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C4W4L04 Triplet loss

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{'title': 'C4W4L04 Triplet loss', 'heatmap': [{'end': 204.589, 'start': 145.049, 'weight': 0.701}, {'end': 504.921, 'start': 387.067, 'weight': 0.845}, {'end': 541.027, 'start': 518.125, 'weight': 0.732}, {'end': 624.048, 'start': 611.181, 'weight': 0.701}], 'summary': 'Discusses the use of triplet loss function in neural networks to encode images, explaining the adjustments made to distances between anchor-positive and anchor-negative encodings, neural network modifications to prevent trivial outputs, and the use of margin modification with an example using a margin of 0.2 for improved computational efficiency in training neural networks for face recognition.', 'chapters': [{'end': 88.17, 'segs': [{'end': 66.711, 'src': 'embed', 'start': 18.942, 'weight': 0, 'content': [{'end': 27.125, 'text': 'For example, given this picture, to learn the parameters of the neural network, you have to look at several pictures at the same time.', 'start': 18.942, 'duration': 8.183}, {'end': 33.527, 'text': 'For example, given this pair of images, you want their encodings to be similar because these are the same person.', 'start': 27.645, 'duration': 5.882}, {'end': 40.989, 'text': 'Whereas given this pair of images, you want their encodings to be quite different because these are different persons.', 'start': 34.047, 'duration': 6.942}, {'end': 44.832, 'text': 'In the terminology of the triplet loss.', 'start': 41.989, 'duration': 2.843}, {'end': 55.241, 'text': "what you're going to do is always look at one anchor image and then you want the distance between the anchor and a positive image really a positive example,", 'start': 44.832, 'duration': 10.409}, {'end': 63.468, 'text': "meaning it's the same person to be similar, whereas you want the anchor, when pairs or compared with a negative example,", 'start': 55.241, 'duration': 8.227}, {'end': 66.711, 'text': 'for their distances to be much further apart.', 'start': 63.468, 'duration': 3.243}], 'summary': 'Neural network parameters learned from images; aim for similar encodings for same person, different for different persons, using triplet loss.', 'duration': 47.769, 'max_score': 18.942, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU18942.jpg'}], 'start': 0.489, 'title': 'Learning with triplet loss function', 'summary': 'Explains the use of triplet loss function to encode images in a neural network by comparing pairs of images and adjusting distances between anchor-positive and anchor-negative encodings.', 'chapters': [{'end': 88.17, 'start': 0.489, 'title': 'Learning with triplet loss function', 'summary': 'Explains how to use triplet loss function for learning parameters of a neural network to encode images, by comparing pairs of images and adjusting the distances between anchor-positive and anchor-negative image encodings.', 'duration': 87.681, 'highlights': ['To learn the parameters of the neural network, you have to look at several pictures at the same time. The process of learning the neural network parameters involves simultaneous analysis of multiple images.', 'Encodings of similar images (same person) are desired to be similar, while encodings of different images (different persons) are desired to be quite different. The goal is to make the encodings of images of the same person similar and of different persons quite different.', 'The triplet loss involves looking at an anchor image, a positive image (same person), and a negative image (different person) simultaneously. The triplet loss function involves comparing three images at a time: an anchor, a positive (same person), and a negative (different person) image.']}], 'duration': 87.681, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU489.jpg', 'highlights': ['The triplet loss function involves comparing three images at a time: an anchor, a positive (same person), and a negative (different person) image.', 'Encodings of similar images (same person) are desired to be similar, while encodings of different images (different persons) are desired to be quite different.', 'To learn the parameters of the neural network, you have to look at several pictures at the same time.']