Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

DEFT: Differentiable Automatic Test Pattern Generation

Wei Li, Yang Zou, Yixin Liang, José Moura, Shawn Blanton

TL;DR

DEFT tackles the challenge of efficiently generating test patterns for hard-to-detect faults by recasting ATPG as a differentiable optimization problem. It introduces a probabilistic reparameterization and a differentiable surrogate, using a Gumbel-Softmax framework to preserve discrete fault-detection semantics while enabling gradient-based search, and augments this with a complementary explore objective to avoid vanishing gradients. The framework is bolstered by a custom CUDA kernel and gradient normalization to scale to industrial circuits, and it supports multi-fault/multi-pattern optimization and practical ATPG extensions like X-bits. Empirical results on NCU and MAC benchmarks show substantial HTD fault-detection gains (up to 48.9% on average) with comparable runtimes, plus significant reductions in pattern length and access to a scalable, end-to-end differentiable ATPG engine. Overall, DEFT offers a promising, extensible complement to traditional heuristics and SAT-based approaches for modern, HTD-focused ATPG tasks.

Abstract

Modern IC complexity drives test pattern growth, with the majority of patterns targeting a small set of hard-to-detect (HTD) faults. This motivates new ATPG algorithms to improve test effectiveness specifically for HTD faults. This paper presents DEFT (Differentiable Automatic Test Pattern Generation), a new ATPG approach that reformulates the discrete ATPG problem as a continuous optimization task. DEFT introduces a mathematically grounded reparameterization that aligns the expected continuous objective with discrete fault-detection semantics, enabling reliable gradient-based pattern generation. To ensure scalability and stability on deep circuit graphs, DEFT integrates a custom CUDA kernel for efficient forward-backward propagation and applies gradient normalization to mitigate vanishing gradients. Compared to a leading commercial tool on two industrial benchmarks, DEFT improves HTD fault detection by 21.1% and 48.9% on average under the same pattern budget and comparable runtime. DEFT also supports practical ATPG settings such as partial assignment pattern generation, producing patterns with 19.3% fewer 0/1 bits while still detecting 35% more faults. These results indicate DEFT is a promising and effective ATPG engine, offering a valuable complement to existing heuristic.

DEFT: Differentiable Automatic Test Pattern Generation

TL;DR

DEFT tackles the challenge of efficiently generating test patterns for hard-to-detect faults by recasting ATPG as a differentiable optimization problem. It introduces a probabilistic reparameterization and a differentiable surrogate, using a Gumbel-Softmax framework to preserve discrete fault-detection semantics while enabling gradient-based search, and augments this with a complementary explore objective to avoid vanishing gradients. The framework is bolstered by a custom CUDA kernel and gradient normalization to scale to industrial circuits, and it supports multi-fault/multi-pattern optimization and practical ATPG extensions like X-bits. Empirical results on NCU and MAC benchmarks show substantial HTD fault-detection gains (up to 48.9% on average) with comparable runtimes, plus significant reductions in pattern length and access to a scalable, end-to-end differentiable ATPG engine. Overall, DEFT offers a promising, extensible complement to traditional heuristics and SAT-based approaches for modern, HTD-focused ATPG tasks.

Abstract

Modern IC complexity drives test pattern growth, with the majority of patterns targeting a small set of hard-to-detect (HTD) faults. This motivates new ATPG algorithms to improve test effectiveness specifically for HTD faults. This paper presents DEFT (Differentiable Automatic Test Pattern Generation), a new ATPG approach that reformulates the discrete ATPG problem as a continuous optimization task. DEFT introduces a mathematically grounded reparameterization that aligns the expected continuous objective with discrete fault-detection semantics, enabling reliable gradient-based pattern generation. To ensure scalability and stability on deep circuit graphs, DEFT integrates a custom CUDA kernel for efficient forward-backward propagation and applies gradient normalization to mitigate vanishing gradients. Compared to a leading commercial tool on two industrial benchmarks, DEFT improves HTD fault detection by 21.1% and 48.9% on average under the same pattern budget and comparable runtime. DEFT also supports practical ATPG settings such as partial assignment pattern generation, producing patterns with 19.3% fewer 0/1 bits while still detecting 35% more faults. These results indicate DEFT is a promising and effective ATPG engine, offering a valuable complement to existing heuristic.
Paper Structure (24 sections, 1 theorem, 9 equations, 8 figures, 3 tables)

This paper contains 24 sections, 1 theorem, 9 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Automatic Test Pattern Generation (ATPG)
  4. Differentiable Programming for EDA
  5. Problem Formulation
  6. Differentiable Reparameterization for ATPG
  7. Probabilistic Reframing
  8. Differentiable Surrogate via Reparameterization
  9. Gradient Calculation of the Exploit Signal
  10. Handling Zero Gradients: The Explore Objective
  11. DEFT Framework
  12. DEFT Framework and Graph Construction
  13. Scaling to Industrial Circuits
  14. Custom CUDA Kernel for Efficient Propagation
  15. Gradient Normalization for Deep Graphs
  16. ...and 9 more sections

Key Result

Theorem 4.1

The discrete problem equation eq:p1 from sec:problem has a solution (i.e., a detecting pattern $x^*$ exists) if and only if the optimal value of the probabilistic problem equation eq:p2 is 1.

Figures (8)

  • Figure 1: The reparameterization technique in DEFT vs. naive continuous relaxation.
  • Figure 2: Overview of the DEFT Framework.
  • Figure 3: Analogy Between Neural Network Training and Differentiable ATPG in DEFT. Green (blue) boxes represent trainable (fixed) components.
  • Figure 4: An example of DEFT for a stuck-at-1 fault at net n1. The green represents gradient flow and red means the copied fanout cone introduced by fault.
  • Figure 5: Illustration of continuous value propagation using custom CUDA kernel in DEFT.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Theorem 4.1: Formulation Equivalence