(1) We (Grace Lindsay) used convolutional neural nets to model attention, by scaling the input/output function of neurons in an imagenet-trained network according to their selectivity for the feature or object category being attended. While this was effective in improving performance on difficult tasks, it was far less effective in earlier than in later layers. This indicated that neurons selective for a feature in earlier layers did not necessarily drive neurons selective for that feature in later layers. In contrast, applying attention according to the gradient for improving task performance worked well in early as well as late layers. This raises the question whether biological attentional modulation might reflect task requirements and not only the features of the stimuli to be attended. We suggest a simple experiment to answer this question, which we hope to convince an appropriate lab to carry out. (2) In E/I networks, a "paradoxical" response to stimulation has been shown: If the excitatory neurons would be unstable by themselves, but are stabilized by feedback inhibition (an "inhibition-stabilized network", or ISN), then, in response to addition of excitatory input to inhibitory neurons, their steady-state firing rates paradoxically decrease. In circuits with multiple inhibitory cell types, this has been generalized: in an ISN, if there is an added stimulus only to inhibitory cells, there will be a paradoxical change in the net inhibition received by excitatory cells -- e.g., if excitatory firing rates increase, so too will the net inhibition they receive. This does not imply that the firing rates of any particular inhibitory cell type will change paradoxically. Here we (Agostina Palmigiano along with Francesco Fumarola, and experimental work of Dan Mossing in the Adesnik lab) generalize the conditions for a paradoxical firing rate response, including in responses to partial as well as full perturbation of the neurons of a given cell type. We work in the context of the circuit with three inhibitory cell types (PV, SOM, VIP) in mouse V1. We show that, if a given cell type shows a paradoxical response to its own full stimulation, then the circuit without that cell type is unstable. This and experimental results to date, as well as our models fitted to data, suggest that PV but not SOM interneurons stabilize the circuit of layer 2/3 of mouse V1, at least for smaller visual stimulus sizes. For partial perturbations of a fraction f of a cell type that responds paradoxically to a full perturbation, there is a "fractional paradoxical effect": the proportion of all the cells of that type, stimulated and unstimulated, that respond opposite to the stimulation (i.e. negative response to excitation), changes non-monotonically, approaching 1 for f->0, decreasing with increasing f, and then increasing again to again approach 1 as f->1. I'll explain the origins of this behavior.3) We (Mario Dipoppa, in collaboration with the experimental work of Andy Keller and Morgane Roth from the Scanziani lab) have studied the E-PV-SOM-VIP circuit underlying contextual modulation in layer 2/3 of mouse V1. Experiments showed that E, PV, and VIP are suppressed by a surround stimuus that has the same orientation as, but not by one orthogonal to, the center stimulus. SOM neurons show the opposite behavior, being suppressed by an orthogonal but much less by a parallel surround. A combination of theory and optogenetic experiments show that the disinhibitory circuit -- VIP inhibits SOM, which inhibits E -- modulate responses between the two conditions. However, it does so, as part of the recurrent circuit, primarily by changing the recurrent excitation E cells receive, rather than by directly changing the inhibition received, in a manner reminiscent of the paradoxical response.