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than the 20 layers of the previous state of the art such as the vgg 19 residual connections gave rise to their own weight initialization problems and strategies these are sometimes called normalization free methods since using residual connection could stabilize the training of a deep neural network so much that normalizations become unnecessary fixup initialization is designed specifically for networks with residual connections and without batch normalization as follows 18 initialize the classification layer and the last layer of each residual branch to 0 initialize every other layer using a standard method such as he initialization and scale only the weight layers inside residual branches by l 1 2 m 2 displaystyle l frac 1 2m 2 add a scalar multiplier initialized at 1 in every branch and a scalar bias initialized at 0 before each convolution linear and element wise activation layer similarly t fixup initialization is designed for transformers without layer normalization 19 9 others edit instead of initializing all weights with random values on the order of o 1 n displaystyle o 1 sqrt n sparse initialization initialized only a small subset of the weights with larger random values and the other weights zero so that the total variance is still on the order of o 1 displaystyle o 1 20 random walk initialization was designed for mlp so that during backpropagation the l2 norm of gradient at each layer performs an unbiased random walk as one moves from the last layer to the first 21 looks linear initialization was designed to allow the neural network to behave like a deep linear network at initialization since w r e l u x w r e l u x w x displaystyle w mathrm relu x w mathrm relu x wx it initializes a matrix w displaystyle w of shape r n 2 m displaystyle mathbb r frac n 2 times m by any method such as orthogonal initialization then let the r n m displaystyle mathbb r n times m weight matrix to be the concatenation of w w displaystyle w w 22 miscellaneous edit for hyperbolic tangent activation function a particular scaling is sometimes used 1 7159 tanh 2 x 3 displaystyle 1 7159 tanh 2x 3 this was sometimes called lecun s tanh it was designed so that it maps the interval 1 1 displaystyle 1 1 to itself thus ensuring that the overall gain is around 1 in normal operating conditions and that f x displaystyle f x is at maximum when x 1 1 displaystyle x 1 1 which improves convergence at the end of training 23 5 in self normalizing neural networks the selu activation function s e l u x λ x if x 0 α e x α if x 0 displaystyle mathrm selu x lambda begin cases x text if x 0 alpha e x alpha text if x leq 0 end cases with parameters λ 1 0507 α 1 6733 displaystyle lambda approx 1 0507 alpha approx 1 6733 makes it such that the mean and variance of the output of each layer has 0 1 displaystyle 0 1 as an attracting fixed point this makes initialization less important though they recommend initializing weights randomly with variance 1 n l 1 displaystyle 1 n_ l 1 24 history edit random weight initialization was used since frank rosenblatt s perceptrons an early work that described weight initialization specifically was lecun et al 1998 5 before the 2010s era of deep learning it was common to initialize models by generative pre training using an unsupervised learning algorithm that is not backpropagation as it was difficult to directly train deep neural networks by backpropagation 25 26 for example a deep belief network was trained by using contrastive divergence layer by layer starting from the bottom 27 martens 2010 20 proposed hessian free optimization a quasi newton method to directly train deep networks the work generated considerable excitement that initializing networks without pre training phase was possible 28 however a 2013 paper demonstrated that with well chosen hyperparameters momentum gradient descent with weight initialization was sufficient for training neural networks without needing either quasi newton method or generative pre training a combination that is still in use as of 2024 29 since then the impact of initialization on tuning the variance has become less important with methods developed to automatically tune variance like batch normalization tuning the variance of the forward pass 30 and momentum based optimizers tuning the variance of the backward pass 31 there is a tension between using careful weight initialization to decrease the need for normalization and using normalization to decrease the need for careful weight initialization with each approach having its tradeoffs for example batch normalization causes training examples in the minibatch to become dependent an undesirable trait while weight initialization is architecture dependent 32 see also edit backpropagation normalization machine learning gradient descent vanishing gradient problem references edit le quoc v jaitly navdeep hinton geoffrey e 2015 a simple way to initialize recurrent networks of rectified linear units arxiv 1504 00941 