NVIDIA·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jul 2026

Summary

NVIDIA software engineer interview with a NumPy coding problem that looked straightforward on the surface but had a specific constraint that tripped me up a bit.

Questions Asked (1)

Implement a 2D convolution on a 4x4 input with a 3x3 filter at stride 1 using NumPy, but without writing any explicit Python loops. Return the resulting 2x2 output.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The no-loops constraint is what makes this non-trivial.

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AI HintsAI Generated

Suggested Approach

Leverage NumPy's stride tricks (as_strided) or einsum to extract all overlapping 3x3 patches from the 4x4 input simultaneously, then perform a vectorized dot product against the filter to produce the 2x2 output. This avoids explicit Python loops while staying numerically equivalent to a naive nested-loop convolution. Briefly explain the shape math (output size = (4-3)/1 + 1 = 2) before writing any code.

Pro tip: Mentioning that this patch-extraction approach is essentially the 'im2col' technique used inside cuDNN and other GPU-accelerated deep learning libraries will immediately signal GPU/systems awareness — highly valued at NVIDIA — and opens a natural discussion about memory layout, cache efficiency, and why GEMM-based convolution dominates in practice.

1. Clarify & Compute Output Shape

State the output size formula: out = (input_size - kernel_size) / stride + 1, giving (4-3)/1+1 = 2, so the result is 2x2. Confirm there is no padding and stride is 1.

2. Extract Patches via Stride Tricks (im2col)

Use np.lib.stride_tricks.as_strided or a sliding-window view (np.lib.stride_tricks.sliding_window_view in NumPy ≥1.20) to create a (2, 2, 3, 3) array of all overlapping 3x3 patches without copying data or looping.

3. Vectorized Dot Product

Reshape the patches to (4, 9) and the filter to (9,), then use np.dot or np.einsum('ijkl,kl->ij', patches, kernel) to compute all four output values in one operation, reshaping the result to (2, 2).

4. Validate Correctness

Cross-check the result against scipy.signal.correlate2d or a manual reference computation on a small example to confirm the vectorized output is numerically identical.

5. Discuss Trade-offs & Extensions

Note memory vs. compute trade-offs (as_strided shares memory but can be unsafe; sliding_window_view is safer), and mention how this generalizes to batched inputs, multiple channels, and GPU execution via cuDNN's im2col + GEMM pipeline.

Key Points to Mention

Output size formula: (N - K) / S + 1, yielding a 2x2 result for this problem
np.lib.stride_tricks.sliding_window_view or as_strided for zero-copy patch extraction
np.einsum or np.tensordot for a fully vectorized, loop-free dot product across all patches
im2col connection: this is the same technique used in cuDNN and deep learning frameworks to convert convolution into a GEMM operation
Memory layout considerations: contiguous vs. strided arrays and their impact on cache performance and GPU memory coalescing
Distinction between convolution (180° kernel flip) and cross-correlation, and which one deep learning frameworks actually implement

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.