---
title: "Full-Stack Audit: LLaMA-70B Training"
subtitle: "One model, six domains, twelve walls --- a complete systems analysis in 60 seconds."
description: "Compose 6+ solvers across all six taxonomy domains to produce a holistic training analysis. Discover that the binding constraint is compute, but checkpoint overhead is the hidden cost."
categories: ["capstone", "advanced"]
---

## The Question

What does a **complete** systems analysis look like? No single solver captures the full
picture. Training a 70B-parameter model on 512 H100 GPUs involves compute walls, memory
walls, communication overhead, checkpoint I/O, energy costs, and carbon emissions ---
simultaneously. This tutorial traces all six taxonomy domains and exercises 12 of the 22
systems walls through a single workload.

::: {.callout-note}
## Prerequisites
Complete [Tutorial 0: Hello, Roofline](00_hello_roofline.qmd),
[Tutorial 1: The Memory Wall](01_memory_wall.qmd),
[Tutorial 6: Scaling to 1000 GPUs](06_scaling_1000_gpus.qmd), and
[Tutorial 9: Sensitivity Analysis](09_sensitivity.qmd). You should understand
roofline analysis, distributed training, and binding constraint identification.
:::

::: {.callout-note}
## What You Will Learn

- **Compose** six solver families across all taxonomy domains into a holistic analysis
- **Identify** which of the 22 systems walls bind for a real training workload
- **Quantify** the hidden costs: checkpoint overhead, carbon, water, and TCO
- **Produce** a summary table mapping domain -> solver -> binding wall
:::

::: {.callout-tip}
## Solver Quick Reference

This capstone uses solvers from all six domains. If you arrived via an accelerated
learning path, here is what each solver does:

| Solver | Domain | What It Computes |
|:-------|:-------|:-----------------|
| `SingleNodeModel` | Node | Roofline bottleneck, latency, throughput |
| `DataModel` | Data | Whether the data pipeline can sustain GPU demand |
| `ScalingModel` | Algorithm | Compute-optimal training budget (Chinchilla) |
| `DistributedModel` | Fleet | Communication overhead and scaling efficiency |
| `ReliabilityModel` | Fleet | Cluster MTBF and optimal checkpoint intervals |
| `EconomicsModel` | Ops | CapEx, OpEx, and total cost of ownership (TCO) |
| `SustainabilityModel` | Ops | Energy, carbon footprint, and water usage |
| `SensitivitySolver` | Analysis | Partial derivatives identifying the binding constraint |
| `SynthesisSolver` | Analysis | Minimum hardware specs from a latency target |
:::

::: {.callout-tip}
## Background: The Six Taxonomy Domains

The MLSys wall taxonomy organizes 22 systems walls into six domains:

| Domain | Walls | What It Covers |
|:-------|:------|:---------------|
| Node | 1--3 | Compute, memory capacity, memory bandwidth |
| Data | 8--10 | Storage throughput, data pipeline stalls |
| Algorithm | 11--13 | Scaling laws, compute-optimal training |
| Fleet | 14--16 | Communication, synchronization, reliability |
| Ops | 17--20 | TCO, energy, carbon, water, safety |
| Analysis | 21--22 | Sensitivity, inverse synthesis |

No single solver spans all six. The insight emerges from **composition**.
:::

