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 $(K_h, K_w, C_{out})$:

$MAC_{operations} = H_{out} \times W_{out} \times C_{out} \times K_h \times K_w \times C_{in}$

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 $d$:

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

LLM Token Generation: Memory bandwidth requirement per token: $BW_{required} = \frac{W_{model}}{t_{generation}}$ 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: $Hit_{rate_{traditional}} = \sum_{i}(P_i \times H_i) \text{ for } i \in cache\_lines$

Q-Cache Hit Rate Enhancement: The Q-cache leverages predetermined access patterns: $Hit_{rate_{qcache}} = Hit_{rate_{base}} + \Delta_{prefetch} + \Delta_{locality}$

Where:

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

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

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: $Reuse_{factor} = \frac{Total\_data\_accessed}{Data\_loaded\_from\_external\_memory}$

Bandwidth Utilization: $BW_{utilization} = \frac{MAC_{operations} \times Precision}{BW_{available} \times Time_{execution}}$

Memory Efficiency Metric: $Memory_{efficiency} = Operations\_per\_byte = \frac{MAC_{ops}}{Bytes\_transferred}$

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: $Reuse_{min} = \frac{BW_{input}}{BW_{output}}$

Where $BW_{input}$ and $BW_{output}$ are the bandwidth requirements for input and output data flows.

4.2 3.2 Three-Dimensional Optimization Framework

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

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: $\text{maximize: } Reuse_{factor}(H_{tile}, W_{tile}, C_{tile})$ $\text{subject to: } M_{tile} \leq M_{budget}$ $H_{tile} \leq H_{max}, W_{tile} \leq W_{max}, C_{tile} \leq C_{max}$

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: $TOPS_{theoretical} = N_{MAC,total} \times f_{clock} \times 2 \times 10^{-12}$

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

Area Efficiency: $Area_{efficiency} = \frac{TOPS_{measured}}{Area_{die}} = \frac{41.64 \text{ TOPS}}{12 \text{ mm}^2} = 3.47 \text{ TOPS/mm}^2$

Measured Performance (1,196 MHz):

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

5.2 4.2 Memory Bandwidth Analysis

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

For EDSR Network: $Throughput_{EDSR} = 140.3 \text{ inferences/second}$ $BW_{effective} = Data\_per\_inference \times Throughput_{EDSR}$

For LVM U-net: $Throughput_{Unet} = 8.3 \text{ inferences/second}$ $Model\_complexity_{Unet} > Model\_complexity_{EDSR} \text{ (due to lower throughput)}$

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: $Power_{density} = \frac{P_{total}}{Area_{die}} = \frac{P_{total}}{12 \text{ mm}^2}$

6.2 5.2 Process Technology Impact

3rd Generation 4nm Improvements: $Performance_{gain_{RO}} = 11\% \text{ (Ring Oscillator frequency improvement)}$

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: $E_{MAC} = \frac{P_{average}}{MAC_{utilization} \times f_{clock} \times N_{MAC,active}}$

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

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

8. 7. Mathematical Verification and Benchmarking

8.1 7.1 MLPerf Performance Verification

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

Efficiency Metrics: $Operations\_per\_Watt = \frac{TOPS_{measured}}{P_{measured}}$ $Operations\_per\_mm^2 = \frac{TOPS_{measured}}{Area_{die}}$

8.2 7.2 Memory Hierarchy Validation

Cache Hit Rate Measurement: $Hit_{rate} = \frac{Cache\_hits}{Cache\_hits + Cache\_misses}$

Average Memory Access Time: $AMAT = Hit_{time} + Miss_{rate} \times Miss_{penalty}$

Memory Wall Mitigation Factor: $Mitigation_{factor} = \frac{AMAT_{baseline}}{AMAT_{optimized}}$

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: $BW_{utilization\_LLM} = \frac{Model\_size \times Tokens\_per\_second}{BW_{available}}$

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: $Efficiency_{ratio} = \frac{TOPS\_per\_mm^2_{Samsung}}{TOPS\_per\_mm^2_{competitor}}$

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

10.2 9.2 Technology Scaling Benefits

Process Node Advantage: $Transistor\_density_{4nm} = 2 \times Transistor\_density_{5nm} \text{ (approximate)}$ $Performance\_per\_area\_gain \approx 1.4\times \text{ (considering design optimizations)}$

11. 10. Future Implications and Technology Roadmap

11.1 10.1 Scalability Analysis

Next Generation Projections: $TOPS_{3nm} \approx TOPS_{4nm} \times 1.5 \text{ (process scaling)}$ $Efficiency_{3nm} \approx Efficiency_{4nm} \times 1.3 \text{ (architectural improvements)}$

11.2 10.2 Emerging Workload Considerations

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

Real-time Constraints: $Latency_{total} = Latency_{compute} + Latency_{memory} + Latency_{communication} \leq Latency_{budget}$

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.