AI News, Random Ponderings
However, I would like to argue that the reasons stated for the success of deep neural nets would apparently work as well for kernel machines (if you were to train them using an efficient algorithm that is not quadratic in the number of examples, and it is not hopeless to achieve that).
I have written about the expressive power of deep nets (see recent Montufar et al NIPS paper, for example) and about their ability to generalize far from the training examples (NIPS'2005 and my 2009 book and 2013 PAMI review), which a Gaussian kernel machine or a decision tree could not do.
Now this is associated with priors that are coming with the deep net (there is no free lunch and it will not work for *any* function), such as the priors associated with distributed representations (the existence of underlying factors that generate the data, so that one can learn about each factor without having to observe all the configurations of values of all the others) and with depth (the assumption of a hierarchy of factors).
I don't see a particular difference between a shallow net with a reasonable number of neurons and a kernel machine with a reasonable number of support vectors (its not useful to consider Kernel machines with exponentially many support vectors just like there isn't a point in considering the universal approximation theorem as both require exponential resources) --- both of these models are nearly identical, and thus equally unpowerful.
The LDNN can sort, do integer-multiplication, compute analytic functions, decompose an input into small pieces and recombine it later in a higher level representation, partition the input space into an exponential number of non-arbitrary tiny regions, etc.
Ultimately, if the LDNN has 10,000 layers, then it can, in principle, execute any parallel algorithm that runs in fewer than 10,000 steps, giving this LDNN an incredible expressive power.
Thus, I don't think that the argument in the article suggests that huge kernel machines should be able to solve these hard problems --- they would need to have exponentially many support vectors.Although I didn't define it in the article, generalization (to me) means that the gap between the training and the test error is small.
It follows that generalization is easy to achieve whenever the capacity of the model (as measured by the number of parameters or its VC-dimension) is limited --- we merely need to use more training cases than the model has parameters / VC dimension.
I don't know the answer but I have two theories: 1) if they weren't solvable by an efficient computer program, then humans and animals wouldn't be solving them in the first place;
This assumption also arises naturally if you first assume something that appears very straightforward: the input data we observe are the effects of some underlying causes, and these causes are marginally related to each other in simple ways (e.g.
Some functions representable very efficiently by the neural net can require an exponential number of support vectors for the kernel SVM (this idea is found in several papers, including in the most crisp way in our last NIPS paper on the number of regions associated with shallow and deep rectifier nets).-- Yoshua Bengio
At the same time, I think that independent hidden factors are not the whole story, and that there may be models whose representations will so different from the ones we are dealing with now that we may not think of them as of conventional distributed representations at all (although they will necessarily be distributed, strictly speaking).
For convex models trained with SGD, finding the optimal learning rate schedule is purely an optimization problem and therefore the optimal learning rate schedule should only depend on the training data and the loss function it-self.
It is my understanding that there should be no need to use an held out validation set to find the optimal learning rate schedule in that case (leaving overfitting issues aside, assuming we have enough labeled samples to train on).However for deep nets, you explicitly mentions that you need to decay learning rate based on the lack of improvement on the loss computed on some held-out validation set rather than using evolution of the cost of the training set.What can go wrong when you do the learning rate scheduling based on the training cost instead of using an held-out validation set?
by getting stuck on a plateau near a saddle point more easily)?It seems that for deep networks, it might no longer be possible to separate the optimization problem from the learning / estimation problem.
Which is why, when you see that validation error no longer makes any progress with the large LR (so it may start increasing soon, which is bad), you reduce the LR, to get an additional gain.I am pretty sure that this effect will hold true for convex problem as well -- this particular learning rate schedule attempts to find a parameter setting with the lowest validation error, which is something we care about much more than training error, which is relevant only to the extent it is correlated with the test error.Optimization and generalization are intertwined, and that it is possible to optimize the training set better while doing worse on the test set.
Ysong - I've taken the liberty of linking to this post from my own Deep Neural blog.I would like to thank Ilya for giving away all that sacred knowledge for free :)Ilya, do you think recurrent nets will now be much more commonly used thanks to your work?
comments from all comers seem to be allowed - I always think that the fact that these nets work just shows that we look at stuff that is adapted to our vision - in other words we have built alphabets for our hand, eyes,and quills;
"Sometimes, when the input dimension varies by orders of magnitude, it is better to take the log(1 + x) of that dimension."Is it bad to use log(1 + x) also when the input dimension doesn't vary alot.
