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Many daily activities and psychophysical experiments involve keeping multiple items in working memory. When items take continuous values (e.g., orientation, contrast, length, loudness) they must be stored in a continuous structure of appropriate dimensions. We investigate how this structure is represented in neural circuits by training recurrent networks to report two previously shown stimulus orientations. We find the activity manifold for the two orientations resembles a Clifford torus. Although a Clifford and standard torus (the surface of a donut) are topologically equivalent, they have important functional differences. A Clifford torus treats the two orientations equally and keeps them in orthogonal subspaces, as demanded by the task, whereas a standard torus does not. We find and characterize the connectivity patterns that support the Clifford torus. Moreover, in addition to attractors that store information via persistent activity, our networks also use a dynamic code where units change their tuning to prevent new sensory input from overwriting the previously stored one. We argue that such dynamic codes are generally required whenever multiple inputs enter a memory system via shared connections. Finally, we apply our framework to a human psychophysics experiment in which subjects reported two remembered orientations. By varying the training conditions of the RNNs, we test and support the hypothesis that human behavior is a product of both neural noise and reliance on the more stable and behaviorally relevant memory of the ordinal relationship between the two orientations. This suggests that suitable inductive biases in RNNs are important for uncovering how the human brain implements working memory. Together, these results offer an understanding of the neural computations underlying a class of visual decoding tasks, bridging the scales from human behavior to synaptic connectivity. 

Many theories assume that a sensory neuron’s higher firing rate indicates a greater probability of its preferred stimulus. However, this contradicts 1) the adaptation phenomena where prolonged exposure to, and thus increased probability of, a stimulus reduces the firing rates of cells tuned to the stimulus; and 2) the observation that unexpected (low probability) stimuli capture attention and increase neuronal firing. Other theories posit that the brain builds predictive/efficient codes for reconstructing sensory inputs. However, they cannot explain that the brain preserves some information while discarding other. We propose that in sensory areas, projection neurons’ firing rates are proportional to optimal code length (i.e., negative log estimated probability), and their spike patterns are the code, for useful features in inputs. This hypothesis explains adaptation-induced changes of V1 orientation tuning curves, and bottom-up attention. We discuss how the modern minimum-description-length (MDL) principle may help understand neural codes. Because regularity extraction is relative to a model class (defined by cells) via its optimal universal code (OUC), MDL matches the brain’s purposeful, hierarchical processing without input reconstruction. Such processing enables input compression/understanding even when model classes do not contain true models. Top-down attention modifies lower-level OUCs via feedback connections to enhance transmission of behaviorally relevant information. Although OUCs concern lossless data compression, we suggest possible extensions to lossy, prefix-free neural codes for prompt, online processing of most important aspects of stimuli while minimizing behaviorally relevant distortion. Finally, we discuss how neural networks might learn MDL’s normalized maximum likelihood (NML) distributions from input data.