Fundamental limits of reservoir computing: stability vs. reach Reservoir computing (RC) uses the natural dynamics of a large recurrent network to generate time-varying signals. You only train a simple readout, not the whole network, which makes RC appealing both for neuroscience models and for physical implementations (photonic chips, mechanical oscillators, cultured neurons). Yet RC often behaves unpredictably: sometimes it learns a target sequence easily, sometimes it cannot hold the pattern or never gets close. Daoyuan Qian and Ila Fiete show that these failures come from two distinct causes. First is stability—the network must have a feedback-stabilized orbit that actually sustains the target output. If the orbit is unstable, the network can match the target during training but drifts away as soon as training stops. Second is reach—even if a stable orbit exists, the learning rule must be able to steer the system close enough to it. FORCE learning generally has greater reach than teacher-forcing, and adding controlled “forgetting” can improve reach further. The key insight is that stability and reach are separate. Increasing reservoir size helps reach (more expressive dynamics), but also makes stability harder (more modes near instability). Simply scaling up a network is not always better. Designing reservoirs with multiple neuron types can improve this trade-off—retaining expressive power while keeping the dynamics stable. The result is a clearer, more practical view of how to design and train reservoir systems. If the target lies outside the stability region, change the reservoir. If it lies inside but training stalls, change the learning rule. This framework connects engineered RC systems with ideas from neural dynamics in the brain, where biological circuits must also balance flexibility with stability. Paper: journals.aps.org/pre/abstrac…