RESUMEN
Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stablility in recurrent video processing models without a significant performance loss.
RESUMEN
We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term 'dichotomous feedback'. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process's architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than 'molecular sequestration' and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.