}, {'end': 304.263, 'segs': [{'end': 118.556, 'src': 'embed', 'start': 88.17, 'weight': 3, 'content': [{'end': 96.225, 'text': 'So, to formalize this, what you want is for the parameters of your neural network or for your encodings to have the following property,', 'start': 88.17, 'duration': 8.055}, {'end': 104.929, 'text': 'which is that you want the encoding between the anchor minus the encoding of the positive example.', 'start': 96.225, 'duration': 8.704}, {'end': 107.891, 'text': 'you want this to be small and, in particular,', 'start': 104.929, 'duration': 2.962}, {'end': 118.556, 'text': 'you want this to be less than or equal to the distance or the squared norm between the encoding of the anchor and the encoding of the negative.', 'start': 107.891, 'duration': 10.665}], 'summary': 'Neural network parameters should ensure small encoding difference between anchor and positive, less than distance from anchor to negative.', 'duration': 30.386, 'max_score': 88.17, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU88170.jpg'}, {'end': 204.589, 'src': 'heatmap', 'start': 145.049, 'weight': 0.701, 'content': [{'end': 151.432, 'text': "I'm gonna take the right-hand side now minus f of n squared.", 'start': 145.049, 'duration': 6.383}, {'end': 154.995, 'text': 'you want this to be less than or equal to 0..', 'start': 151.432, 'duration': 3.563}, {'end': 158.418, 'text': "But now we're gonna make a slight change to this expression,", 'start': 154.995, 'duration': 3.423}, {'end': 164.363, 'text': 'which is one trivial way to make sure this is satisfied is to just learn everything equals 0..', 'start': 158.418, 'duration': 5.945}, {'end': 170.589, 'text': 'If f always outputs 0, then this is 0 minus 0, which is 0, this is 0 minus 0, which is 0.', 'start': 164.363, 'duration': 6.226}, {'end': 180.794, 'text': 'And so, well, by saying f of any image, equals a vector of all zeros, you can, you know, almost trivially satisfy this equation.', 'start': 170.589, 'duration': 10.205}, {'end': 187.598, 'text': "So to make sure that the neural network doesn't just output zero for all the encodings,", 'start': 181.674, 'duration': 5.924}, {'end': 192.481, 'text': "or to make sure that it doesn't set all the encodings equal to another each other, right?", 'start': 187.598, 'duration': 4.883}, {'end': 200.266, 'text': 'Another way for the neural network to um give a trivial output is if the encoding for every image was identical to the encoding to every other image,', 'start': 192.561, 'duration': 7.705}, {'end': 204.589, 'text': 'in which case you again get zero um, zero, minus zero.', 'start': 200.266, 'duration': 4.323}], 'summary': 'Ensuring f outputs 0 can trivially satisfy the equation, preventing trivial outputs.', 'duration': 59.54, 'max_score': 145.049, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU145049.jpg'}, {'end': 208.429, 'src': 'embed', 'start': 181.674, 'weight': 4, 'content': [{'end': 187.598, 'text': "So to make sure that the neural network doesn't just output zero for all the encodings,", 'start': 181.674, 'duration': 5.924}, {'end': 192.481, 'text': "or to make sure that it doesn't set all the encodings equal to another each other, right?", 'start': 187.598, 'duration': 4.883}, {'end': 200.266, 'text': 'Another way for the neural network to um give a trivial output is if the encoding for every image was identical to the encoding to every other image,', 'start': 192.561, 'duration': 7.705}, {'end': 204.589, 'text': 'in which case you again get zero um, zero, minus zero.', 'start': 200.266, 'duration': 4.323}, {'end': 208.429, 'text': 'So to prevent a neural network from doing that.', 'start': 205.464, 'duration': 2.965}], 'summary': 'Preventing neural network from trivial outputs is crucial for accurate encoding.', 'duration': 26.755, 'max_score': 181.674, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU181674.jpg'}, {'end': 276.698, 'src': 'embed', 'start': 229.462, 'weight': 0, 'content': [{'end': 233.165, 'text': 'then this prevents the neural network from outputting the trivial solutions.', 'start': 229.462, 'duration': 3.703}, {'end': 238.809, 'text': 'And by convention, usually we write plus alpha instead of negative alpha there.', 'start': 233.746, 'duration': 5.063}, {'end': 245.435, 'text': "And this is also called a margin, uh, which is terminology that you'd be familiar with.", 'start': 239.77, 'duration': 5.665}, {'end': 252.063, 'text': "if you've also seen the literature on support vector machines, but don't worry about it if you haven't.", 'start': 246.627, 'duration': 5.436}, {'end': 257.694, 'text': 'And we can also modify this equation on top by adding this margin parameter.', 'start': 252.833, 'duration': 4.861}, {'end': 263.575, 'text': "So to give an example, let's say the margin is set to 0.2.", 'start': 258.154, 'duration': 5.421}, {'end': 269.777, 'text': 'If in this example, d of the anchor and the positive is equal to 0.5,,', 'start': 