---

## 1. Setup: Build the Fleet

We construct a 512-GPU training cluster: 64 DGX H100 nodes, 8 GPUs per node,
NVLink intra-node, InfiniBand NDR inter-node, powered by Quebec's hydroelectric grid.

```{python}
#| echo: false
#| output: false
import mlsysim  # installed via `pip install mlsysim` (see workflow)
import mlsysim
```

```python
import mlsysim
from mlsysim.systems.types import Fleet, Node, NetworkFabric
from mlsysim.core.constants import Q_
```

```{python}
from mlsysim.systems.types import Fleet, Node, NetworkFabric
from mlsysim.infra.registry import Grids
from mlsysim.core.constants import Q_, NVLINK_H100_BW, INFINIBAND_NDR_BW

model = mlsysim.Models.Language.Llama3_70B
h100 = mlsysim.Hardware.Cloud.H100

# Build the DGX H100 node: 8 GPUs connected by NVLink 4.0
node = Node(
    name="DGX H100",
    accelerator=h100,
    accelerators_per_node=8,
    intra_node_bw=NVLINK_H100_BW
)

# Build the cluster fabric: InfiniBand NDR (400 Gbps)
fabric = NetworkFabric(
    name="InfiniBand NDR",
    topology="fat-tree",
    bandwidth=INFINIBAND_NDR_BW
)

# Build the fleet: 64 nodes = 512 GPUs, Quebec grid
fleet = Fleet(
    name="Training Cluster",
    node=node,
    count=64,
    fabric=fabric,
    region=Grids.Quebec
)

from mlsysim.show import table, info, banner

info("Fleet Configuration",
     Model=f"{model.name} ({model.parameters.to('Bparam'):.1f~})",
     Fleet=f"{fleet.count} nodes x {node.accelerators_per_node} GPUs = {fleet.total_accelerators} GPUs",
     Intra_node=f"NVLink 4.0 ({NVLINK_H100_BW.to('GB/s'):.0f~})",
     Inter_node=f"IB NDR ({INFINIBAND_NDR_BW.to('Gbps'):.0f~})",
     Region=Grids.Quebec.name)
```

---

## 2. Node (Walls 1--3): Single-GPU Roofline

First, classify the per-GPU forward-backward pass. Is each GPU compute-bound or
memory-bound during training?

```{python}
from mlsysim import SingleNodeModel

node_solver = SingleNodeModel()
node_result = node_solver.solve(
    model=model, hardware=h100,
    batch_size=4, precision="fp16"
)

banner("Domain: Node (Walls 1-3)")
info(Bottleneck=node_result.bottleneck,
     Per_GPU_latency=node_result.latency.to('ms'),
     Throughput=f"{node_result.throughput:.0f} samples/s")
```

Training at batch size 4 per GPU puts us in the compute-bound regime --- unlike inference,
training has high arithmetic intensity due to the backward pass. Wall 1 (Compute) is the
binding constraint at the node level.

Compute-bound is good news --- it means the GPU is doing useful work, not waiting for data.
But can the data pipeline actually keep up with 512 GPUs demanding training samples?

---

## 3. Data (Walls 8--10): Can the Pipeline Keep Up?

The roofline tells us each GPU can consume data at a certain rate. But can the storage and
preprocessing pipeline actually deliver data that fast? If not, the GPUs stall --- and
"compute-bound" becomes a meaningless label.

```{python}
from mlsysim import DataModel

# Estimate data demand per step: 4 samples/GPU * 512 GPUs * 2048 tokens * 2 bytes ≈ 8 MB/step
# At ~1 step/sec, this is ~8 MB/s — tokenized text is compact
data_demand = Q_("8 MB/s")

data_solver = DataModel()
data_result = data_solver.solve(
    workload_data_rate=data_demand,
    hardware=h100
)

banner("Domain: Data (Walls 8-10)")
info(Data_demand=data_result.demand_bw,
     Data_supply=data_result.supply_bw,
     Utilization=f"{data_result.utilization:.1%}",
     Stalled=data_result.is_stalled,
     Bottleneck=data_result.bottleneck)
```

For text-based training, the data pipeline is rarely the bottleneck --- tokenized text
is compact. But for image or video training, this wall can dominate.

The data pipeline can keep up. The GPUs are compute-bound and well-fed. But are we
spending our compute budget wisely? A 30-day run on 512 GPUs is an enormous investment
--- the scaling laws tell us whether we are allocating it optimally.