NanoNets : How to use Deep Learning when you have Limited Data
Disclaimer: I’m building nanonets.com to help build ML with less data There has been a recent surge in popularity of Deep Learning, achieving state of the art performance in various tasks like Language Translation, playing Strategy Games and Self Driving Cars requiring millions of data points.
Basic reasoning is that your model should be large enough to capture relations in your data (eg textures and shapes in images, grammar in text and phonemes in speech) along with specifics of your problem (eg number of categories).
With transfer learning, we can take a pretrained model, which was trained on a large readily available dataset (trained on a completely different task, with the same input but different output).
This smaller network only needs to learn the relations for your specific problem having already learnt about patterns in the data from the pretrained model.
This way a model trained to detect Cats can be reused to Reproduce the work of Van Gogh Another major advantage of using transfer learning is how well the model generalizes.
Larger models tend to overfit (ie modeling the data more than the underlying phenomenon) the data and don’t work as well when you test it out on unseen data.
Calculating the number of parameters needed to train for this problem using transfer learning: No of parameters = [Size(inputs) + 1] * [Size(outputs) + 1] =
Deep learning (also known as deep structured learning or hierarchical learning) is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms.
Deep learning architectures such as deep neural networks, deep belief networks and recurrent neural networks have been applied to fields including computer vision, speech recognition, natural language processing, audio recognition, social network filtering, machine translation, bioinformatics, drug design and board game programs, where they have produced results comparable to and in some cases superior to human experts.
Deep learning models are vaguely inspired by information processing and communication patterns in biological nervous systems yet have various differences from the structural and functional properties of biological brains, which make them incompatible with neuroscience evidences.
Most modern deep learning models are based on an artificial neural network, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in Deep Belief Networks and Deep Boltzmann Machines.
No universally agreed upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth >
For supervised learning tasks, deep learning methods obviate feature engineering, by translating the data into compact intermediate representations akin to principal components, and derive layered structures that remove redundancy in representation.
The universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions.
By 1991 such systems were used for recognizing isolated 2-D hand-written digits, while recognizing 3-D objects was done by matching 2-D images with a handcrafted 3-D object model.
But while Neocognitron required a human programmer to hand-merge features, Cresceptron learned an open number of features in each layer without supervision, where each feature is represented by a convolution kernel.
In 1994, André de Carvalho, together with Mike Fairhurst and David Bisset, published experimental results of a multi-layer boolean neural network, also known as a weightless neural network, composed of a 3-layers self-organising feature extraction neural network module (SOFT) followed by a multi-layer classification neural network module (GSN), which were independently trained.
In 1995, Brendan Frey demonstrated that it was possible to train (over two days) a network containing six fully connected layers and several hundred hidden units using the wake-sleep algorithm, co-developed with Peter Dayan and Hinton.
Simpler models that use task-specific handcrafted features such as Gabor filters and support vector machines (SVMs) were a popular choice in the 1990s and 2000s, because of ANNs' computational cost and a lack of understanding of how the brain wires its biological networks.
These methods never outperformed non-uniform internal-handcrafting Gaussian mixture model/Hidden Markov model (GMM-HMM) technology based on generative models of speech trained discriminatively.
The principle of elevating 'raw' features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the 'raw' spectrogram or linear filter-bank features in the late 1990s,
Many aspects of speech recognition were taken over by a deep learning method called long short-term memory (LSTM), a recurrent neural network published by Hochreiter and Schmidhuber in 1997.
showed how a many-layered feedforward neural network could be effectively pre-trained one layer at a time, treating each layer in turn as an unsupervised restricted Boltzmann machine, then fine-tuning it using supervised backpropagation.
The impact of deep learning in industry began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US, according to Yann LeCun.
was motivated by the limitations of deep generative models of speech, and the possibility that given more capable hardware and large-scale data sets that deep neural nets (DNN) might become practical.
However, it was discovered that replacing pre-training with large amounts of training data for straightforward backpropagation when using DNNs with large, context-dependent output layers produced error rates dramatically lower than then-state-of-the-art Gaussian mixture model (GMM)/Hidden Markov Model (HMM) and also than more-advanced generative model-based systems.
offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major speech recognition systems.
In 2010, researchers extended deep learning from TIMIT to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by decision trees.
