deepspeed inference,deployment
Microsoft's library for efficient LLM serving.
9,967 technical terms and definitions
Microsoft's library for efficient LLM serving.
Random walk-based graph embeddings.
# The Full Stack AI Build: A Comprehensive Analysis
## Overview
The 5-Layer AI Stack represents the complete vertical integration required to build frontier AI systems:
$$
\text{Energy} \rightarrow \text{Chips} \rightarrow \text{Infrastructure} \rightarrow \text{Models} \rightarrow \text{Applications}
$$
## Layer 1: Energy (Electricity)
The foundational constraint upon which all other layers depend.
### Key Metrics
- **Training Energy Consumption**: A frontier LLM requires approximately $50-100+ \text{ GWh}$
- **Power Usage Effectiveness (PUE)**:
$$
\text{PUE} = \frac{\text{Total Facility Energy}}{\text{IT Equipment Energy}}
$$
- **Target PUE**: $\text{PUE} \leq 1.2$ for modern AI data centers
### Critical Concerns
- Reliability and uptime requirements: $99.999\%$ availability
- Cost optimization: USD per kWh directly impacts training costs
- Carbon footprint: $\text{kg CO}_2/\text{kWh}$ varies by source
- Geographic availability constraints
### Energy Cost Model
$$
C_{\text{energy}} = P_{\text{peak}} \times T_{\text{training}} \times \text{PUE} \times \text{Cost}_{\text{kWh}}
$$
Where:
- $P_{\text{peak}}$ = Peak power consumption (MW)
- $T_{\text{training}}$ = Training duration (hours)
- $\text{Cost}_{\text{kWh}}$ = Energy cost per kilowatt-hour
## Layer 2: Chips
The computational substrate transforming electricity into useful operations.
### 2.1 Design Chips
#### Architecture Decisions
- **GPU vs TPU vs Custom ASIC**: Trade-offs in flexibility vs efficiency
- **Core compute unit**: Matrix multiplication engines
$$
C = A \times B \quad \text{where } A \in \mathbb{R}^{m \times k}, B \in \mathbb{R}^{k \times n}
$$
- **Operations count**:
$$
\text{FLOPs}_{\text{matmul}} = 2 \times m \times n \times k
$$
#### Memory Bandwidth Optimization
The real bottleneck for transformer models:
$$
\text{Arithmetic Intensity} = \frac{\text{FLOPs}}{\text{Bytes Accessed}}
$$
For transformers:
$$
\text{AI}_{\text{attention}} = \frac{2 \times n^2 \times d}{n^2 + 2nd} \approx O(d) \text{ (memory bound)}
$$
#### Numerical Precision Trade-offs
| Precision | Bits | Dynamic Range | Use Case |
|-----------|------|---------------|----------|
| FP32 | 32 | $\pm 3.4 \times 10^{38}$ | Reference |
| FP16 | 16 | $\pm 65504$ | Training |
| BF16 | 16 | $\pm 3.4 \times 10^{38}$ | Training |
| FP8 | 8 | $\pm 448$ (E4M3) | Inference |
| INT8 | 8 | $[-128, 127]$ | Quantized inference |
| INT4 | 4 | $[-8, 7]$ | Extreme quantization |
Quantization error bound:
$$
\|W - W_q\|_F \leq \frac{\Delta}{2}\sqrt{n}
$$
Where $\Delta$ is the quantization step size.
#### Power Efficiency
$$
\text{Efficiency} = \frac{\text{FLOPS}}{\text{Watt}} \quad [\text{FLOPS/W}]
$$
Modern targets:
- Training: $> 300 \text{ TFLOPS/chip}$ at $< 700\text{W}$
- Inference: $> 1000 \text{ TOPS/W}$ (INT8)
### 2.2 Wafer Fabrication
#### Process Technology
- **Transistor density**:
$$
D = \frac{N_{\text{transistors}}}{A_{\text{die}}} \quad [\text{transistors/mm}^2]
$$
- **Node progression**: $7\text{nm} \rightarrow 5\text{nm} \rightarrow 3\text{nm} \rightarrow 2\text{nm}$
#### Yield Optimization
Defect density model (Poisson):
$$
Y = e^{-D_0 \times A}
$$
Where:
- $Y$ = Yield (probability of good die)
- $D_0$ = Defect density (defects/cm²)
- $A$ = Die area (cm²)
#### Advanced Packaging
- **CoWoS** (Chip-on-Wafer-on-Substrate)
- **Chiplets**: Disaggregated design
- **3D Stacking**: HBM memory integration
Bandwidth scaling:
$$
\text{BW}_{\text{HBM3}} = N_{\text{stacks}} \times \text{BW}_{\text{per\_stack}} \approx 6 \times 819 = 4.9 \text{ TB/s}
$$
## Layer 3: Infrastructure
Systems layer orchestrating chips into usable compute.
