This was the part that stressed me out most.
Start by reproducing the garbage output and confirming the model runs without crashing, then systematically isolate the bug by testing each component (tokenization, embeddings, attention, positional encoding, causal masking, layer norm, output projection) against a reference implementation. Use a divide-and-conquer strategy: first verify the forward pass with a known input, then check autoregressive generation step by step, and finally validate the training/inference consistency.
Pro tip: Emphasize that you would first check the causal mask and positional encoding, as these are the most common sources of garbage output in decoder-only transformers, and mention that you would write unit tests for each submodule to catch silent logical errors.
Run the model with a fixed seed and simple prompt to confirm the garbage output, and note whether it's random noise, repetitive, or partially coherent to narrow down the cause.
Feed a simple sequence through the model and compare intermediate activations (e.g., embeddings, attention scores, layer outputs) against a reference or hand-computed values to locate the first divergence.
Check causal masking (ensuring no future tokens are attended to), positional encoding (correct application and no off-by-one), layer normalization (correct axis and epsilon), and attention scaling (dividing by sqrt(d_k)).
Verify that the generation loop correctly appends new tokens, updates the key/value cache (if used), and shifts the input window; ensure the model is in eval mode and dropout is disabled.
Apply the fix, then run the model on a small dataset to check for coherent output, and add unit tests for the fixed component to prevent future regressions.
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Felt okay on the concept but fumbled the implementation detail of which axis to concatenate along.
Start by clarifying the bug fix and the current decoding loop, then explain how KV caching changes the attention computation to use only the cached keys and values for the prefix. Walk through the implementation steps, including cache initialization, updating the cache at each step, and adjusting the attention mask, while highlighting trade-offs like memory usage and latency improvements.
Pro tip: Emphasize that KV caching is not just an optimization but a fundamental shift in how you manage state during inference; mention that you'd validate correctness by comparing outputs with and without caching and monitor memory growth for long sequences.
Confirm that the generation bug is resolved and that the model produces correct outputs without caching. Establish a baseline for performance and memory usage to measure the impact of caching.
Decide on the cache shape and data type (e.g., per-layer key and value tensors of shape [batch, num_heads, seq_len, head_dim]). Consider whether to preallocate or grow dynamically, and how to handle batch size and beam search.
At each decode step, compute the query for the new token only, and attend over the concatenation of cached keys/values and the new key/value. Update the cache with the new key/value for the next step.
Ensure the attention mask correctly prevents attending to future tokens and that positional encodings are applied appropriately to the new token relative to the cached prefix.
Compare outputs with and without caching to ensure correctness. Measure latency and memory improvements, and test with varying sequence lengths and batch sizes to understand trade-offs.
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Start by deriving the memory formula for KV cache: 2 * batch_size * num_layers * num_heads * head_dim * seq_len * bytes_per_element. Then explain how it scales linearly with context length and batch size, and discuss trade-offs of reduction techniques like MQA, GQA, quantization, and paged attention.
Pro tip: Quantify the impact: for a 70B model with 80 layers, 64 heads, head_dim 128, and FP16, each token adds ~2.6 MB to the cache. This concrete number shows you understand real-world implications.
Write the KV cache size formula: 2 (for K and V) * batch_size * num_layers * num_heads * head_dim * seq_len * bytes_per_element. Explain each term and why it's multiplied.
Show that memory grows linearly with sequence length and batch size. For long contexts (e.g., 128k tokens), the cache can exceed model weights, becoming a bottleneck.
Cover architectural changes (MQA, GQA), quantization (FP8, INT8), memory management (PagedAttention, vLLM), and algorithmic optimizations (sliding window, sparse attention).
For each technique, mention impact on memory, compute, and model quality. E.g., MQA reduces memory but may hurt quality; quantization saves memory but adds dequant overhead.
Summarize that the best approach depends on constraints: GQA for quality-sensitive, quantization for memory-bound, PagedAttention for serving many requests.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by explaining the purpose of the KV cache and causal mask in autoregressive generation. Then describe how batching sequences of different lengths requires padding and careful masking to avoid cross-contamination. Finally, discuss the interaction: the KV cache stores keys/values per sequence, and the causal mask must be adjusted to prevent attending to padding tokens and future tokens.
Pro tip: Mention that efficient implementations often use sequence lengths to pack sequences without padding (e.g., via block-diagonal masks or varlen attention) to maximize GPU utilization and avoid wasted computation on padding.
Define KV cache as a mechanism to store past keys and values for each layer to avoid recomputation. Explain causal mask as a lower-triangular matrix ensuring each position attends only to previous positions.
In a batch, sequences have different lengths, so they are padded to the maximum length. This introduces padding tokens that should not influence the generation of real tokens.
Each sequence in the batch has its own KV cache, typically stored as a tensor of shape [batch, num_heads, max_len, head_dim]. The cache is updated only for valid positions, and padding positions are ignored or masked.
The causal mask must be combined with a padding mask to prevent attending to padding tokens. This is often done by setting attention scores to -inf for padding positions and future positions.
Padding wastes computation and memory. Techniques like sequence packing, varlen attention, or block-diagonal masks can avoid padding and improve efficiency.
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The derivation part is where you either know it or you don't.
Start by defining the custom autograd function class with static forward and backward methods, then derive the gradients for both operands using matrix calculus. In the backward pass, compute gradients with respect to inputs using the chain rule and return them in the correct order.
Pro tip: Emphasize that the backward pass must handle non-contiguous tensors and broadcasting correctly, and mention that using torch.autograd.gradcheck validates your implementation. This shows attention to correctness and testing.