263.575, 'duration': 6.202}, {'end': 276.698, 'text': "then you won't be satisfied if d between the anchor and the negative was just a little bit bigger, say 0.2..", 'start': 269.777, 'duration': 6.921}], 'summary': 'Neural network avoids trivial solutions, uses margin parameter, e.g., margin=0.2.', 'duration': 47.236, 'max_score': 229.462, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU229462.jpg'}], 'start': 88.17, 'title': 'Neural network modifications', 'summary': 'Discusses neural network encodings and margin modification aiming to prevent trivial outputs by minimizing differences between encodings of anchor and positive examples, while maximizing differences between anchor and negative examples. it also includes an example using a margin of 0.2.', 'chapters': [{'end': 204.589, 'start': 88.17, 'title': 'Neural network encodings', 'summary': 'Discusses the properties of neural network encodings, aiming to minimize the difference between the encoding of the anchor and the positive example while maximizing the difference between the encoding of the anchor and the negative example, thus preventing trivial outputs.', 'duration': 116.419, 'highlights': ['The goal is to minimize the difference between the encoding of the anchor and the positive example, and to maximize the difference between the encoding of the anchor and the negative example.', 'Ensuring the neural network does not output trivial results involves preventing it from always outputting zero for all encodings or setting all encodings equal to each other.', 'By setting f of any image to equal a vector of all zeros, the equation is almost trivially satisfied.']}, {'end': 304.263, 'start': 205.464, 'title': 'Neural network margin modification', 'summary': 'Discusses modifying the objective of a neural network to include a margin parameter, preventing the output of trivial solutions, and aiming for a specific margin gap, illustrated with an example using a margin of 0.2.', 'duration': 98.799, 'highlights': ['By modifying the objective to include a margin parameter, such as setting it to 0.2, it prevents the neural network from outputting trivial solutions, ensuring a margin gap of at least 0.2, as illustrated in the example.', 'Setting the margin to 0.2 ensures that the distance between the anchor and the negative needs to be much larger than the distance between the anchor and the positive, aiming for a gap of at least 0.7 or higher.', "The modification aims to ensure that the neural network does not output trivial solutions by setting a margin parameter, enhancing the network's performance and robustness.", 'The chapter explains the concept of a margin parameter, drawing parallels with the literature on support vector machines, and its role in preventing trivial solutions in neural networks.']}], 'duration': 216.093, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU88170.jpg', 'highlights': ["The modification aims to ensure that the neural network does not output trivial solutions by setting a margin parameter, enhancing the network's performance and robustness.", 'By modifying the objective to include a margin parameter, such as setting it to 0.2, it prevents the neural network from outputting trivial solutions, ensuring a margin gap of at least 0.2, as illustrated in the example.', 'Setting the margin to 0.2 ensures that the distance between the anchor and the negative needs to be much larger than the distance between the anchor and the positive, aiming for a gap of at least 0.7 or higher.', 'The goal is to minimize the difference between the encoding of the anchor and the positive example, and to maximize the difference between the encoding of the anchor and the negative example.', 'Ensuring the neural network does not output trivial results involves preventing it from always outputting zero for all encodings or setting all encodings equal to each other.']}, {'end': 929.649, 'segs': [{'end': 356.756, 'src': 'embed', 'start': 325.83, 'weight': 1, 'content': [{'end': 334.892, 'text': "So let's take this equation we have here at the bottom and on the next slide, formalize it and define the triplet loss function.", 'start': 325.83, 'duration': 9.062}, {'end': 340.453, 'text': 'So the triplet loss function is defined on triples of images.', 'start': 335.372, 'duration': 5.081}, {'end': 348.872, 'text': 'So given three images, A, P, and N, the anchor, positive and negative examples.', 'start': 340.874, 'duration': 7.998}, {'end': 356.756, 'text': 'So the positive examples is of the same person as the anchor, but the negative is of a different person than the anchor.', 