2014)
- [What is the dynamical regime of cerebral cortex?](https://mlsanity.com/paper/1908.10101/) (2019)
- [Dynamics of Random Neural Networks with Bistable Units](https://mlsanity.com/paper/1409.2535/) (2014)
- [Learning recurrent dynamics in spiking networks](https://mlsanity.com/paper/1803.06622/) (2018)
- [Intrinsically-generated fluctuating activity in excitatory-inhibitory networks](https://mlsanity.com/paper/1605.04221/) (2016)
- [Training dynamically balanced excitatory-inhibitory networks](https://mlsanity.com/paper/1812.11424/) (2018)
- [On the low dimensional dynamics of structured random networks](https://mlsanity.com/paper/1509.02546/) (2015)
- [How single neuron properties shape chaotic dynamics and signal transmission in random neural networks](https://mlsanity.com/paper/1812.06925/) (2018)
- [Predictive coding in balanced neural networks with noise, chaos and delays](https://mlsanity.com/paper/2006.14178/) (2020)
- [Macroscopic Fluctuations Emerge in Balanced Networks with Incomplete Recurrent Alignment](https://mlsanity.com/paper/2103.06954/) (2021)

## Built on by (most cited first, 3 of 3)

- [Gradient Flossing: Improving Gradient Descent through Dynamic Control of Jacobians](https://mlsanity.com/paper/2312.17306/) (2023)
- [Neuronal architecture extracts statistical temporal patterns](https://mlsanity.com/paper/2301.10203/) (2023)
- [Neuronal correlations shape the scaling behavior of memory capacity and nonlinear computational capability of reservoir recurrent neural networks](https://mlsanity.com/paper/2504.19657/) (2025)

## Abstract (arXiv)

Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A unique feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far easier to suppress chaos with independent inputs into each neuron than through common input. To study this phenomenon we develop a non-stationary dynamic mean-field theory that determines how the activity statistics and largest Lyapunov exponent depend on frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We also show that uncorrelated inputs facilitate learning in balanced networks.