Exynos 2400 NPU

1. Executive Summary

This document provides a comprehensive technical analysis of Samsung's Exynos 2400 Neural Processing Unit (NPU), featuring a heterogeneous architecture optimized for on-device generative AI workloads. The NPU achieves 3.48 TOPS/mm² area efficiency through innovative memory hierarchy design, thermal management solutions, and specialized processing engines.

2. 1. Architecture Overview and Mathematical Foundation

2.1 1.1 Heterogeneous Processing Architecture

The NPU implements a heterogeneous computing paradigm consisting of:

Processing Units Configuration:

• General Tensor Engine (GTE): $N_{MAC,GTE}=8,192$ MAC units
• Shallow Tensor Engine (STE): $N_{MAC,STE}=512$ MAC units
• Vector Engines (VE): $N_{VE}=4\times 32$-way SIMD units
• Total MAC Units: $N_{MAC,total}=2\times N_{MAC,GTE}+2\times N_{MAC,STE}=2\times 8,192+2\times 512=17,408$ MAC units

Memory Hierarchy:

• NPUMEM: $M_{shared}=6$ MB shared scratchpad memory
• L1 Q-cacheQ-cache (Queuing Cache): Specialized cache that reduces miss penalties using predetermined access patterns. Features temporal decoupling, queue-based management, and predictive eviction. Enables latency hiding without complex scheduling - perfect for NPU workloads with predictable access patterns.: $M_{L1}$ per engine with queuing mechanism
• L0 Q-cache: $M_{L0}$ per engine for immediate data access

2.2 1.2 Computational Complexity Analysis

Traditional CNN Operations: For a convolution layer with input dimensions $(H_{in},W_{in},C_{in})$ and kernel $(K_h,K_w,C_{out})$:

$MA{C}_{operations}=H_{out}\times W_{out}\times C_{out}\times K_h\times K_w\times C_{in}$

Where: $H_{out}=\frac{H_{in}-K_h+2P}{S}+1$, $W_{out}=\frac{W_{in}-K_w+2P}{S}+1$

Transformer-based Operations: For self-attention mechanism with sequence length $N$ and hidden dimension $d$:

$MA{C}_{attention}=3\times N\times d^2\text{ (Q,K,V projections)}+N^2\times d\text{ (attention computation)}$

LLM Token Generation: Memory bandwidth requirement per token: $B{W}_{required}=\frac{W_{model}}{t_{generation}}$ Where $W_{model}$ = model weight size (GB), $t_{generation}$ = time per token generation

3. 2. Memory Optimization and Q-Cache Mathematics

3.1 2.1 Queue-Based Cache Design

Traditional Cache Hit Rate: $Hi{t}_{rat{e}_{traditional}}={\sum }_i(P_i\times H_i)\text{ for }i\in cache\_lines$

Q-Cache Hit Rate Enhancement: The Q-cache leverages predetermined access patterns: $Hi{t}_{rat{e}_{qcache}}=Hi{t}_{rat{e}_{base}}+{\Delta }_{prefetch}+{\Delta }_{locality}$

Where:

• ${\Delta }_{prefetch}$: Improvement from predictive prefetching
• ${\Delta }_{locality}$: Improvement from understanding temporal/spatial locality

Prefetch Efficiency: $Efficienc{y}_{prefetch}=\frac{T_{miss}-T_{prefetch}}{T_{miss}}\times 100\%$

Where $T_{miss}$ = cache miss penalty, $T_{prefetch}$ = prefetch latency

3.2 2.2 Memory Access Pattern Optimization

Data Reuse Factor Calculation: For a given tile size and memory hierarchy: $Reus{e}_{factor}=\frac{Total\_data\_accessed}{Data\_loaded\_from\_external\_memory}$

Bandwidth Utilization: $B{W}_{utilization}=\frac{MA{C}_{operations}\times Precision}{B{W}_{available}\times Tim{e}_{execution}}$

Memory Efficiency Metric: $Memor{y}_{efficiency}=Operations\_per\_byte=\frac{MA{C}_{ops}}{Bytes\_transferred}$

4. 3. Skewness Analysis and Tiling Mathematics

4.1 3.1 Skewness Definition and Calculation

Matrix Skewness: For matrices $A(M\times K)$ and $B(K\times N)$: $Skewness=\frac{\max (M\times K,K\times N)}{\min (M\times K,K\times N)}$

Minimum Reuse Factor: $Reus{e}_{min}=\frac{B{W}_{input}}{B{W}_{output}}$

Where $B{W}_{input}$ and $B{W}_{output}$ are the bandwidth requirements for input and output data flows.