Create a subclass of torch.autograd.Function with static forward and backward methods. In forward, save the input tensors needed for backward and return the output.
For C = A @ B, the gradient with respect to A is grad_output @ B.T and with respect to B is A.T @ grad_output. Explain the derivation using the chain rule and matrix calculus.
In backward, compute grad_A and grad_B using the derived formulas, ensuring correct handling of batch dimensions and broadcasting. Return gradients in the same order as forward inputs.
Use torch.autograd.gradcheck to verify the gradients numerically. Also test with different shapes and non-contiguous inputs to ensure robustness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
You have to sum over the broadcast axes to get the gradient back to the original shape.
Start by recalling the forward pass of matrix multiplication with broadcasting, then derive the backward pass using the chain rule and the fact that gradients of a broadcast operation require summing over the broadcasted axes. Emphasize that the summation axes correspond to the dimensions that were expanded during the forward pass, and that the gradient with respect to the non-broadcasted operand is computed by contracting over the appropriate axes.
Pro tip: When explaining, use a concrete example like a weight matrix (A) multiplied by a batch of inputs (B) where B has an extra batch dimension, and show how the gradient for A sums over the batch dimension. This demonstrates practical understanding and avoids abstract confusion.
Describe the forward pass: if A is a weight matrix of shape (m, n) and B is a batch of inputs of shape (k, n, p) broadcasted to (k, m, p), then the output C has shape (k, m, p). Identify which dimensions are broadcasted.
For the operand that is not broadcasted (e.g., A), the gradient is obtained by summing over the broadcasted axes. In the example, dL/dA = sum over k of (dL/dC_k @ B_k^T), effectively summing over the batch dimension.
For the operand that is broadcasted (e.g., B), the gradient is computed by summing over the broadcasted axes after multiplying with the other operand. In the example, dL/dB_k = A^T @ dL/dC_k, and if B was broadcasted from shape (n, p) to (k, n, p), then dL/dB = sum over k of dL/dB_k.
State the general rule: for any broadcasted dimension, the gradient is summed over that dimension. The summation axes are exactly the axes that were expanded (size 1) in the forward pass.
Mention that in practice, deep learning frameworks handle this automatically via broadcasting semantics in autograd, but understanding the summation axes is crucial for debugging and custom implementations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This was the follow-up I felt least prepared for.
Start by explaining the tiled accumulation in matrix multiply and how a parallel prefix scan can replace sequential accumulation across tiles. Then discuss the conditions under which Hillis-Steele scan provides speedup, such as large numbers of tiles and sufficient parallelism, and when it doesn't, like small tile counts or when memory bandwidth is the bottleneck.
Pro tip: Emphasize that the scan's benefit depends on the ratio of tiles to available parallel resources; in practice, for typical matrix sizes, the overhead often outweighs gains, so it's crucial to profile before adopting.
Explain that matrix multiply is often tiled to improve cache locality, and accumulation across tiles is typically sequential. This sequential dependency limits parallelism.
Define Hillis-Steele scan as an inclusive scan that computes prefix sums in O(log n) steps with O(n log n) work, using parallel processors. It can compute all partial sums of tile contributions in parallel.
Show how to treat each tile's contribution as an element in a sequence, then use a parallel prefix scan to compute cumulative sums across tiles. This allows each tile's output to be computed independently once the scan is done.
Discuss scenarios where it helps: large number of tiles (e.g., many K-dimension tiles), abundant parallel hardware (many cores/threads), and when the scan's logarithmic depth reduces critical path. Also note it helps when tile contributions are independent and can be computed in parallel.
Discuss limitations: small number of tiles (overhead dominates), memory bandwidth bound (scan adds extra memory traffic), and when the sequential accumulation is already fast due to small K. Also note that scan increases total work (O(n log n) vs O(n)), which may not be worth it if parallelism is limited.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Short answer: Blelloch does O(n) work but needs two passes (reduce then downsweep), so it's better when work efficiency matters more than latency.
Start by contrasting the work and step complexity of Hillis-Steele and Blelloch scans, then explain that Blelloch is preferable when work efficiency is critical, such as on memory-constrained or throughput-oriented hardware. Discuss the tradeoff: Blelloch requires more steps (2n-1) and synchronization, making it less suitable for latency-sensitive or small-scale parallel systems.
Pro tip: Mention that in practice, hybrid approaches or using Blelloch for large arrays and Hillis-Steele for small arrays can balance work and step efficiency. Also, relate to ML: Blelloch is useful for parallelizing operations like prefix sums in attention mechanisms or gradient computations where work efficiency matters.
Briefly describe Hillis-Steele and Blelloch scans, highlighting their work and step complexities: Hillis-Steele O(n log n) work, O(log n) steps; Blelloch O(n) work, O(log n) steps but with more constant factors.
Explain scenarios where work efficiency is paramount: limited memory bandwidth, large n, throughput-oriented hardware (GPUs), or when energy efficiency is critical. Also, when the algorithm is part of a larger computation where total work dominates.
Highlight that Blelloch has higher step complexity (2n-1 steps vs. n log n? Actually, Blelloch has O(log n) steps but with two phases and more synchronization) and may have lower parallelism for small n. It also requires more complex implementation (up-sweep and down-sweep).
Connect to ML engineering: e.g., prefix sums in parallel algorithms for training (e.g., computing cumulative sums for attention or normalization), where work efficiency can reduce memory usage and improve scalability.
Summarize that choice depends on hardware, problem size, and whether latency or throughput is more important. Mention that often a hybrid or adaptive approach is used.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.