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B(t)≈B0⋅2(t−t0)/τB(t) \approx B_0 \cdot 2^{(t - t_0)/\tau}

Why this formula appears here

With two verified anchor points — HBM3 in 2022 at roughly 0.82 terabytes per second per stack, HBM4 in 2025 at up to 2.0 terabytes per second per stack [ 1 , 2 ] — it is possible to build an explicit, falsifiable trajectory rather than a vague “bandwidth will keep rising.” Model the growth as a simple exponential in calendar time, B(t)≈B0⋅2(t−t0)/τB(t) \approx B_0 \cdot 2^{(t - t_0)/\tau}. where B0B_0 is the bandwidth at reference year t0t_0 and τ\tau is the doubling time implied by the data. Solving for τ\tau from the two JEDEC anchor points gives

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BB

Symbol B

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tt

Symbol t

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t0t_0

Symbol t_0

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Published contexts (1)

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B(t)≈B0⋅2(t−t0)/τ,B(t) \approx B_0 \cdot 2^{(t - t_0)/\tau},

Equation 1 · Semiconductors

AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

This equation gives an approximation: it relates the quantities while allowing an approximation.

With two verified anchor points — HBM3 in 2022 at roughly 0.82 terabytes per second per stack, HBM4 in 2025 at up to 2.0 terabytes per second per stack [ 1 , 2 ] — it is possible to build an explicit, falsifiable trajectory rather than a vague “bandwidth will keep rising.” Model the growth as a simple exponential in calendar time, B(t)≈B0⋅2(t−t0)/τB(t) \approx B_0 \cdot 2^{(t - t_0)/\tau}. where B0B_0 is the bandwidth at reference year t0t_0 and τ\tau is the doubling time implied by the data. Solving for τ\tau from the two JEDEC anchor points gives

Meanings in this article

  • B0B_0: the bandwidth at reference year t0t_0.
  • τ\tau: the doubling time implied by the data.
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