4.2 3.2 Three-Dimensional Optimization Framework

Memory Constraint Equation: $M_{tile}\le M_{available}$

Where: $M_{tile}=M_{input}+M_{weight}+M_{output}+M_{intermediate}$

$M_{tile}=(H_{tile}\times W_{tile}\times C_{in})+(K_h\times K_w\times C_{in}\times C_{out})+(H_{out}\times W_{out}\times C_{out})+M_{buffer}$

Optimization Objective: $\text{maximize: }Reus{e}_{factor}(H_{tile},W_{tile},C_{tile})$

$\text{subject to: }{M}_{tile}\le M_{budget}$

$H_{tile}\le H_{max},W_{tile}\le W_{max},C_{tile}\le C_{max}$

Greedy TilingAdvanced Tiling: Hierarchical L2/L1 approach where L2 tiles fit 6MB NPUMEM and L1 tiles optimize Q-cache usage. Enables tile-level pipelining between TEs and VEs, with engine-specific optimizations (GTE for compute-intensive, STE for memory-intensive operations). Algorithm:

for each tiling iteration:
    candidates = {tile_H/2, tile_W/2, tile_C/2}
    select argmax(Reuse_factor(candidate)) 
    update tile_size

5. 4. Performance Analysis and Calculations

5.1 4.1 Throughput Calculations

Peak Theoretical Performance: $TOP{S}_{theoretical}=N_{MAC,total}\times f_{clock}\times 2\times 10^{-12}$

Where $f_{clock}$ = maximum frequency (1,196 MHz) $TOP{S}_{theoretical}=17,408\times 1.196\times 10^9\times 2\times 10^{-12}=41.64\text{ TOPS}$

Area Efficiency: $Are{a}_{efficiency}=\frac{TOP{S}_{measured}}{Are{a}_{die}}=\frac{41.64\text{ TOPS}}{12{\text{ mm}}^2}=3.47{\text{ TOPS/mm}}^2$

Measured Performance (1,196 MHz):

• MobileNetEdgeTPU: $Performanc{e}_{new}=1.81\times Performanc{e}_{baseline}$
• MobileDet: $Performanc{e}_{new}=2.37\times Performanc{e}_{baseline}$
• Mosaic: $Performanc{e}_{new}=2.65\times Performanc{e}_{baseline}$

5.2 4.2 Memory Bandwidth Analysis

Required Memory Bandwidth: $B{W}_{required}=\frac{Input\_data+Weight\_data+Output\_data}{Execution\_time}$

For EDSR Network: $Throughpu{t}_{EDSR}=140.3\text{ inferences/second}$

$B{W}_{effective}=Data\_per\_inference\times Throughpu{t}_{EDSR}$

For LVM U-net: $Throughpu{t}_{Unet}=8.3\text{ inferences/second}$

$Model\_complexit{y}_{Unet}>Model\_complexit{y}_{EDSR}\text{ (due to lower throughput)}$

6. 5. Thermal Management and Packaging Analysis

6.1 5.1 Thermal Resistance Calculations

Junction Temperature Equation: $T_{junction}=T_{ambient}+P_{dissipated}\times R_{thermal}$

Thermal Resistance Improvement: $R_{thermal,FOWLP}=13.83°C/W$

$R_{thermal,I-PoP}=16.52°C/W$

$Improvement=\frac{16.52-13.83}{16.52}\times 100\%=16.3\%$

Power Density: $Powe{r}_{density}=\frac{P_{total}}{Are{a}_{die}}=\frac{P_{total}}{12{\text{ mm}}^2}$

6.2 5.2 Process Technology Impact

3rd Generation 4nm Improvements: $Performanc{e}_{gai{n}_{RO}}=11\%\text{ (Ring Oscillator frequency improvement)}$

Effective Capacitance Reduction: $C_{eff,new}=C_{eff,old}\times (1-{\alpha }_{improvement})$

Resistance Reduction: $R_{eff,new}=R_{eff,old}\times (1-{\beta }_{improvement})$

Combined Performance Impact: $f_{max,new}=f_{max,old}\times (1+0.11)\times (1+{\gamma }_{thermal})=f_{max,old}\times 1.30$

Where ${\gamma }_{thermal}=19\%$ improvement from FOWLP thermal enhancement.

6.3 5.3 Dynamic Thermal Management

Frequency Scaling Equation: $f_{scaled}=f_{max}\times \frac{T_{max}-T_{current}}{T_{max}-T_{ambient}}$

Power-Performance Relationship: $P_{dynamic}=\alpha \times C_{load}\times V_{dd}^2\times f_{clock}$

Where $\alpha$ = switching activity factor, $C_{load}$ = load capacitance

7. 6. Energy Efficiency and Power Analysis

7.1 6.1 Power Consumption Modeling

Dynamic Power: $P_{dynamic}={\sum }_i(N_{MAC,i}\times f_i\times V_i^2\times {\alpha }_i\times C_i)$

For each processing engine type $i$.