---

## 4. Algorithm (Walls 11--13): Compute-Optimal Budget

Is our training budget compute-optimal? The Chinchilla scaling law says
D = 20P (tokens = 20x parameters) for optimal allocation.

```{python}
from mlsysim import ScalingModel

# MFU (Model FLOP Utilization): the fraction of peak hardware FLOP/s that goes
# to useful model computation (excluding communication, idle time, overhead).
# MFU = 0.4 means 40% of theoretical peak -- typical for large-scale LLM training.
# Published values: 0.30-0.45 (Llama-2/3), up to 0.50 (highly optimized runs).
# Compute budget: 512 GPUs * 989 TFLOPs * 30 days * 86400s * 0.4 MFU
gpu_flops = h100.compute.peak_flops.to("flop/s").magnitude
total_flops = 512 * gpu_flops * 30 * 86400 * 0.4
compute_budget = Q_(total_flops, "flop")

scaling_solver = ScalingModel()
scaling_result = scaling_solver.solve(
    compute_budget=compute_budget,
    target_model_size=model.parameters
)

banner("Domain: Algorithm (Walls 11-13)")
info(Compute_budget=compute_budget.to('EFLOP'),
     Optimal_tokens=f"{scaling_result.optimal_tokens.magnitude:.2e}",
     Tokens_per_parameter=f"{scaling_result.tokens_per_parameter:.1f}",
     Chinchilla_ratio=f"{'OVER' if scaling_result.tokens_per_parameter > 20 else 'UNDER'}-trained")
```

If the tokens-per-parameter ratio is significantly above or below 20, the training
budget is not optimally allocated. Over-training wastes compute; under-training wastes
model capacity.

So far, everything looks manageable: compute-bound GPUs, adequate data pipeline,
reasonable training budget. If we throw 512 GPUs at this, we should scale linearly,
right? The fleet-level analysis reveals what single-node reasoning misses.

---

## 5. Fleet (Walls 14--16): Communication and Reliability

The distributed solver models AllReduce overhead and pipeline bubbles.
The reliability solver computes cluster MTBF and optimal checkpoint intervals.

```{python}
from mlsysim import DistributedModel, ReliabilityModel

# 3D parallelism: TP=8 (within node), PP=1, DP=64
dist_solver = DistributedModel()
dist_result = dist_solver.solve(
    model=model, fleet=fleet,
    batch_size=2048, precision="fp16",
    tp_size=8, pp_size=1,
    overlap_comm=True, seq_len=2048
)

banner("Domain: Fleet (Walls 14-16)")
info(Scaling_efficiency=f"{dist_result.scaling_efficiency:.2%}",
     Step_latency=dist_result.step_latency_total.to('ms'),
     DP_comm_latency=dist_result.dp_communication_latency.to('ms'),
     TP_comm_latency=dist_result.tp_communication_latency.to('ms'),
     Bubble_fraction=f"{dist_result.bubble_fraction:.2%}")
```

```{python}
# Reliability: 30-day training job
rel_solver = ReliabilityModel()
rel_result = rel_solver.solve(
    fleet=fleet,
    job_duration_hours=30*24,
    checkpoint_time_s=120
)

info(Fleet_MTBF=rel_result.fleet_mtbf.to('hour'),
     Failure_probability=f"{rel_result.failure_probability:.2%}",
     Expected_failures=f"{rel_result.expected_failures:.1f}",
     Optimal_ckpt_interval=rel_result.optimal_checkpoint_interval.to('minute'))
```

At 512 GPUs, the cluster MTBF shrinks significantly. Checkpoint overhead becomes a
non-trivial fraction of wall-clock time --- this is the "hidden cost" that single-node
analysis misses entirely.

The reliability analysis tells us HOW OFTEN the cluster fails. But failures cost money ---
and so does the energy to keep 512 GPUs running for 30 days. The operational domain
quantifies these costs.

