user: text: Write a concise one-sentence TLDR summary of the scientific paper content below.

Title: Input Alignment along Chaotic directions increases Stability in Recurrent Neural Networks

Paper content:
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations.
However, it remains unclear how neural circuits encode complex spatio-temporal patterns.
We show that neural dynamics are strongly influenced by the phase alignment between the input and the spontaneous chaotic activity.
Input alignment along the dominant chaotic projections causes the chaotic trajectories to become stable channels (or attractors), hence, improving the computational capability of a recurrent network.
Using mean field analysis, we derive the impact of input alignment on the overall stability of attractors formed.
Our results indicate that input alignment determines the extent of intrinsic noise suppression and hence, alters the attractor state stability, thereby controlling the network's inference ability.
Brain actively untangles the input sensory data and fits them in behaviorally relevant dimensions that enables an organism to perform recognition effortlessly, in spite of variations DiCarlo et al. (2012) ; Thorpe et al. (1996) ; DiCarlo & Cox (2007) .
For instance, in visual data, object translation, rotation, lighting changes and so forth cause complex nonlinear changes in the original input space.
However, the brain still extracts high-level behaviorally relevant constructs from these varying input conditions and recognizes the objects accurately.
What remains unknown is how brain accomplishes this untangling.
Here, we introduce the concept of chaos-guided input alignment in a recurrent network (specifically, reservoir computing model) that provides an avenue to untangle stimuli in the input space and improve the ability of a stimulus to entrain neural dynamics.
Specifically, we show that the complex dynamics arising from the recurrent structure of a randomly connected reservoir Rajan & Abbott (2006) ; Kadmon & Sompolinsky (2015) ; Stern et al. (2014) can be used to extract an explicit phase relationship between the input stimulus and the spontaneous chaotic neuronal response.
Then, aligning the input phase along the dominant projections determining the intrinsic chaotic activity, causes the random chaotic fluctuations or trajectories of the network to become locally stable channels or dynamic attractor states that, in turn, improve its' inference capability.
In fact, using mean field analysis, we derive the effect of introducing varying phase association between the input and the network's spontaneous chaotic activity.
Our results demonstrate that successful formation of stable attractors is strongly determined from the input alignment.
We also illustrate the effectiveness of input alignment on a complex motor pattern generation task with reliable generation of learnt patterns over multiple trials, even in presence of external perturbations.
Models of cortical networks often use diverse plasticity mechanisms for effective tuning of recurrent connections to suppress the intrinsic chaos (or fluctuations) Laje & Buonomano (2013) ; Panda & Roy (2017) .
We show that input alignment alone produces stable and repeatable trajectories, even, in presence of variable internal neuronal dynamics for dynamical computations.
Combining input alignment with recurrent synaptic plasticity mechanism can further enable learning of stable correlated network activity at the output (or readout layer) that is resistant to external perturbation to a large extent.
Furthermore, since input subspace alignment allows us to operate networks at low amplitude while maintaining a stable network activity, it provides an additional advantage of higher dimensionality.
A network of higher dimensionality offers larger number of disassociated principal chaotic projections along which different inputs can be aligned (see Appendix A, Fig. A1(c) ).
Thus, for a classification task, wherein the network has to discriminate between 10 different inputs (of varying frequencies and underlying statistics), our notion of untangling with chaos-guided input alignment can, thus, serve as a foundation for building robust recurrent networks with improved inference ability.
Further investigation is required to examine which orientations specifically improve the discrimination capability of the network and the impact of a given alignment on the stability of the readout dynamics around an output target.
In summary, the analyses we present suggest that input alignment in the chaotic subspace has a large impact on the network dynamics and eventually determines the stability of an attractor state.
In fact, we can control the network's convergence toward different stable attractor channels during its voyage in the neural state space by regulating the input orientation.
This indicates that, besides synaptic strength variance Rajan & Abbott (2006) , a critical quantity that might be modified by modulatory and plasticity mechanisms controlling neural circuit dynamics is the input stimulus alignment.

assistant: text: Input Structuring along Chaos for Stability