Static Power: $P_{static}=V_{dd}\times I_{leakage}$

Total Power: $P_{total}=P_{dynamic}+P_{static}+P_{io}$

7.2 6.2 Energy per Operation

Energy per MAC Operation: $E_{MAC}=\frac{P_{average}}{MA{C}_{utilization}\times f_{clock}\times N_{MAC,active}}$

Energy per Inference: $E_{inference}=P_{average}\times t_{inference}$

Comparison with Previous Generation: $Efficienc{y}_{improvement}=\frac{E_{per\_op,2200}}{E_{per\_op,2400}}$

8. 7. Mathematical Verification and Benchmarking

8.1 7.1 MLPerf Performance Verification

Normalized Performance Score: $Scor{e}_{normalized}=\frac{Operations\_per\_second}{Reference\_implementation}$

Efficiency Metrics: $Operations\_per\_Watt=\frac{TOP{S}_{measured}}{P_{measured}}$

$Operations\_per\_m{m}^2=\frac{TOP{S}_{measured}}{Are{a}_{die}}$

8.2 7.2 Memory Hierarchy Validation

Cache Hit Rate Measurement: $Hi{t}_{rate}=\frac{Cache\_hits}{Cache\_hits+Cache\_misses}$

Average Memory Access Time: $AMAT=Hi{t}_{time}+Mis{s}_{rate}\times Mis{s}_{penalty}$

Memory Wall Mitigation Factor: $Mitigatio{n}_{factor}=\frac{AMA{T}_{baseline}}{AMA{T}_{optimized}}$

9. 8. Workload-Specific Analysis

9.1 8.1 Large Language Model Optimization

Token Generation Rate: $Tokens\_per\_second=\frac{f_{effective}}{Cycles\_per\_token}$

Memory Bandwidth Utilization: $B{W}_{utilization\_LLM}=\frac{Model\_size\times Tokens\_per\_second}{B{W}_{available}}$

9.2 8.2 Large Visual Model Performance

Image Generation Throughput: For Stable Diffusion U-net: $Images\_per\_second=8.3\text{ (measured)}$

$Cycles\_per\_image=\frac{f_{clock}}{Images\_per\_second}=\frac{1.196\times 10^9}{8.3}=1.44\times 10^8\text{ cycles}$

Computational Intensity: $Intensity=\frac{Operations\_per\_image}{Bytes\_per\_image}$

10. 9. Comparative Analysis and Industry Position

10.1 9.1 Performance Density Comparison

Area Efficiency Benchmark: $Efficienc{y}_{ratio}=\frac{TOPS\_per\_m{m}_{Samsung}^2}{TOPS\_per\_m{m}_{competitor}^2}$

Power Efficiency: $TOPS\_per\_Watt=\frac{Peak\_TOPS}{TDP}$

10.2 9.2 Technology Scaling Benefits

Process Node Advantage: $Transistor\_densit{y}_{4nm}=2\times Transistor\_densit{y}_{5nm}\text{ (approximate)}$

$Performance\_per\_area\_gain\approx 1.4\times \text{ (considering design optimizations)}$

11. 10. Future Implications and Technology Roadmap

11.1 10.1 Scalability Analysis

Next Generation Projections: $TOP{S}_{3nm}\approx TOP{S}_{4nm}\times 1.5\text{ (process scaling)}$

$Efficienc{y}_{3nm}\approx Efficienc{y}_{4nm}\times 1.3\text{ (architectural improvements)}$

11.2 10.2 Emerging Workload Considerations

Multi-modal AI Requirements: $B{W}_{multimodal}=B{W}_{text}+B{W}_{image}+B{W}_{audio}+B{W}_{synchronization}$

Real-time Constraints: $Latenc{y}_{total}=Latenc{y}_{compute}+Latenc{y}_{memory}+Latenc{y}_{communication}\le Latenc{y}_{budget}$

12. Conclusion

The Samsung Exynos 2400 NPU represents a significant advancement in mobile AI processing, achieving 3.48 TOPS/mm² through innovative heterogeneous architecture, advanced memory hierarchy with Q-caches, and superior thermal management via FOWLP packaging. The mathematical analysis reveals optimized data flow patterns, efficient resource utilization, and substantial performance improvements over previous generations.

Key Mathematical Results:

• 41.64 TOPS theoretical peak performance
• 16.3% thermal resistance improvement
• 30% frequency improvement through combined process and packaging enhancements
• 2.37× average performance improvement across benchmarks

This NPU enables sophisticated on-device generative AI applications while maintaining mobile power constraints and thermal limits.

13. References

[1] A. Vaswani, et al., "Attention Is All You Need", NeurIPS, 2017. [2] A. Dubey, et al., "The Llama3 Herd of Models", ArXiv, 2024. [3] R. Rombach, et al., "High-resolution image synthesis with latent diffusion models", ArXiv, 2021. [4] J.R. Stevens, et al., "Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers", DAC, 2021.

Document compiled from "An On-Device Generative AI Focused Neural Processing Unit in 4nm Flagship Mobile SoC with Fan-Out Wafer-Level Package" by Park et al., IEEE ISSCC 2025.