2.2
تابع تلفات تعبیه. ما محدودیت های در بدست آوردن عملی مان را به روشی استاندارد با استفاده از تلفات hinge تبدیل می کنیم. تابع تلفات منتجه به صورت زیر است:
![](data:image/png;base64,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)
که در آن مجموع ها همه در طول سه گانه تعریف شده به صورت در محدودیت های (1-4) می باشند. حاشیه m می تواند برای انواع مختلف فاصله و یا حتی موارد مختلف، متفاوت باشد. اما برای اینکه آن برای بهینه سازی آسان باشد، ما m را برای تمام عبارات در تمام نمونه های آموزشی ثابت می کنیم (M = 0.1 در آزمایش ها). λ1 وزن نقاط قوت از هر دو عبارات رتبه بندی را متعادل می کند. در پژوهش دیگر با تلفات رتبه بندی دو جهته [22، 23، 25، 43]، این است که همیشه بر روی 1 تنظیم می شود، اما در مورد ما، ما متوجه شدیم که λ1 = 2 بهترین نتایج را تولید می کند. اوزان λ2، λ3 اهمیت عبارات ساختار حفظ را کنترل می کند، که به عنوان تنظیم کننده ها برای وظایف بازیابی دو طرفه عمل می کند. ما معمولا هر دو را بر روی مقادیر کوچک مانند 0.1 یا 0.2 تنظیم می کنیم(بخش 3 برای جزئیات بیشتر).
نمونه برداری سه گانه. تلفات ما شامل تمام سه گانه های متشکل از یک نمونه هدف، یک تطبیق مثبت و یک تطبیق منفی است. بهینه سازی در طول چنین سه گانه هایی از نظر محاسباتی نشدنی و غیر عملی است. بنابراین، ما سه گانه های در داخل هر دسته کوچک را نمونه برداری نموده و تابع تلفات مان را با استفاده از SGD بهینه سازی می کنیم. با الهام از [21، 40]، به جای انتخاب متخلف(متناقض) ترین تطبیق منفی در تمام فضای نمونه، ما بالای K متخلف ترین تطبیق در هر دسته کوچک را انتخاب می کنیم. این با محاسبه شباهت های دو به دو بین همه (XI، YJ)، (XI، XJ) و (yi, yj) در داخل هر دسته کوچک انجام می شود. برای هر جفت مثبت (یعنی یک جفت جمله -تصویر واقعی، دو عکس مجاور، یا دو جمله مجاور، بنابراین ما بالا ترین K دارای نقض از هر قید مربوطه را می یابیم (از K = 50 در اجرا استفاده می کنیم، اگر چه اکثر جفت ها در بسیاری از موارد، نقض های بسیار کمتر دارند). از بعد نظری تضمین چنین استراتژی نمونه برداری در مرجع [40] بحث شده است، هر چند نه در متن یادگیری عمیق. در آزمایش های مان، ما شاهد همگرایی در عرض 30 دوره به طور متوسط هستیم.
در بخش 3، ما عملکرد روش مان را هم با و هم بدون محدودیت حفظ ساختار نشان می دهیم. در بدست آوردن شبکه بدون این محدودیت ها، ما به طور تصادفی1500 جفت (XI، yi) را به شکل دسته های کوچک نمونه برداری می کنیم. برای آزمایش های با محدودیت های حفظ ساختار، به منظور رسیدن به یک مجموعه غیر تهی از محدودیت های سه گانه، ما به تعداد متوسطی از جفت های مثبت در هر دسته کوچک نیاز داریم (یعنی، در حداقل دو جمله که در تصویر یکسان تطبیق یافته اند). با این حال، نمونه گیری تصادفی از جفت ها نمی تواند این را تضمین کند. بنابراین، برای هر xiدر یک دسته کوچک مورد نظر، ما یک جمله مثبت تر که متمایز از آنهایی است که در حال حاضر ممکن است شامل جفت های نمونه برداری شده باشد، اضافه می کنیم، در نتیجه در دسته کوچک با اندازه متغیر است.
3. آزمایش ها
در این بخش، ما سهم های اجزای مختلف روش مان را تجزیه و تحلیل نموده و آن را در بازیابی تصویر به جمله و جمله به تصویر در پایگاه های داده ای محبوب Flickr30K [51] و MSCOCO [28] و بر روی محلی سازی عبارت در مجموعه داده هویت (نهاد) های جدید Flickr30K [37] ارزیابی می کنیم.