'start': 349.072, 'duration': 7.684}], 'summary': 'Defining triplet loss function for image recognition.', 'duration': 30.926, 'max_score': 325.83, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU325830.jpg'}, {'end': 504.921, 'src': 'heatmap', 'start': 387.067, 'weight': 0.845, 'content': [{'end': 391.853, 'text': 'And what you want is for this to be less than or equal to 0.', 'start': 387.067, 'duration': 4.786}, {'end': 399.299, 'text': "So to define the loss function, let's take the max between this, and 0.", 'start': 391.853, 'duration': 7.446}, {'end': 407.142, 'text': 'So the effect of taking the max here is that so long as this is less than 0, then the loss is 0,', 'start': 399.299, 'duration': 7.843}, {'end': 412.863, 'text': 'because the max of something less than or equal to 0 with 0 is, uh, going to be 0..', 'start': 407.142, 'duration': 5.721}, {'end': 416.804, 'text': "So so long as you achieve the goal of making this thing I've underlined in green,", 'start': 412.863, 'duration': 3.941}, {'end': 424.266, 'text': "so long as you've achieved the objective of making that less than or equal to 0, then the loss on this example is equal to 0..", 'start': 416.804, 'duration': 7.462}, {'end': 432.457, 'text': 'But if, on the other hand, if this is greater than 0, then if you take the max, the max will end up selecting this thing of underlying and green,', 'start': 424.266, 'duration': 8.191}, {'end': 434.7, 'text': 'and so you would have a positive loss.', 'start': 432.457, 'duration': 2.243}, {'end': 437.624, 'text': 'So by trying to minimize this.', 'start': 435.742, 'duration': 1.882}, {'end': 446.682, 'text': "this has the effect of trying to send this thing to be 0 or less than, or equal to 0, and then, so long as it's 0 or less than or equal to 0,", 'start': 437.624, 'duration': 9.058}, {'end': 448.783, 'text': "the neural network doesn't care.", 'start': 446.682, 'duration': 2.101}, {'end': 451.344, 'text': 'um how much further neg- negative it is.', 'start': 448.783, 'duration': 2.561}, {'end': 457.086, 'text': 'So this is how you define the loss on a single triplet and the overall cost.', 'start': 452.064, 'duration': 5.022}, {'end': 466.269, 'text': 'function for your neural network can be sum over a training set of these individual losses on different um triplets.', 'start': 457.086, 'duration': 9.183}, {'end': 477.875, 'text': 'So, if you have a training set of, say, 10, 000 pictures with 1, 000 different persons, what you have to do is take your 10,', 'start': 468.01, 'duration': 9.865}, {'end': 483.057, 'text': '000 pictures and use it to generate, to select triplets like this,', 'start': 477.875, 'duration': 5.182}, {'end': 488.02, 'text': 'and then train your learning algorithm using gradient descent on this type of cost function,', 'start': 483.057, 'duration': 4.963}, {'end': 492.662, 'text': 'which is really defined on triplets of images drawn from your training set.', 'start': 488.02, 'duration': 4.642}, {'end': 504.921, 'text': 'Notice that in order to define this dataset of triplets, you do need some pairs of A and P, pairs of pictures of the same person.', 'start': 494.594, 'duration': 10.327}], 'summary': 'Define loss function to achieve <=0, minimizing positive loss, for neural network training.', 'duration': 117.854, 'max_score': 387.067, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU387067.jpg'}, {'end': 511.646, 'src': 'embed', 'start': 483.057, 'weight': 4, 'content': [{'end': 488.02, 'text': 'and then train your learning algorithm using gradient descent on this type of cost function,', 'start': 483.057, 'duration': 4.963}, {'end': 492.662, 'text': 'which is really defined on triplets of images drawn from your training set.', 'start': 488.02, 'duration': 4.642}, {'end': 504.921, 'text': 'Notice that in order to define this dataset of triplets, you do need some pairs of A and P, pairs of pictures of the same person.', 'start': 494.594, 'duration': 10.327}, {'end': 511.646, 'text': 'So the purpose of training your system, you do need a dataset where you have multiple pictures of the same person.', 'start': 505.462, 'duration': 6.184}], 'summary': "Train algorithm using triplets of images to learn on pairs of the same person's pictures.", 'duration': 28.589, 'max_score': 483.057, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU483057.jpg'}, {'end': 546.73, 'src': 'heatmap', 'start': 518.125, 'weight': 0.732, 'content': [{'end': 524.072, 'text': 'so maybe you have 10 pictures on average of each of your 1, 000 persons to make up your entire dataset.', 'start': 518.125, 'duration': 5.947}, {'end': 