Along sensory pathways, representations of environmental stimuli become increasingly sparse and expanded. If additionally the feed-forward synaptic weights are structured according to the inherent organization of stimuli, the increase in sparseness and expansion leads to a reduction of sensory noise. However, it is unknown how the synapses in the brain form the required structure, especially given the omnipresent noise of environmental stimuli. Here, we employ a combination of synaptic plasticity and intrinsic plasticity—adapting the excitability of each neuron individually—and present stimuli with an inherent organization to a feed-forward network. We observe that intrinsic plasticity maintains the sparseness of the neural code and thereby allows synaptic plasticity to learn the organization of stimuli in low-noise environments. Nevertheless, even high levels of noise can be handled after a subsequent phase of readaptation of the neuronal excitabilities by intrinsic plasticity. Interestingly, during this phase the synaptic structure has to be maintained. These results demonstrate that learning and recalling in the presence of noise requires the coordinated interplay between plasticity mechanisms adapting different properties of the neuronal circuit. Author Summary Everyday life requires living beings to continuously recognize and categorize perceived stimuli from the environment. To master this task, the representations of these stimuli become increasingly sparse and expanded along the sensory pathways of the brain. In addition, the underlying neuronal network has to be structured according to the inherent organization of the environmental stimuli. However, how the neuronal network learns the required structure even in the presence of noise remains unknown. In this theoretical study, we show that the interplay between synaptic plasticity—controlling the synaptic efficacies—and intrinsic plasticity—adapting the neuronal excitabilities—enables the network to encode the organization of environmental stimuli. It thereby structures the network to correctly categorize stimuli even in the presence of noise. After having encoded the stimuli’s organization, consolidating the synaptic structure while keeping the neuronal excitabilities dynamic enables the neuronal system to readapt to arbitrary levels of noise resulting in a near-optimal classification performance for all noise levels. These results provide new insights into the interplay between different plasticity mechanisms and how this interplay enables sensory systems to reliably learn and categorize stimuli from the surrounding environment.