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SMLP: Symbolic Machine Learning Prover

Franz Brauße, Zurab Khasidashvili, Konstantin Korovin

TL;DR

SMLP addresses the challenge of robust design, verification, and optimization for ML-driven systems in analog hardware by fusing data-driven learning with formal methods in a unified exploration loop. It introduces the GEAR-formulated symbolic framework, stability guarantees via a $\theta$-region, and multiple exploration modes (stable synthesis, optimization, querying, root cause analysis) backed by GearSAT_$\delta$ and GearOPT_$\delta$ algorithms. The approach is realized in an open-source architecture with DOE, various ML models, and SMT solvers, enabling targeted model refinement and industrial applicability as demonstrated in Intel contexts and prior real-world datasets. The work lays groundwork for scalable, robust exploration of design spaces under uncertainty, with practical impact for analog hardware design and potential extensions to ONNX/vnn-lib ecosystems and richer solver pipelines.

Abstract

Symbolic Machine Learning Prover (SMLP) is a tool and a library for system exploration based on data samples obtained by simulating or executing the system on a number of input vectors. SMLP aims at exploring the system based on this data by taking a grey-box approach: SMLP combines statistical methods of data exploration with building and exploring machine learning models in close feedback loop with the system's response, and exploring these models by combining probabilistic and formal methods. SMLP has been applied in industrial setting at Intel for analyzing and optimizing hardware designs at the analog level. SMLP is a general purpose tool and can be applied to systems that can be sampled and modeled by machine learning models.

SMLP: Symbolic Machine Learning Prover

TL;DR

SMLP addresses the challenge of robust design, verification, and optimization for ML-driven systems in analog hardware by fusing data-driven learning with formal methods in a unified exploration loop. It introduces the GEAR-formulated symbolic framework, stability guarantees via a -region, and multiple exploration modes (stable synthesis, optimization, querying, root cause analysis) backed by GearSAT_ and GearOPT_ algorithms. The approach is realized in an open-source architecture with DOE, various ML models, and SMT solvers, enabling targeted model refinement and industrial applicability as demonstrated in Intel contexts and prior real-world datasets. The work lays groundwork for scalable, robust exploration of design spaces under uncertainty, with practical impact for analog hardware design and potential extensions to ONNX/vnn-lib ecosystems and richer solver pipelines.

Abstract

Symbolic Machine Learning Prover (SMLP) is a tool and a library for system exploration based on data samples obtained by simulating or executing the system on a number of input vectors. SMLP aims at exploring the system based on this data by taking a grey-box approach: SMLP combines statistical methods of data exploration with building and exploring machine learning models in close feedback loop with the system's response, and exploring these models by combining probabilistic and formal methods. SMLP has been applied in industrial setting at Intel for analyzing and optimizing hardware designs at the analog level. SMLP is a general purpose tool and can be applied to systems that can be sampled and modeled by machine learning models.
Paper Structure (16 sections, 10 equations, 4 figures)

This paper contains 16 sections, 10 equations, 4 figures.

Table of Contents

  1. Introduction
  2. SMLP architecture
  3. Symbolic representation of models and constraints
  4. Symbolic representation of the ML model exploration
  5. Problem specification in SMLP
  6. SMLP exploration modes of ML models
  7. Stable parameter synthesis
  8. Querying conditions on the model
  9. Verifying assertions on a model
  10. Stable optimized synthesis
  11. Design of experiments
  12. Root cause analysis
  13. Model refinement loop
  14. Implementation
  15. Experimental results
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Exploration Cube
  • Figure 2: SMLP Tool Architecture
  • Figure 3: Example of SMLP's format specifying the problem conditions for the displayed model of the system.
  • Figure 4: SMLP max-min optimization. On both plots, $p$ denote the knobs. On the right plot we also consider inputs $x$ (which are universally quantified) as part of $f$.