cs ne jozefowicz rafal zaremba wojciech sutskever ilya 2015 06 01 an empirical exploration of recurrent network architectures proceedings of the 32nd international conference on machine learning pmlr 2342 2350 goodfellow ian bengio yoshua courville aaron 2016 deep learning adaptive computation and machine learning cambridge massachusetts the mit press isbn 978 0 262 03561 3 lu lu shin yeonjong su yanhui karniadakis george em 2019 dying relu and initialization theory and numerical examples communications in computational physics 28 5 1671 1706 arxiv 1903 06733 doi 10 4208 cicp oa 2020 0165 1 2 3 lecun yann bottou leon orr genevieve b müller klaus robert 1998 efficient backprop in orr genevieve b müller klaus robert eds neural networks tricks of the trade berlin heidelberg springer pp 9 50 doi 10 1007 3 540 49430 8_2 isbn 978 3 540 49430 0 retrieved 2024 10 05 glorot xavier bengio yoshua 2010 03 31 understanding the difficulty of training deep feedforward neural networks proceedings of the thirteenth international conference on artificial intelligence and statistics jmlr workshop and conference proceedings 249 256 kumar siddharth krishna 2017 on weight initialization in deep neural networks arxiv 1704 08863 cs lg he kaiming zhang xiangyu ren shaoqing sun jian 2015 delving deep into rectifiers surpassing human level performance on imagenet classification arxiv 1502 01852 cs cv saxe andrew m mcclelland james l ganguli surya 2013 exact solutions to the nonlinear dynamics of learning in deep linear neural networks arxiv 1312 6120 cs ne hu wei xiao lechao pennington jeffrey 2020 provable benefit of orthogonal initialization in optimizing deep linear networks arxiv 2001 05992 cs lg 1 2 martens james ballard andy desjardins guillaume swirszcz grzegorz dalibard valentin sohl dickstein jascha schoenholz samuel s 2021 rapid training of deep neural networks without skip connections or normalization layers using deep kernel shaping arxiv 2110 01765 cs lg balduzzi david frean marcus leary lennox lewis j p ma kurt wan duo mcwilliams brian 2017 07 17 the shattered gradients problem if resnets are the answer then what is the question proceedings of the 34th international conference on machine learning pmlr 342 350 xiao lechao bahri yasaman sohl dickstein jascha schoenholz samuel pennington jeffrey 2018 07 03 dynamical isometry and a mean field theory of cnns how to train 10 000 layer vanilla convolutional neural networks proceedings of the 35th international conference on machine learning pmlr 5393 5402 arxiv 1806 05393 arjovsky martin shah amar bengio yoshua 2016 06 11 unitary evolution recurrent neural networks proceedings of the 33rd international conference on machine learning pmlr 1120 1128 arxiv 1511 06464 henaff mikael szlam arthur lecun yann 2017 03 15 recurrent orthogonal networks and long memory tasks arxiv 1602 06662 cs ne mishkin dmytro matas jiri 2016 02 19 all you need is a good init arxiv 1511 06422 xie di xiong jiang pu shiliang 2017 all you need is beyond a good init exploring better solution for training extremely deep convolutional neural networks with orthonormality and modulation ieee conference on computer vision and pattern recognition cvpr pp 6176 6185 zhang hongyi dauphin yann n ma tengyu 2019 fixup initialization residual learning without normalization arxiv 1901 09321 cs lg huang xiao shi perez felipe ba jimmy volkovs maksims 2020 11 21 improving transformer optimization through better initialization proceedings of the 37th international conference on machine learning pmlr 4475 4483 1 2 martens james 2010 06 21 deep learning via hessian free optimization proceedings of the 27th international conference on international conference on machine learning icml 10 madison wi usa omnipress 735 742 isbn 978 1 60558 907 7 cite journal cs1 maint periodical has isbn link sussillo david abbott l f 2014 random walk initialization for training very deep feedforward networks arxiv 1412 6558 cs ne balduzzi david frean marcus leary lennox lewis jp kurt wan duo ma mcwilliams brian 2017 the shattered gradients problem if resnets are the answer then what is the question arxiv 1702 08591 cs ne lecun y 1989 generalization and network design strategies pdf in pfeifer r schreter z fogelman f steels l eds connectionism in perspective proceedings of the international conference connectionism in perspective university of zurich 10 13 october 1988 amsterdam elsevier klambauer günter unterthiner thomas mayr andreas hochreiter sepp 2017 self normalizing neural networks advances in neural information processing systems 30 curran associates inc bengio y 2009 learning deep architectures for ai pdf foundations and trends in machine learning 2 1 127 doi 10 1561 2200000006 erhan dumitru courville aaron bengio yoshua vincent pascal 2010 03 31 why does unsupervised pre training help deep learning proceedings of the thirteenth international conference on artificial intelligence and statistics jmlr workshop and conference proceedings 201 208 bengio yoshua lamblin pascal