Lissafin Kuskuren Ƙididdigewa da aka Tabbatar don Matsa Tsarin Ƙirar Sadarwar Jijiya

1. Gabatarwa

Matsa tsarin ƙirar sadarwar jijiya yana magance ƙalubalen lissafi na zurfin hanyoyin sadarwar jijiya akan na'urori da aka saka a cikin tsarin masana'antu. Girman girma mai nisa a cikin rikitarwar hanyar sadarwar jijiya yana haifar da nauyin lissafi mai mahimmanci, kamar yadda aka tabbatar da Tsarin Transformer yana buƙatar sa'o'i 274,120 na horo akan GPU 8 na NVIDIA P100. Dabarun ƙididdigewa suna rage ƙaramin ƙafar ƙwaƙwalwar ajiya ta hanyar rage daidaiton bit na ma'auni da kunnawa, amma suna gabatar da saɓanin aiki waɗanda ke buƙatar cikakken binciken kuskure.

2. Hanyar Aiki

2.1 Gina Cibiyar Sadarwar Jijiya da aka Haɗa

Babban ƙirƙira ya ƙunshi gina cibiyar sadarwar jijiya da aka haɗa wacce ta haɗa duka hanyar sadarwar jijiya ta asali da takwarorinta masu ƙididdigewa. Wannan gine-ginen yana ba da damar lissafin bambance-bambancen fitarwa kai tsake tsakanin hanyoyin sadarwa biyu, yana samar da tushe don iyakokin kuskure da aka tabbatar.

2.2 Binciken Isarwa

Aiwatar da hanyoyin da suka danganci ingantawa da binciken isarwa ga cibiyar sadarwar jijiya da aka haɗa yana ba da damar lissafin iyakokin kuskuren ƙididdigewa da aka tabbatar. Wannan hanyar tana ba da tabbaci na yau da kullun akan matsakaicin karkatwa tsakanin fitarwar hanyar sadarwa ta asali da ta ƙididdigewa.

3. Aiwatar da Fasaha

3.1 Tsarin Lissafi

Lissafin kuskuren ƙididdigewa ya dogara da dabarun tabbatarwa na yau da kullun. Idan aka ba da hanyar sadarwar jijiya ta asali $f(x)$ da sigar ƙididdigewa $f_q(x)$, hanyar sadarwa da aka haɗa tana lissafin:

$\Delta(x) = |f(x) - f_q(x)|$

Iyakar kuskure da aka tabbatar $\epsilon$ tana gamsar da:

$\forall x \in \mathcal{X}, \Delta(x) \leq \epsilon$

inda $\mathcal{X}$ ke wakiltar yankin shigarwa mai ban sha'awa.

3.2 Ƙirar Algorithm

Algorithm ɗin yana amfani da lissafin tazara da yaduwa ta alama ta cikin yadudduka na hanyar sadarwa don lissafin iyakokin fitarwa. Wannan hanyar ta ginu akan kafaffen tsarorin tabbatar da hanyar sadarwar jijiya kamar Marabou da ReluVal, amma tana magance kurakurai da ƙididdigewa ta haifar musamman.

4. Sakamakon Gwaji

Tabbacin lambobi yana nuna dacewar hanyar da tasirinta a duk faɗin gine-ginen hanyar sadarwa. Sakamakon gwaji ya nuna:

• Ƙididdigewa daga 32-bit zuwa 8-bit yana gabatar da iyakantattun kurakurai yawanci ƙasa da 5% don hanyoyin sadarwa masu kyawun horo
• Hanyar hanyar sadarwa da aka haɗa tana rage lokacin lissafi da 40% idan aka kwatanta da binciken hanyar sadarwa daban
• Tabbacin na yau da kullun yana ba da kwarin gwiwa don aikace-aikacen da suka danganci aminci

5. Aiwatar da Lambar

import torch
import torch.nn as nn

class MergedNetwork(nn.Module):
    def __init__(self, original_net, quantized_net):
        super().__init__()
        self.original = original_net
        self.quantized = quantized_net
        
    def forward(self, x):
        out_original = self.original(x)
        out_quantized = self.quantized(x)
        error = torch.abs(out_original - out_quantized)
        max_error = torch.max(error)
        return max_error

# Reachability analysis implementation
def compute_guaranteed_error(merged_net, input_bounds):
    """Compute guaranteed error bounds using interval propagation"""
    # Implementation of interval arithmetic through network layers
    lower_bounds, upper_bounds = input_bounds
    
    # Propagate bounds through each layer
    for layer in merged_net.layers:
        if isinstance(layer, nn.Linear):
            # Interval matrix multiplication
            weight = layer.weight
            bias = layer.bias
            center = (upper_bounds + lower_bounds) / 2
            radius = (upper_bounds - lower_bounds) / 2
            
            new_center = torch.matmul(center, weight.T) + bias
            new_radius = torch.matmul(radius, torch.abs(weight.T))
            
            lower_bounds = new_center - new_radius
            upper_bounds = new_center + new_radius
            
    return upper_bounds[-1]  # Maximum error bound

6. Aikace-aikacen Gaba

Hanyar lissafin kuskure da aka tabbatar tana da muhimman tasiri ga:

• Tsarin Mulkin Kai: Aikace-aikacen da suka danganci aminci waɗanda ke buƙatar tabbaci na yau da kullun akan aikin tsarin da aka matsa
• Gefen AI: Tura matsanan tsare-tsare akan na'urori masu ƙunci mai ƙarfi tare da tabbacin aiki
• Hoton Magani: Kiyaye daidaiton bincike yayin rage buƙatun lissafi
• Masana'antu IoT: Ƙididdiga na ainihin-lokaci akan tsarin da aka saka tare da iyakantattun haƙuri na kuskure

7. Nassoshi

1. He, K., et al. "Koyo mai zurfi na ragowar don Gane Hoton." CVPR 2016.
2. Jacob, B., et al. "Ƙididdigewa da Horar da Hanyoyin Sadarwar Jijiya don Ƙididdiga Mai Tasiri Kawai." CVPR 2018.
3. Katz, G., et al. "Tsarin Marabou don Tabbatarwa da Binciken Zurfin Hanyoyin Sadarwar Jijiya." CAV 2019.
4. Zhu, J.Y., et al. "Fassarar Hoton-zuwa-Hoto mara Biyu ta amfani da Cibiyoyin Sadarwar Masu Adawa da Zagayowar." ICCV 2017.
5. Wang, J., et al. "HAQ: Kayan Aiki-Mai wayo Automated Ƙididdigewa." CVPR 2019.
6. Krishnamoorthi, R. "Ƙididdigar zurfin hanyoyin sadarwa masu haɗawa don ƙididdiga mai tasiri: Takarda fari." arXiv:1806.08342.

8. Binciken Kwararre