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Applied intuition·Machine Learning Engineer·Onsite - System Design / Architecture·Senior

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May 2026

Summary

Applied Intuition ML engineer interview, system design round focused entirely on KV caching for transformer inference. Pretty deep technically, they wanted actual tensor shapes and API signatures, not just hand-waving about attention.

Questions Asked (3)

Q1

Design and implement a key-value caching system for autoregressive inference in a Transformer decoder. Include tensor shapes, a per-layer cache API that works across decoding steps and batched inputs, memory limit handling, and support for both greedy and beam search.

System DesignTechnical Trade-offsAlgorithms & Data Structures
Author's notes

This one took me a minute to scope properly.

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AI HintsAI Generated

Suggested Approach

Start by explaining the purpose of KV caching in autoregressive decoding and the core data structures involved. Then walk through the per-layer cache API, covering tensor shapes, batched inputs, and memory management. Finally, discuss how the cache integrates with greedy and beam search, highlighting trade-offs and optimizations.

Pro tip: Emphasize that the cache should be pre-allocated to the maximum sequence length to avoid dynamic memory allocation during decoding, which is critical for latency-sensitive inference. Also, mention that beam search requires careful handling of cache reordering to maintain correct associations between beams and cached keys/values.

1. Clarify requirements and constraints

Ask about expected sequence lengths, batch sizes, memory limits, and whether the system needs to support multiple concurrent requests. This sets the stage for design decisions.

2. Design the cache data structure and API

Define a per-layer cache that stores keys and values tensors. Specify shapes: for a batch of size B, H attention heads, and head dimension D, each cache tensor is [B, H, max_seq_len, D]. Provide methods like update (to append new keys/values) and get (to retrieve the full cache).

3. Handle batched inputs and decoding steps

Explain how the cache is updated incrementally: at each decoding step, new keys/values of shape [B, H, 1, D] are computed and appended to the cache. The attention mechanism then uses the entire cached keys/values up to the current step.

4. Implement memory limit handling

Discuss strategies such as pre-allocating to max length, using a circular buffer for sliding window attention, or evicting old entries. Mention trade-offs between memory usage and recomputation.

5. Support greedy and beam search

For greedy, the cache is straightforward. For beam search, maintain a separate cache per beam and reorder them when beams are pruned or expanded. Explain how to efficiently copy or index into the cache to avoid unnecessary memory duplication.

Key Points to Mention

  • Tensor shapes: keys and values per layer are [batch_size, num_heads, seq_len, head_dim].
  • Incremental update: at each step, append new key/value of shape [batch_size, num_heads, 1, head_dim].
  • Memory management: pre-allocate to max sequence length, use sliding window or eviction policies for long sequences.
  • Beam search: maintain per-beam caches and reorder them based on beam indices after each step.
  • Efficiency: avoid dynamic memory allocation during decoding; use in-place updates or pre-allocated buffers.
  • Integration: the cache is used in the attention computation to avoid recomputing keys/values for previous tokens.

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

Q2

Walk through the complexity analysis and expected speedup of KV caching compared to full recomputation at each decoding step.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

Felt more comfortable here.

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AI HintsAI Generated

Suggested Approach

Start by defining the problem: autoregressive decoding where each step predicts the next token. Then contrast the naive full recomputation approach with KV caching, deriving the time complexity for each and highlighting the quadratic vs linear scaling. Conclude with the expected speedup and practical implications.

Pro tip: Quantify the speedup in terms of sequence length L: full recomputation is O(L^2) per step, KV caching is O(L) per step, so the speedup grows linearly with L. Mention that memory becomes the bottleneck, not compute, and that this trade-off is why techniques like PagedAttention exist.

1. Define the decoding process

Explain that autoregressive decoding generates one token at a time, and at each step the model computes attention over all previously generated tokens.

2. Analyze full recomputation

Show that without caching, each decoding step recomputes key and value projections for all previous tokens, leading to O(L^2) time per step and O(L^3) total for generating L tokens.

3. Introduce KV caching

Describe how caching stores the key and value tensors from previous steps, so each new step only computes projections for the new token and attends to cached keys/values.

4. Derive complexity with KV cache

Show that with caching, each step is O(L) for attention (since it attends to L cached tokens) and O(1) for projections, leading to O(L^2) total for generating L tokens.

5. Compare and quantify speedup

Contrast the per-step and total complexities, concluding that KV caching reduces per-step time from O(L^2) to O(L), yielding a speedup factor of O(L) per step and O(L) overall.

Key Points to Mention

  • Autoregressive decoding generates tokens sequentially, each depending on all previous tokens.
  • Full recomputation recomputes key/value projections for all tokens at every step, causing quadratic per-step cost.
  • KV caching stores key/value tensors from previous steps, avoiding redundant computation.
  • With KV caching, per-step attention cost is linear in sequence length, and total generation cost is quadratic instead of cubic.
  • The speedup is proportional to sequence length L, making it crucial for long sequences.
  • Memory usage grows linearly with sequence length, introducing a trade-off between speed and memory.

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

Q3

How would you test correctness of the KV cache implementation, particularly for edge cases like an end-of-sequence token appearing in the middle of a batch?

System DesignTechnical Trade-offs
Author's notes

Blanked a little.

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AI HintsAI Generated

Suggested Approach

Start by defining what 'correctness' means for a KV cache—it must produce identical outputs to a no-cache baseline for all sequences, including those with EOS tokens mid-batch. Then outline a testing strategy that combines unit tests for edge cases, integration tests with real models, and property-based tests to cover the combinatorial space of batch compositions and sequence lengths.

Pro tip: Emphasize that you would test with a reference implementation (e.g., a naive forward pass without cache) and use differential testing to catch subtle bugs, especially around EOS handling where attention masks and position IDs can easily go wrong.

1. Define Correctness Criteria

Establish that the KV cache must yield bitwise-identical (or within tolerance) outputs to a no-cache baseline for any input sequence, including those with EOS tokens in the middle of a batch. Specify that EOS tokens should not affect subsequent tokens' computations in other sequences.

2. Design Edge Case Tests

Create test cases with EOS tokens at various positions: beginning, middle, end, and multiple EOS tokens. Include batches where some sequences have EOS and others don't, and vary sequence lengths to test padding and masking.

3. Implement Differential Testing

Run the same inputs through a reference implementation (no cache) and the cached implementation, comparing outputs at each step. Use random input generation to cover a wide range of scenarios.

4. Validate Internal State

Inspect the KV cache contents (keys and values) to ensure they are correctly updated and not polluted by EOS tokens from other sequences. Check that attention masks properly ignore EOS tokens for subsequent steps.

5. Stress Test and Monitor

Test with large batches, long sequences, and mixed EOS positions to uncover race conditions or memory issues. Add assertions and logging to catch anomalies during inference.

Key Points to Mention

  • Attention mask handling: ensure EOS tokens are masked appropriately so they don't influence other tokens' attention.
  • Position ID management: EOS tokens should not shift position IDs for subsequent tokens in other sequences.
  • Batch independence: each sequence's cache should be isolated; EOS in one sequence must not affect others.
  • Cache eviction/update: when EOS is encountered, the cache for that sequence should stop updating or be handled per model semantics.
  • Numerical stability: compare outputs with tolerance to account for floating-point differences.
  • Performance overhead: ensure testing doesn't introduce significant slowdown, and cache correctness doesn't degrade with optimizations like paged attention.

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