popovici dan larochelle hugo 2006 greedy layer wise training of deep networks advances in neural information processing systems 19 mit press glorot xavier bordes antoine bengio yoshua 2011 06 14 deep sparse rectifier neural networks proceedings of the fourteenth international conference on artificial intelligence and statistics jmlr workshop and conference proceedings 315 323 sutskever ilya martens james dahl george hinton geoffrey 2013 05 26 on the importance of initialization and momentum in deep learning pdf proceedings of the 30th international conference on machine learning pmlr 1139 1147 bjorck nils gomes carla p selman bart weinberger kilian q 2018 understanding batch normalization advances in neural information processing systems 31 curran associates inc arxiv 1806 02375 balles lukas hennig philipp 2018 07 03 dissecting adam the sign magnitude and variance of stochastic gradients proceedings of the 35th international conference on machine learning pmlr 404 413 arxiv 1705 07774 brock andrew de soham smith samuel l simonyan karen 2021 high performance large scale image recognition without normalization arxiv 2102 06171 cs cv further reading edit goodfellow ian bengio yoshua courville aaron 2016 8 4 parameter initialization strategies deep learning adaptive computation and machine learning cambridge mass the mit press isbn 978 0 262 03561 3 narkhede meenal v bartakke prashant p sutaone mukul s june 28 2021 a review on weight initialization strategies for neural networks artificial intelligence review 55 1 springer science and business media llc 291 322 doi 10 1007 s10462 021 10033 z issn 0269 2821 v t e artificial intelligence ai history timeline glossary lists algorithms companies institutions projects software open source proprietary concepts automated reasoning automated planning constraint satisfaction knowledge representation parameter hyperparameter loss functions regression bias variance tradeoff double descent overfitting clustering gradient descent sgd quasi newton method conjugate gradient method backpropagation attention convolution normalization batchnorm activation softmax sigmoid rectifier gating weight initialization regularization datasets augmentation prompt engineering reinforcement learning q learning sarsa imitation policy gradient diffusion latent diffusion model autoregression adversary rag uncanny valley llm post training rlhf self supervised learning reflection recursive self improvement hallucination word embedding vibe coding blended ai open source ai sovereign ai symbolic ai neuro symbolic ai situated approach actor critic algorithm applications automated theorem proving general game playing machine learning in context learning artificial neural network deep learning language model large nmt reasoning model context protocol intelligent agent ai agent artificial human companion humanity s last exam lethal autonomous weapons laws generative ai weak ai hypothetical artificial general intelligence agi artificial superintelligence asi agent2agent protocol physical ai implementations audio visual alexnet wavenet human image synthesis hwr ocr computer vision speech synthesis 15 ai elevenlabs speech recognition whisper facial recognition alphafold text to image models aurora dall e firefly flux gpt image ideogram imagen midjourney recraft stable diffusion text to video models dream machine runway gen hailuo ai kling sora seedance veo music generation riffusion suno udio world models genie oasis text list of large language models project debater ibm watson ibm watsonx decisional alphago alphazero openai five self driving car muzero action selection autogpt robot control reasoning systems deductive classifiers expert systems inference engines knowledge based systems logic programs procedural reasoning systems semantic reasoners rule based systems cognitive architectures act r soar clarion lida opencog knowledge bases conceptnet wikidata dbpedia yago people alan turing warren sturgis mcculloch walter pitts john von neumann christopher d manning claude shannon shun ichi amari kunihiko fukushima takeo kanade marvin minsky john mccarthy nathaniel rochester allen newell cliff shaw herbert a simon oliver selfridge frank rosenblatt bernard widrow joseph weizenbaum seymour papert seppo linnainmaa paul werbos geoffrey hinton john hopfield jürgen schmidhuber yann lecun yoshua bengio lotfi a zadeh stephen grossberg alex graves james goodnight andrew ng fei fei li alex krizhevsky ilya sutskever oriol vinyals quoc v le ian goodfellow demis hassabis david silver andrej karpathy ashish vaswani noam shazeer aidan gomez john schulman mustafa suleyman jan leike daniel kokotajlo françois chollet neural network architectures neural turing machine differentiable neural computer transformer vision transformer vit recurrent neural network rnn long short term memory lstm gated recurrent unit gru echo state network multilayer perceptron mlp convolutional neural network cnn residual neural ne...
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