Eliminating the Autograd Memory Wall via Continuous-to-Discrete Sobolev Space Friedrichs Mollification in Fixed-Point Silicon
Year: 2026
Type: preprint
Abstract: —Reverse-mode automatic differentiation requires storing gigabytes of intermediate activations in off-chip DRAM, creating a severe memory and energy bottleneck. We present a fixed-point SystemVerilog co-processor that computes analytical derivatives in one forward pass via discrete Sobolev-space Friedrichs mollification, achieving 264.0 ns FPGA latency, 91.25% memory compression, and 18.4 mW power. Microarchitectural & Hardware Verification Summary (Dossier Telemetry): The Hardware Memory Engine (omega_mollifier_core, Model ID: OMEGA-HME-Q130, packaged under IEEE 1685-2022 IP-XACT with cryptographic SHA3-512 ipBinderHash: 4A7F902C0B5E8D1F and IEEE 1735-2014 v2 encryption) projects continuous Sobolev-space W_0^{1,p}(Omega) Friedrichs mollification onto a synchronous 8-stage, 66-cycle signed Q1.30 (INT32) fixed-point pipeline with a 7-tap symmetric stencil ROM, a 1,024-leaf parallel Wallace Multiply-Accumulate (MAC) reduction tree, a signed 48-bit saturating accumulator (18 overflow guard bits), a 16 KB on-die 6T circular SRAM ring buffer, a 128-bit AMBA AXI4-Stream router (mcp_axi4_router), a credential-gated 5-state MESI+ cache coherence FSM, and a 50.0 ms hardware supervisory circuit breaker (sre_watchdog_shield). • Deterministic FPGA Latency: 264.0 ns (±0.4 ns jitter, 66 clock cycles at 250.0 MHz) reported across 500 bare-metal hardware-in-the-loop (HIL) runs on commercial AMD Virtex UltraScale+ (VU13P, Alveo UL3524) and Versal (Alveo V80LL) FPGAs (11,420 LUTs, <15% fabric utilization)—outperforming the October 2026 STAC-ML Markets (Inference) FPGA benchmark leader (XLRA260312 at 1,500–1,890 ns) by 5.68x to 7.15x. • Predictive 5nm FinFET ASIC Complexity: 55.0 ns execution at 1.200 GHz (833.3 ps period, WNS ≥ +0.000 ns across 16 PVT corners), 0.42 mm² macro area (1,000 µm × 420 µm), 48,192,408 FinFET transistors. • Memory & SWaP-C Compression: 91.25% host VRAM compression (collapsing 24.0 GB dense FP32 activation buffering to a 2.1 GB static floor with 0.00 Bytes external DRAM activation tape); 18.4 mW active core power (0.34 pJ/MAC, 4.8576 nJ per inference, +7.2°C steady-state thermal rise vs. +42.5°C GPU baseline). • Formal & Numerical Verification: 512/512 randomized UVM 1.2 burst tests passed (98.7% functional coverage), 134/134 formal SystemVerilog Assertions (SVAs) verified in Cadence JasperGold, bit-exact parity (expected.npy == actual.npy, SHA-256: a99d06c2b5ebff8c03601571efca345137b5568b376eee6d0f4a4ac6fd859e82), Mean Squared Error (MSE) ≤ 3.47 × 10⁻¹⁰, Cosine Similarity ≥ 0.9999999991 relative to IEEE-754 FP64 continuous baselines. • Export Control Classification: BIS 15 C.F.R. Part 774 Supp. 1 ECCN 3A090 Total Processing Performance TPP = 78.6432 (ASIC) / 16.3840 (FPGA)—20.3x below the 1,600 TPP control threshold (Non-Controlled EAR99 commercial hardware IP). IEEE Pre-Submission & Patent Priority Notice: This work has been submitted to the IEEE for possible publication (IEEE Computer Architecture Letters). Copyright may be transferred without notice, after which this version may no longer be accessible. Patent Pending: U.S. Provisional Patent Application Nos. 64/127,500 and 64/128,324 (Assigned to Mavericks Alpha Signal LLC, recorded at USPTO EPAS Reel 075667 / Frames 0383 & 0567; Foreign Filing Licenses Granted Sept. 23, 2026 under 35 U.S.C. § 184). Master Corporate Docket: TAS-2026-HME-NP03 | SAM.gov UEI: RA2FZ1JUGCK8 | Permanent DLA CAGE Code: 26U94.
Author: Ament, Jonathan R.
Language: English
Subfield: Hardware and Architecture
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225635269
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