[OpenVINO backend] Implements extract_sequences, erfinv, and solve in the math suite

[goyaladitya05]

This PR implements the following ops for the math suite of the OpenVINO backend.

• extract_sequences using a gather based sliding window approach.
• erfinv via Winitzki approximation + one Newton-Raphson refinement step using the native erf op
• math.solve by delegating to the already implemented linalg.solve
• Removed relevent tests from excluded_concrete_tests.txt

Closes: openvinotoolkit/openvino/issues/34412

[gemini-code-assist]

Summary of Changes

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This pull request significantly enhances the OpenVINO backend's mathematical capabilities by adding support for several key operations: extract_sequences, erfinv, and math.solve. These additions allow for more complex numerical computations to be performed efficiently using OpenVINO, thereby improving the backend's overall functionality and compatibility with Keras's math suite. The implementation details involve using native OpenVINO operations for sequence extraction and a robust approximation method for the inverse error function, while solve is delegated to an existing linear algebra function.

Highlights

• New Math Operations: Implemented extract_sequences, erfinv, and math.solve for the OpenVINO backend, expanding the range of supported mathematical computations.
• extract_sequences Implementation: The extract_sequences operation was implemented using a gather-based sliding-window approach with OpenVINO operations.
• erfinv Implementation: The erfinv (inverse error function) was implemented using the Winitzki approximation combined with a single Newton-Raphson refinement step, leveraging the native erf operation.
• math.solve Delegation: The math.solve function now delegates its implementation to the already existing linalg.solve function within the OpenVINO backend.
• Test Unblocking: Removed previously excluded tests for extract_sequences and erfinv from excluded_concrete_tests.txt, indicating these operations are now functional and tested.

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Changelog

• keras/src/backend/openvino/excluded_concrete_tests.txt
  • Removed ExtractSequencesOpTest::test_extract_sequences_call from the exclusion list.
  • Removed MathOpsCorrectnessTest::test_erfinv_operation_basic from the exclusion list.
  • Removed MathOpsCorrectnessTest::test_erfinv_operation_dtype from the exclusion list.
  • Removed MathOpsCorrectnessTest::test_erfinv_operation_edge_cases from the exclusion list.
  • Removed MathOpsCorrectnessTest::test_extract_sequences from the exclusion list.
• keras/src/backend/openvino/math.py
  • Implemented the extract_sequences function using OpenVINO ops for shape manipulation, indexing, and gathering.
  • Implemented the erfinv function using a Winitzki approximation and Newton-Raphson refinement.
  • Implemented the solve function by importing and delegating to linalg.solve.

Activity

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[gemini-code-assist]

Code Review

This pull request implements extract_sequences, erfinv, and solve for the OpenVINO backend. No security vulnerabilities were found. The implementations are functionally correct, and suggestions have been provided to improve the readability and maintainability of extract_sequences and erfinv by refactoring them to use more constants and intermediate variables.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 0% with 61 lines in your changes missing coverage. Please review.
✅ Project coverage is 76.62%. Comparing base (4f85917) to head (df9f1ef).

Files with missing lines	Patch %	Lines
keras/src/backend/openvino/math.py	0.00%	61 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (4f85917) and HEAD (df9f1ef). Click for more details.

HEAD has 2 uploads less than BASE

Flag	BASE (4f85917)	HEAD (df9f1ef)
keras	5	4
keras-openvino	1	0

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #22320      +/-   ##
==========================================
- Coverage   82.73%   76.62%   -6.12%     
==========================================
  Files         594      594              
  Lines       65732    65793      +61     
  Branches    10266    10266              
==========================================
- Hits        54385    50413    -3972     
- Misses       8711    12947    +4236     
+ Partials     2636     2433     -203     

Flag	Coverage Δ
keras	76.45% <0.00%> (-6.11%)	⬇️
keras-jax	60.86% <0.00%> (-0.06%)	⬇️
keras-numpy	55.06% <0.00%> (-0.06%)	⬇️
keras-openvino	?
keras-tensorflow	62.10% <0.00%> (-0.06%)	⬇️
keras-torch	60.96% <0.00%> (-0.06%)	⬇️

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