Repository: tensorflow
Issue: Significant Discrepancy in `tf.linalg.triangular_solve` Results Between CPU and GPU
Labels: type:bug,comp:ops,TF 2.18

### Issue type

Bug

### Have you reproduced the bug with TensorFlow Nightly?

No

### Source

binary

### TensorFlow version

v2.18.0-rc2-4-g6550e4bd802 2.18.0

### Custom code

Yes

### OS platform and distribution

Ubuntu 22.04.4 LTS x86_64

### Mobile device

_No response_

### Python version

3.10.0

### Bazel version

_No response_

### GCC/compiler version

_No response_

### CUDA/cuDNN version

_No response_

### GPU model and memory

_No response_

### Current behavior?

When using `tf.linalg.triangular_solve` with large matrices or specific triangular matrix conditions (e.g., `upper=True`, `transpose=True`, `unitriangular=True`), the GPU results significantly differ from the CPU results. 

The discrepancy includes extremely large Mean Absolute Error (MAE) values and infinite Mean Squared Error (MSE) values of the results, indicating a possible issue in the GPU implementation of the function.

### Standalone code to reproduce the issue

[colab](https://colab.research.google.com/drive/1zXcOAkxHV6snaMyWGMeKIukf5IVBd0Bh?usp=sharing)
[Safe Tensors](https://drive.google.com/file/d/1n1JyugXNAS9M2wmnk9u9vCVuHz0uE3R6/view?usp=sharing)

```python
import tensorflow as tf
import numpy as np
from safetensors.torch import load_file

def set_seed(seed_value=42):
    """Sets the random seed for reproducibility."""
    np.random.seed(seed_value)
    tf.random.set_seed(seed_value)

def tensorflow_version(input, cpu=True):
    set_seed()
    if cpu:
        device_string = "/cpu:0"
    else:
        device_string = "/gpu:0"

    with tf.device(device_string):
        b_tensor = tf.constant(input["b"])
        A_tensor = tf.constant(input["A"])

        upper = input.get("upper", True)
        transpose = input.get("transpose", False)
        unitriangular = input.get("unitriangular", False)

        solution = tf.linalg.triangular_solve(
            A_tensor, b_tensor, lower=not upper, adjoint=transpose
        )

        return {"triangular_solve_solution": solution.numpy()}

def load_safe_tensor(file_path):
    safe_tensor_data = load_file(file_path)
    A_tensor = safe_tensor_data["A"]
    b_tensor = safe_tensor_data["b"]

    return {
        "A": tf.convert_to_tensor(A_tensor.numpy()),
        "b": tf.convert_to_tensor(b_tensor.numpy()),
    }

def calculate_differences(cpu_result, gpu_result):
    diff = np.abs(cpu_result - gpu_result)
    mae = np.mean(diff)
    mse = np.mean(diff**2)
    rmse = np.sqrt(mse)
    max_diff = np.max(diff)
    mean_relative_diff = np.mean(diff / (np.abs(cpu_result) + 1e-10))

    return {
        "Mean Absolute Error": mae,
        "Mean Squared Error": mse,
        "Root Mean Squared Error": rmse,
        "Maximum Absolute Difference": max_diff,
        "Mean Relative Difference": mean_relative_diff,
    }

def main():
    file_path = "tensorflow_triangular_solve_3.safetensors"
    input_data = load_safe_tensor(file_path)
    input_data["upper"] = True
    input_data["transpose"] = True
    input_data["unitriangular"] = True

    result_cpu = tensorflow_version(input_data, cpu=True)
    print("CPU Result:")
    print(result_cpu)

    if tf.config.list_physical_devices("GPU"):
        result_gpu = tensorflow_version(input_data, cpu=False)
        print("GPU Result:")
        print(result_gpu)

        if result_gpu:
            cpu_solution = result_cpu["triangular_solve_solution"]
            gpu_solution = result_gpu["triangular_solve_solution"]
            differences = calculate_differences(cpu_solution, gpu_solution)
            for key, value in differences.items():
                print(f"{key}: {value}")
    else:
        print("GPU not available.")

if __name__ == "__main__":
    main()
```

#### **Issue Summary:**
- The `tf.linalg.triangular_solve` function produces vastly different results on the GPU compared to the CPU. The differences include an enormous Mean Absolute Error (MAE) and an infinite Mean Squared Error (MSE), indicating a severe discrepancy between the CPU and GPU results.
- The issue appears to be related to the use of specific arguments like `upper=True`, `transpose=True`, and `unitriangular=True`, suggesting that there might be a numerical precision or stability issue in the GPU implementation.
- It is unclear why these large discrepancies occur, but they point to a critical inconsistency that could impact numerical reliability for users depending on TensorFlow’s triangular solve functionality.


### Relevant log output

```shell
Mean Absolute Error: 1.566790629150662e+21
Mean Squared Error: inf
Root Mean Squared Error: inf
Maximum Absolute Difference: 1.4265324671452624e+26
```