### 3.1 Build AI Infrastructure
#### Cluster Architecture
- **Nodes per cluster**: $N_{\text{nodes}} = 1000-10000+$
- **GPUs per node**: $G_{\text{per\_node}} = 8$ (typical)
- **Total GPUs**:
$$
G_{\text{total}} = N_{\text{nodes}} \times G_{\text{per\_node}}
$$
#### Network Topology
**Fat-tree bandwidth**:
$$
\text{Bisection BW} = \frac{N \times \text{BW}_{\text{link}}}{2}
$$
**All-reduce communication cost**:
$$
T_{\text{all-reduce}} = 2(n-1) \times \frac{M}{n \times \text{BW}} + 2(n-1) \times \alpha
$$
Where:
- $M$ = Message size
- $n$ = Number of participants
- $\alpha$ = Latency per hop
#### Storage Requirements
Training data storage:
$$
S_{\text{data}} = N_{\text{tokens}} \times \text{bytes\_per\_token} \times \text{redundancy}
$$
For 10T tokens:
$$
S \approx 10^{13} \times 2 \times 3 = 60 \text{ PB}
$$
#### Reliability Engineering
**Checkpointing overhead**:
$$
\text{Overhead} = \frac{T_{\text{checkpoint}}}{T_{\text{checkpoint\_interval}}}
$$
**Mean Time Between Failures (MTBF)** for cluster:
$$
\text{MTBF}_{\text{cluster}} = \frac{\text{MTBF}_{\text{component}}}{N_{\text{components}}}
$$
## Layer 4: Models (LLMs)
Where core AI capability emerges.
### 4.1 Build Large Language Models
#### Transformer Architecture
**Self-attention mechanism**:
$$
\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V
$$
Where:
- $Q = XW_Q \in \mathbb{R}^{n \times d_k}$ (Queries)
- $K = XW_K \in \mathbb{R}^{n \times d_k}$ (Keys)
- $V = XW_V \in \mathbb{R}^{n \times d_v}$ (Values)
**Multi-Head Attention (MHA)**:
$$
\text{MHA}(X) = \text{Concat}(\text{head}_1, ..., \text{head}_h)W_O
$$
$$
\text{head}_i = \text{Attention}(XW_Q^i, XW_K^i, XW_V^i)
$$
**Grouped Query Attention (GQA)**:
Reduces KV cache by factor $g$:
$$
\text{KV\_cache} = 2 \times L \times n \times d \times \frac{h}{g} \times \text{bytes}
$$
#### Feed-Forward Network
$$
\text{FFN}(x) = \text{GELU}(xW_1 + b_1)W_2 + b_2
$$
SwiGLU variant:
$$
\text{SwiGLU}(x) = (\text{Swish}(xW_1) \odot xW_3)W_2
$$
#### Model Parameter Count
For decoder-only transformer:
$$
P = 12 \times L \times d^2 + V \times d
$$
Where:
- $L$ = Number of layers
- $d$ = Model dimension
- $V$ = Vocabulary size
#### Mixture of Experts (MoE)
$$
y = \sum_{i=1}^{N} G(x)_i \cdot E_i(x)
$$
Where $G(x)$ is the gating function:
$$
G(x) = \text{TopK}(\text{softmax}(xW_g))
$$
### 4.2 Pre-training
#### Training Objective
**Next-token prediction (autoregressive)**:
$$
\mathcal{L} = -\sum_{t=1}^{T} \log P(x_t | x_{
Defects per unit area.
Defect density maps visualize spatial distribution of defects across wafers identifying problem regions.
Spatial distribution of defects.
Defect density models like Poisson and negative binomial relate defect counts to die area predicting yield from defect measurements.
Number of defects per unit area affects yield.
Find and fix failure causes.
Automated optical or e-beam inspection to find particles scratches defects.
Rank defect types by frequency.
Defect Pareto analysis ranks defect types by frequency to prioritize yield improvement efforts on the most impactful defect categories.
Quality metric for shipped parts.
Fraction of units with defects.
High-resolution follow-up of detected defects.
Defect review classifies detected defects by type size and source enabling targeted process improvements.
Trace defects to source.
Flaw vs unit with flaw.
Defect waste produces nonconforming products requiring rework or scrap.
Making defective products.
Defect-level prediction estimates outgoing defect rate from fault coverage and defect density models.
Quality metric.
Layer multiple safety mechanisms for robustness.
Resolve "the X" references.
Three-level screening in few runs.
Remove molding flash.
Align with learned deformations.
Learn offset locations for attention.
Adapt sampling locations geometrically.
Models that can deform to fit data.
Deformation fields warp canonical representations to model non-rigid motion.
Doping so heavy Fermi level enters band.
Analyze partially degraded units.
Degraded mode operation continues at reduced capacity or performance during partial failure.
Train ViT efficiently with distillation.
Signal arrives too late.
Delay testing detects excessive path delays caused by parametric variations or defects using transition patterns.
Main agent delegates subtasks to specialized sub-agents.
Use special markers to separate sections.
Delta Lake adds ACID transactions to data lakes. Time travel, schema enforcement.
Delta-I noise results from rapid current changes flowing through power distribution inductance causing voltage transients on supply rails.
Demand control ventilation modulates outdoor air intake based on occupancy reducing conditioning loads.
Demand forecasting predicts future material requirements based on production schedules and market trends.
Build demos quickly to validate ideas. Prototypes get feedback. POC proves feasibility before full build.
Democratic co-learning trains multiple diverse models that teach each other through weighted voting on unlabeled examples.
Demographic parity requires equal positive prediction rates across groups.
Demographic parity: equal positive rates across groups. May conflict with accuracy. Choose metric carefully.
Model outputs same distribution for all demographic groups.
Demonstration retrieval searches example databases for relevant few-shot demonstrations.
Demonstration selection chooses optimal few-shot examples maximizing task performance.