529.218, 'text': "If you had just one picture of each person, then you can't actually train this system.", 'start': 524.573, 'duration': 4.645}, {'end': 531.381, 'text': 'But of course, after training.', 'start': 529.939, 'duration': 1.442}, {'end': 541.027, 'text': "If you're applying this, but of course, after having trained the system, you can then apply it to your one-shot learning problem, where,", 'start': 532.702, 'duration': 8.325}, {'end': 546.73, 'text': 'for your face recognition system, maybe you have only a single picture of someone you might be trying to recognize.', 'start': 541.027, 'duration': 5.703}], 'summary': 'To train a face recognition system, an average of 10 pictures per person is needed, but the system can be applied to one-shot learning with just a single picture.', 'duration': 28.605, 'max_score': 518.125, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU518125.jpg'}, {'end': 652.978, 'src': 'heatmap', 'start': 611.181, 'weight': 0, 'content': [{'end': 614.663, 'text': 'But if a and n are two randomly chosen different persons,', 'start': 611.181, 'duration': 3.482}, {'end': 621.707, 'text': "then there's a very high chance that this will be much bigger more than the margin alpha than that term on the left,", 'start': 614.663, 'duration': 7.044}, {'end': 624.048, 'text': "and so the neural network won't learn much from it.", 'start': 621.707, 'duration': 2.341}, {'end': 630.871, 'text': 'So to construct your training set, what you want to do is to choose triplets a, p, and n that are hard to train on.', 'start': 624.488, 'duration': 6.383}, {'end': 637.695, 'text': 'So, in particular, what you want is for all triplets, that this constraint be satisfied.', 'start': 631.432, 'duration': 6.263}, {'end': 652.978, 'text': 'So a triplet that is hard would be if you choose values for a p and n, so that maybe d a p is actually quite close to d a n.', 'start': 639.415, 'duration': 13.563}], 'summary': 'Choosing triplets a, p, and n that are hard to train on is crucial for effective neural network learning.', 'duration': 31.271, 'max_score': 611.181, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU611181.jpg'}, {'end': 884.713, 'src': 'embed', 'start': 858.277, 'weight': 2, 'content': [{'end': 865.041, 'text': "Now it turns out that today's face recognition systems, especially the large scale commercial face recognition systems,", 'start': 858.277, 'duration': 6.764}, {'end': 867.002, 'text': 'are trained on very large datasets.', 'start': 865.041, 'duration': 1.961}, {'end': 870.104, 'text': 'Datasets north of a million images is not uncommon.', 'start': 867.422, 'duration': 2.682}, {'end': 877.869, 'text': 'Some companies are using north of 10 million images, and some companies have north of 100 million images with which to try to train these systems.', 'start': 870.424, 'duration': 7.445}, {'end': 879.93, 'text': 'So, these are very large datasets.', 'start': 878.269, 'duration': 1.661}, {'end': 884.713, 'text': 'Even by modern standards, these dataset assets are not easy to acquire.', 'start': 880.29, 'duration': 4.423}], 'summary': 'Commercial face recognition systems are trained on datasets exceeding 100 million images, posing acquisition challenges.', 'duration': 26.436, 'max_score': 858.277, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU858277.jpg'}], 'start': 304.263, 'title': 'Triplet loss function in neural networks', 'summary': 'Introduces the triplet loss function, emphasizing the margin parameter and hard triplet selection in training neural networks for improved computational efficiency. it discusses training for face recognition using triplet loss, involving anchor-positive-negative triples and gradient descent, with systems trained on datasets of over 100 million images.', 'chapters': [{'end': 747.698, 'start': 304.263, 'title': 'Triplet loss function in neural networks', 'summary': 'Introduces the triplet loss function, highlighting the importance of the margin parameter and the selection of hard triplets in training neural networks, as well as the computational efficiency it brings, with examples from a paper by florent schroff, dmitry kalinichenko, and james philbin.', 'duration': 443.435, 'highlights': ['The triplet loss function is defined on triples of images, where the goal is to minimize a specific equation by ensuring it is less than or equal to 0, with the margin parameter alpha set to 0.2.', 'In training neural networks, selecting hard triplets, where the distance between the anchor and positive is close to the distance between the anchor and negative, is essential for computational efficiency and effective learning.', 'Choosing triplets that are hard to train on increases the computational efficiency of the learning algorithm by ensuring that gradient descent has to work to push quantities further away from each other.']