Fig. 5: Classification of 3 × 3-bit patterns.

a 3 × 3-bit patterns for “z”, “v”, and “n”. Each pattern category consists of one ideal pattern and nine noisy patterns. Each noisy pattern has one-bit flip from the ideal pattern. Three target vectors are shown on the right, in which “H” represents high target values and “L” represents low values. b Simulated receiver output presented in 3D. The weights were obtained using the gradient-based method. Three output graphs are shown separately for three weight vectors in distinct colors. Each colored curve consists of 30 dots, corresponding to the 30 patterns (10 patterns × 3 categories), in the order of “z” (patterns 0 to 9), “v” (patterns 10 to 19), and “n” patterns (20 to 29). The shape of each curve is consistent with each target vector. Below is the receiver output for each pattern category. These sub-figures are equivalent to rotating the 3D graph leftward and viewing from the side. For “z” patterns (the left sub-figure), \({\overrightarrow{w}}_{0}\) gives rise to high output, whereas \({\overrightarrow{w}}_{1}\) and \({\overrightarrow{w}}_{2}\) result in low output. Similarly, \({\overrightarrow{w}}_{1}\) results in high output for “v” patterns (the middle sub-figure) and \({\overrightarrow{w}}_{2}\) leads to high output for “n” patterns (the right sub-figure). Dots are overlapped. It is worth noting that there are only ten distinct output values. For example, the high state dots marked in a blue square in the left sub-figure have the same values as the dots in the middle and right sub-figures. c Flow cytometry measurement of receiver output for 3 × 3-bit patterns. In this case, nine groups of senders were selected, corresponding to the nine bits in each pattern and nine elements in weight vectors. Senders of different groups were incubated separately and mixed with receivers. The fluorescence signals from receivers were measured. EYFP and BFP (inset) are presented as mean values of median EYFP ± SEM from independent replicates (n = 3). Median values of individual replicates are marked in circles. Not all products of patterns and weights are presented. As discussed in the text, many pattern-weight products are repetitions (Supplementary Fig. 20). We presented only the unique and non-repeating ones in experiments. The first four bars represent products of \({\overrightarrow{w}}_{0}\) and “z” patterns, which are marked in a blue square in Fig. 5b left sub-figure. The rest bars represent \({\overrightarrow{w}}_{0}\cdot \overrightarrow{v}\), equivalently \({\overrightarrow{w}}_{0}\cdot \overrightarrow{n}\), which are marked in green squares in Fig. 5b middle and right sub-figures, respectively. Source data are available in the Source data file.