KirchhoffLM

Qwen3.5-0.8B: quality on the emulated chips

runbits/bytevs original
Original digital model0.7403—
Design package values only (no physics)0.7398-0.06 %
Emulated chip #00.7623+2.97 %
Emulated chip #10.7573+2.29 %
Emulated chip #20.7626+3.01 %

12 held-out texts (6 Wikipedia, 6 code), 1,024 tokens each; 10-bit chip links; lower bits/byte is better.

Long context (1,024 tokens)

testexact modelemulated chip
Recall a number hidden early in ~981 tokens (20 trials)20 / 2020 / 20
Bits/byte, tokens 0–2560.82500.8514 (+3.2 %)
Bits/byte, tokens 256–5120.79320.8182 (+3.1 %)
Bits/byte, tokens 512–7680.68670.7075 (+3.0 %)
Bits/byte, tokens 768–10230.67480.6994 (+3.6 %)

The hardware error does not grow with context, because the memory of earlier tokens is digital.

Error budget

Where the loss of the AC chain (8-bit links, +5.90 % in total) comes from: removing one effect at a time8-bit links (vs 10-bit)+3.26%ADCs and memory converters+2.83%Multipliers+0.88%Amplifier noise+0.30%Rails (clipping)+0.18%Unit-capacitor rounding+0.11%Norm units+0.03%Capacitor mismatch+0.01%Wire phase delay+0.00%SiLU / sigmoid units+0.00%

Sensitivity per layer

Quality loss when only this layer runs on its chip (AC design, all other layers exact)L0 DeltaNet+0.66%L1 DeltaNet+0.36%L2 DeltaNet+1.26%L3 attention+0.80%L4 DeltaNet+0.39%L5 DeltaNet+0.23%L6 DeltaNet+2.71%L7 attention+0.07%L8 DeltaNet+0.24%L9 DeltaNet+0.25%L10 DeltaNet+0.30%L11 attention+0.16%L12 DeltaNet+0.09%L13 DeltaNet+0.12%L14 DeltaNet+0.58%L15 attention+0.65%L16 DeltaNet+0.27%L17 DeltaNet+0.48%L18 DeltaNet+0.43%L19 attention+0.06%L20 DeltaNet+0.34%L21 DeltaNet+0.50%L22 DeltaNet+0.12%L23 attention+0.34%

Exact circuit solves of one real tile (layer 0 FFN)

designtilewire Rline couplingoutput error (after calibration)
DC resistor 73uS, 0.09 V1280.5 Ω0 fF15.24 %
DC resistor 73uS, 0.09 V1282 Ω0 fF39.93 %
DC resistor 73uS, 0.09 V1284 Ω0 fF57.55 %
AC cap 10fF @100MHz, 0.5 V1280.5 Ω0 fF0.17 %
AC cap 10fF @100MHz, 0.5 V1282 Ω0 fF0.21 %
AC cap 10fF @100MHz, 0.5 V1284 Ω0 fF0.54 %
AC cap 2fF @1GHz, 0.5 V1280.5 Ω0 fF0.83 %
AC cap 2fF @1GHz, 0.5 V1282 Ω0 fF1.05 %
AC cap 2fF @1GHz, 0.5 V1284 Ω0 fF2.61 %
DC resistor 73uS, 0.09 V2560.5 Ω0 fF40.04 %
DC resistor 73uS, 0.09 V2562 Ω0 fF73.58 %
DC resistor 73uS, 0.09 V2564 Ω0 fF86.13 %
AC cap 10fF @100MHz, 0.5 V2560.5 Ω0 fF0.22 %
AC cap 10fF @100MHz, 0.5 V2562 Ω0 fF1.95 %
AC cap 10fF @100MHz, 0.5 V2564 Ω0 fF6.88 %
AC cap 2fF @1GHz, 0.5 V2560.5 Ω0 fF1.08 %
AC cap 2fF @1GHz, 0.5 V2562 Ω0 fF8.61 %
AC cap 2fF @1GHz, 0.5 V2564 Ω0 fF24.03 %

DC resistor grids distort badly through wire voltage drop unless every cell is pre-compensated; the AC capacitor grid at 10 fF / 100 MHz stays within a fraction of a percent.

Small model trained digitally, run on the chip (TinyStories, 5.8M weights)

validation loss
Exact2.2000
Emulated chip #02.2036
Unseen chips #1–42.2043, 2.2038, 2.2040, 2.2037

Speed and energy (estimates)

emulated analog chainM3 Max GPU (measured, digital)H100 (estimated)
Generation, one user~37,384 tokens/s191 tokens/s~800–1,600 tokens/s
Energy per token, one user~16 µJ at 2k context~0.2 J~0.3 J
1,024-token prompt1.2 ms, 8.9 mJ134 ms~3–6 ms, ~2–4 J

Corrections

2026-10-16: an external review found four issues. (1) The converters around the digital memory were not simulated; (2) capacitor mismatch did not grow for small capacitors as Pelgrom's law requires; (3) the design search crashed for capacitor grids; (4) the numerical checks did not assert. Fixing them also exposed (5) a calibration that took the signal peak from a random subsample, so rails clipped real peaks, and (6) a memory ADC with one range for all channels, which rounded quiet heads away. All are fixed, covered by regression tests, and every number on this site was re-measured afterwards. The design now uses per-head ADC ranges (10 bits) into the memory and 12-bit DACs out of it.

Analog numbers come from the circuit timing and energy model of an unbuilt chip; NVIDIA numbers are scaled from the M3 Max measurement using memory bandwidth and compute specs. Treat all of them as order-of-magnitude.