---

## 6. Ops (Walls 17--20): TCO, Energy, Carbon, Water

The economics solver combines CapEx, OpEx, and sustainability into a single financial model.

```{python}
from mlsysim import EconomicsModel, SustainabilityModel

# 30-day training run
econ_solver = EconomicsModel()
econ_result = econ_solver.solve(
    fleet=fleet,
    duration_days=30,
    grid=Grids.Quebec,
    mfu=0.4
)

banner("Domain: Ops (Walls 17-20)")
info(CapEx=f"${econ_result.capex_usd:,.0f}",
     OpEx_energy=f"${econ_result.opex_energy_usd:,.0f}",
     OpEx_maintenance=f"${econ_result.opex_maintenance_usd:,.0f}",
     Total_TCO=f"${econ_result.tco_usd:,.0f}")
```

```{python}
sust_solver = SustainabilityModel()
sust_result = sust_solver.solve(
    fleet=fleet,
    duration_days=30,
    datacenter=Grids.Quebec,
    mfu=0.4
)

info(IT_Energy=sust_result.it_energy_kwh.to('MWh'),
     Total_Energy_PUE=sust_result.total_energy_kwh.to('MWh'),
     Carbon_footprint=f"{sust_result.carbon_footprint_kg:.0f} kg CO2",
     Water_usage=f"{sust_result.water_usage_liters:.0f} liters",
     PUE=sust_result.pue,
     Region=sust_result.region_name)
```

Quebec's hydroelectric grid makes this one of the lowest-carbon training locations in the
world. The same run in Poland (coal-heavy grid) would produce dramatically more CO2 ---
infrastructure geography is a first-class engineering variable.

---

## 7. Analysis (Walls 21--22): Sensitivity and Synthesis

Finally, confirm the binding constraint and derive minimum hardware for a 14-day completion target.

```{python}
from mlsysim import SensitivitySolver, SynthesisSolver

# Sensitivity: confirm compute is the binding constraint for training
sens_solver = SensitivitySolver()
sens_result = sens_solver.solve(
    model=model, hardware=h100, precision="fp16"
)

banner("Domain: Analysis (Walls 21-22)")
info(Binding_constraint=sens_result.binding_constraint)

sens_rows = [[param, f"{val:+.4f}"] for param, val in sens_result.sensitivities.items()]
table(["Parameter", "Sensitivity"], sens_rows)
```

```{python}
# Synthesis: what per-GPU step latency is needed to finish in 14 days?
# Total training FLOPs / (N_GPUs * MFU * peak_FLOPS) = wall_clock_seconds
target_days = 14
target_seconds = target_days * 86400
# Per-GPU step target: total_steps * step_latency = target_seconds
# Approximate: we need each step to complete within a target latency
synth_solver = SynthesisSolver()
synth_result = synth_solver.solve(
    model=model,
    target_latency=Q_("200 ms"),   # per-GPU training step target
    precision="fp16"
)

info("Synthesis (200ms per-GPU training step target)",
     Required_BW=synth_result.required_bw.to('TB/s'),
     Required_FLOPS=synth_result.required_flops.to('TFLOPs/s'),
     Required_memory=synth_result.required_memory.to('GB'))
```

---

## 8. Summary Table: The Complete Picture

We have now traced a single workload through all six domains. Each solver answered one
question in isolation. But the systems engineer's job is synthesis: seeing the complete
picture at once. The table below is that picture --- and its most important property is
that no single row captures the full story.

```{python}
mtbf_hours = rel_result.fleet_mtbf.to('hour').magnitude
summary_rows = [
    ["Node",      "SingleNodeModel",      f"Bottleneck: {node_result.bottleneck}",              "Wall 1: Compute"],
    ["Data",      "DataModel",            f"Util: {data_result.utilization:.0%}",                "Not binding"],
    ["Algorithm", "ScalingModel",         f"Tok/param: {scaling_result.tokens_per_parameter:.0f}","Wall 11"],
    ["Fleet",     "DistributedModel",     f"Efficiency: {dist_result.scaling_efficiency:.0%}",   "Wall 14: Comm"],
    ["Fleet",     "ReliabilityModel",     f"MTBF: {mtbf_hours:.0f}h",                           "Wall 19: Ckpt"],
    ["Ops",       "EconomicsModel",       f"TCO: ${econ_result.tco_usd:,.0f}",                  "Wall 17: Cost"],
    ["Ops",       "SustainabilityModel",  f"CO2: {sust_result.carbon_footprint_kg:.0f} kg",     "Wall 18: Energy"],
    ["Analysis",  "SensitivitySolver",     f"Binding: {sens_result.binding_constraint}",         "Wall 21"],
]

table(["Domain", "Solver", "Key Metric", "Binding Wall"], summary_rows, "<<>>")
```

