FP32 Tensor to Int8 Quantization

Given an FP32 tensor and a floating-point scale, convert the tensor to INT8. Follow-ups add asymmetric quantization with zero point and ask how scale / zero point should change when the input distribution is not symmetric. Requirements Implement a function that takes: def quantize_fp32_to_int8(x: np.ndarray, scale: float) -> np.ndarray: ... Base behavior: x is an FP32 tensor of any shape. Divide every value by scale. Round or cast into signed int8 range. Return an int8 tensor with the same shape. Follow-ups: Add a zero_point parameter for asymmetric quantization. Explain when symmetric quantization is insufficient. Derive how scale and zero_point are used together. Discuss clipping / saturation when values exceed [-128, 127]. Explain what happens to error when the input distribution is skewed or has outliers. Notes A standard asymmetric mapping is: q = clamp(round(x / scale) + zero_point, qmin, qmax) x_hat = scale * (q - zero_point) For signed INT8, qmin = -128 and qmax = 127; for unsigned INT8, qmin = 0 and qmax = 255. If the interviewer does not specify rounding, say what you choose. A practical implementation should use np.rint, clip before casting, and avoid silent wraparound. Key discussion points: Symmetric quantization assumes zero maps cleanly to zero and works best when the distribution is roughly centered. Asymmetric quantization handles non-zero-centered ranges by shifting the integer code space with zero_point. Outliers enlarge the dynamic range and waste most buckets on rare values; per-channel scale, clipping, or calibration can reduce error. INT8 conversion is simple coding, but the signal is whether you understand numerical range, saturation, and inference trade-offs. Preparation Implement the base function in NumPy, then add zero_point, clipping, and dequantization. Walk through a tiny example by hand: x=[-1.0, 0.0, 1.0], scale=0.1. Be ready to explain per-tensor vs per-channel scale and why activations are often harder to quantize than static weights.