In this brief exploratory paper, we present a novel free group based method for error correction, making use of the universal property of free groups (UPFG). Through example, we show that , in certain scenarios, our method of error correction is more efficient and more deterministic than minimum distance error correction. We argue that our method works well under specific conditions that have been shown to have been met by certain neural systems. We hope that this might interest others in the role free groups may play in understanding how error correction of neural codes works .
Recent experimental and theoretical work on neural populations belonging to two separate early sensory systems, olfaction and vision, has challenged the notion that the two operate under different computational paradigms by providing evidence for the respective neural population codes having three central, common features: they are highly redundant; they URLanized such that information is carried in the identity, and not the relative timing, of the active neurons; they are capable of error correction. We present the first model that captures these three properties in a general manner, making it possible to investigate whether similar structure is present in other population codes. Our model also makes specific predictions about additional, as yet unseen, structure in such codes. If these predictions are found in real data, this would provide new evidence that such population codes are operating under more general computational principles .
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In this brief exploratory paper, we present a novel free group based method for error correction, making use of the universal property of free groups (UPFG). Through example, we show that , in certain scenarios, our method of error correction is more efficient and more deterministic than minimum distance error correction. We argue that our method works well under specific conditions that have been shown to have been met by certain neural systems. We hope that this might interest others in the role free groups may play in understanding how error correction of neural codes works
Recent experimental and theoretical work on neural populations belonging to two separate early sensory systems, olfaction and vision, has challenged the notion that the two operate under different computational paradigms by providing evidence for the respective neural population codes having three central, common features: they are highly redundant; they URLanized such that information is carried in the identity, and not the relative timing, of the active neurons; they are capable of error correction. We present the first model that captures these three properties in a general manner, making it possible to investigate whether similar structure is present in other population codes. Our model also makes specific predictions about additional, as yet unseen, structure in such codes. If these predictions are found in real data, this would provide new evidence that such population codes are operating under more general computational principles