Is matrix multiplication a Data flow?

 Data flow

patterson 5th edition solutions

6th ed

Yes — matrix multiplication can be a dataflow.
But only when it’s scheduled and streamed explicitly. Otherwise, it’s just a computation expressed as algebra.

Let’s unpack that cleanly.

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1. What “dataflow” actually means

A dataflow model means:

• Computation happens when data arrives

• Execution order is implicit, not controlled by instructions

• Data moves through fixed operators

• No global “program counter” deciding what runs next

Think:

• Assembly line

• Circuit

• Systolic array

Not:

• CPU/GPU issuing instructions dynamically

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2. Matrix multiplication as math vs execution

The math

$$C_{i,j} = \sum_k A_{i,k} \times B_{k,j}$$

This equation alone:

• ❌ is not dataflow

• It’s just a declarative relationship

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3. When matrix multiplication becomes a dataflow

Example: systolic array (TPU-style)

In a systolic array:

• A values flow horizontally

• B values flow vertically

• Multiply–accumulate units sit at intersections

• Partial sums flow diagonally or stay local

Here:

• Each MAC fires when inputs arrive

• No instruction fetch

• No cache lookups

• Timing is fixed

👉 That is pure dataflow.

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4. GPU matrix multiplication (usually not dataflow)

On GPUs:

• Threads are scheduled dynamically

• Data is pulled from memory

• Caches hide latency

• Execution order depends on warps and occupancy

Even with Tensor Cores:

• Control is still instruction-driven

• Memory access is demand-based

So:

• ⚠️ Mathematically data-parallel

• ❌ Architecturally not dataflow

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5. Compiler-defined dataflow (Groq-style)

Here’s the subtle but important case:

• Compiler builds a static graph

• Every multiply, add, and move is scheduled

• Buffers and wires are fixed

• No runtime decisions

Matrix multiply here:

• Is unrolled

• Placed spatially

• Timed explicitly

This is dataflow even without a systolic array.

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6. The litmus test (easy rule)

Ask this:

Does the compute wait for data, or does data wait for compute?

Model	Answer	Dataflow?
CPU	Data waits	❌
GPU	Mostly data waits	❌
TPU systolic	Compute waits	✅
Groq LPU	Compute waits	✅

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7. Why this matters for inference

Inference:

• Has known shapes

• Has static weights

• Has repeatable access patterns

So matrix multiplication during inference:

• Can be compiled into dataflow

• Should be, if you want determinism and efficiency

Training:

• Dynamic shapes

• Backprop

• Irregular access

So:

• Needs instruction-driven hardware

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Final answer (tight)

Matrix multiplication is not inherently dataflow — but it becomes dataflow when mapped onto hardware with fixed, data-triggered execution (like systolic arrays or compiler-scheduled accelerators).

That distinction is the fault line between:

• GPUs (general, flexible)

• LPUs / TPUs (specialized, deterministic)