}, {'end': 929.649, 'start': 748.576, 'title': 'Training with triplet loss', 'summary': 'Discusses training a neural network for face recognition using triplet loss, which involves mapping the training set to anchor-positive-negative triples and using gradient descent to minimize the cost function, with commercial face recognition systems being trained on datasets often exceeding 100 million images.', 'duration': 181.073, 'highlights': ['Commercial face recognition systems are trained on datasets often exceeding 100 million images, and some companies have north of 10 million images, making them very large datasets.', 'Using triplet loss involves mapping the training set to anchor-positive-negative triples and using gradient descent to minimize the cost function, aiming to back-propagate to all the parameters of the neural network in order to learn an encoding.', "It might be useful to download someone else's pre-trained model rather than train a network from scratch due to the sheer data volume sizes, but understanding how the algorithms were trained is still valuable for applying these ideas in new applications.", 'Training a neural network for face recognition using triplet loss involves defining a training set of anchor-positive-negative triples and using gradient descent to minimize the cost function, aiming to learn an encoding that outputs a good encoding for face recognition.']}], 'duration': 625.386, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/d2XB5-tuCWU/pics/d2XB5-tuCWU304263.jpg', 'highlights': ['In training neural networks, selecting hard triplets is essential for computational efficiency and effective learning.', 'The triplet loss function is defined on triples of images, with the margin parameter alpha set to 0.2.', 'Commercial face recognition systems are trained on datasets often exceeding 100 million images, making them very large datasets.', 'Using triplet loss involves mapping the training set to anchor-positive-negative triples and using gradient descent to minimize the cost function.', 'Training a neural network for face recognition using triplet loss involves defining a training set of anchor-positive-negative triples and using gradient descent to minimize the cost function.']}], 'highlights': ['The triplet loss function involves comparing three images at a time: an anchor, a positive (same person), and a negative (different person) image.', 'Encodings of similar images (same person) are desired to be similar, while encodings of different images (different persons) are desired to be quite different.', 'To learn the parameters of the neural network, you have to look at several pictures at the same time.', "The modification aims to ensure that the neural network does not output trivial solutions by setting a margin parameter, enhancing the network's performance and robustness.", 'By modifying the objective to include a margin parameter, such as setting it to 0.2, it prevents the neural network from outputting trivial solutions, ensuring a margin gap of at least 0.2, as illustrated in the example.', 'Setting the margin to 0.2 ensures that the distance between the anchor and the negative needs to be much larger than the distance between the anchor and the positive, aiming for a gap of at least 0.7 or higher.', 'The goal is to minimize the difference between the encoding of the anchor and the positive example, and to maximize the difference between the encoding of the anchor and the negative example.', 'Ensuring the neural network does not output trivial results involves preventing it from always outputting zero for all encodings or setting all encodings equal to each other.', 'In training neural networks, selecting hard triplets is essential for computational efficiency and effective learning.', 'The triplet loss function is defined on triples of images, with the margin parameter alpha set to 0.2.', 'Commercial face recognition systems are trained on datasets often exceeding 100 million images, making them very large datasets.', 'Using triplet loss involves mapping the training set to anchor-positive-negative triples and using gradient descent to minimize the cost function.', 'Training a neural network for face recognition using triplet loss involves defining a training set of anchor-positive-negative triples and using gradient descent to minimize the cost function.']}