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If you mean the ones I circled in RED, then yes, they are absolutely necessary. They ensure that the reverse voltage across each LED is the same as the forward voltage across it's "antiphase" partner.
Without the "jumpers":
Since the LEDs wouldn't all have the same reverse leakage current, some of the reverse biased LEDs would have a higher voltage across them than the other more leaky LEDs. The low leakage LEDs would break down at this higher reverse voltage and be damaged.
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