::: {.callout-important}
## Key Insight

**No single solver captures the full picture --- the systems view emerges from composition.**
This end-to-end trace exercises 12 of 22 walls through a single model. The per-GPU binding
constraint is compute (Wall 1), but the **hidden costs** only appear at fleet scale:
checkpoint overhead (Wall 19) consumes wall-clock time proportional to the MTBF-driven
checkpoint frequency, and infrastructure geography (Quebec vs. Poland) can change the
carbon footprint by 40x (as [Tutorial 7](07_geography.qmd) demonstrated). A complete
systems analysis is not one solver run --- it is the composition of all six domains.
:::

---

## Your Turn

::: {.callout-caution}
## Exercises

**Exercise 1: Predict before you compute.**
What if you train in Poland instead of Quebec? Before running code, predict how the
TCO and carbon footprint will change. (Hint: Poland's grid is coal-heavy with ~800 g
CO2/kWh vs. Quebec's ~20 g CO2/kWh, and Poland has a higher PUE.) Then re-run the
economics and sustainability solvers with `Grids.Poland` and compare. How close was
your prediction?

**Exercise 2: Double the cluster.**
Scale the fleet to 1024 GPUs (128 nodes). Re-run the distributed solver and reliability
solver. Does scaling efficiency hold? How does the MTBF change? At what cluster size does
the checkpoint overhead exceed 5% of wall-clock time?

**Exercise 3: Minimum viable cluster.**
What is the minimum cluster size to complete Llama-3 70B training in 14 days? Use the
scaling result to determine the required total FLOPS, then work backward to find the
number of H100 GPUs needed at 40% MFU. Verify with the distributed solver that the
communication overhead is acceptable at that scale.

**Exercise 4: Propose a design change.**
Using the full-stack analysis, identify the single highest-leverage change — hardware
upgrade, parallelism strategy, region change, or precision change — that would reduce
TCO by at least 20%. Re-run the relevant solvers with your proposed change and compute
the new TCO. *Write one paragraph justifying why this change has the largest impact,
referencing at least two domains from the summary table.*

**Self-check:** If the fleet MTBF is 4 hours and each checkpoint takes 2 minutes, what
fraction of wall-clock time is spent checkpointing? (Use the Young-Daly formula:
optimal interval = sqrt(2 * delta * MTBF).)
:::

---

## Key Takeaways

::: {.callout-tip}
## Summary

- **Composition is the method**: no single solver spans all six taxonomy domains; the
  systems view emerges only from composing 6+ solvers
- **Compute binds at the node level**, but checkpoint overhead and communication are the
  hidden costs at fleet scale
- **Infrastructure geography matters**: Quebec vs. Poland can change carbon footprint by
  40x and TCO by 20--30%
- **The summary table** is the deliverable: one row per domain, solver, key metric, and
  binding wall
- **12 of 22 walls** are exercised through a single model-fleet pair --- this is what a
  complete analysis looks like
:::

---

## Next Steps

- **[Sensitivity Analysis](09_sensitivity.qmd)** --- Dive deeper into the Analysis domain solvers
- **[GPU vs. Wafer-Scale](10_gpu_vs_wafer.qmd)** --- See how architecture shifts the binding wall
- **[Geography of AI](07_geography.qmd)** --- Explore how datacenter location changes sustainability
- **[The \$9 Million GPU](08_nine_million_dollar.qmd)** --- Deep dive into TCO modeling