In 2009, Nvidia was involved in what was called the “big bang” of deep learning, “as deep-learning neural networks were trained with Nvidia graphics processing units (GPUs).”
In 2014, Hochreiter's group used deep learning to detect off-target and toxic effects of environmental chemicals in nutrients, household products and drugs and won the 'Tox21 Data Challenge' of NIH, FDA and NCATS.
Although CNNs trained by backpropagation had been around for decades, and GPU implementations of NNs for years, including CNNs, fast implementations of CNNs with max-pooling on GPUs in the style of Ciresan and colleagues were needed to progress on computer vision.
In November 2012, Ciresan et al.'s system also won the ICPR contest on analysis of large medical images for cancer detection, and in the following year also the MICCAI Grand Challenge on the same topic.
In 2013 and 2014, the error rate on the ImageNet task using deep learning was further reduced, following a similar trend in large-scale speech recognition.
For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as 'cat' or 'no cat' and using the analytic results to identify cats in other images.
Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as backpropagation, or passing information in the reverse direction and adjusting the network to reflect that information.
Neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.
Despite this number being several order of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, playing 'Go'
The extra layers enable composition of features from lower layers, potentially modeling complex data with fewer units than a similarly performing shallow network.
The training process can be guaranteed to converge in one step with a new batch of data, and the computational complexity of the training algorithm is linear with respect to the number of neurons involved.
that involve multi-second intervals containing speech events separated by thousands of discrete time steps, where one time step corresponds to about 10 ms.
All major commercial speech recognition systems (e.g., Microsoft Cortana, Xbox, Skype Translator, Amazon Alexa, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are based on deep learning.
DNNs have proven themselves capable, for example, of a) identifying the style period of a given painting, b) 'capturing' the style of a given painting and applying it in a visually pleasing manner to an arbitrary photograph, and c) generating striking imagery based on random visual input fields.
Word embedding, such as word2vec, can be thought of as a representational layer in a deep learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset;
Finding the appropriate mobile audience for mobile advertising is always challenging, since many data points must be considered and assimilated before a target segment can be created and used in ad serving by any ad server.
'Deep anti-money laundering detection system can spot and recognize relationships and similarities between data and, further down the road, learn to detect anomalies or classify and predict specific events'.
Deep learning is closely related to a class of theories of brain development (specifically, neocortical development) proposed by cognitive neuroscientists in the early 1990s.
These developmental models share the property that various proposed learning dynamics in the brain (e.g., a wave of nerve growth factor) support the self-organization somewhat analogous to the neural networks utilized in deep learning models.
Like the neocortex, neural networks employ a hierarchy of layered filters in which each layer considers information from a prior layer (or the operating environment), and then passes its output (and possibly the original input), to other layers.
Other researchers have argued that unsupervised forms of deep learning, such as those based on hierarchical generative models and deep belief networks, may be closer to biological reality.
Such techniques lack ways of representing causal relationships (...) have no obvious ways of performing logical inferences, and they are also still a long way from integrating abstract knowledge, such as information about what objects are, what they are for, and how they are typically used.
systems, like Watson (...) use techniques like deep learning as just one element in a very complicated ensemble of techniques, ranging from the statistical technique of Bayesian inference to deductive reasoning.'
As an alternative to this emphasis on the limits of deep learning, one author speculated that it might be possible to train a machine vision stack to perform the sophisticated task of discriminating between 'old master' and amateur figure drawings, and hypothesized that such a sensitivity might represent the rudiments of a non-trivial machine empathy.
In further reference to the idea that artistic sensitivity might inhere within relatively low levels of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained
Learning a grammar (visual or linguistic) from training data would be equivalent to restricting the system to commonsense reasoning that operates on concepts in terms of grammatical production rules and is a basic goal of both human language acquisition
Such a manipulation is termed an “adversarial attack.” In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points and thereby generate images that deceived it.
Another group showed that certain psychedelic spectacles could fool a facial recognition system into thinking ordinary people were celebrities, potentially allowing one person to impersonate another.
ANNs can however be further trained to detect attempts at deception, potentially leading attackers and defenders into an arms race similar to the kind that already defines the malware defense industry.
ANNs have been trained to defeat ANN-based anti-malware software by repeatedly attacking a defense with malware that was continually altered by a genetic algorithm until it tricked the anti-malware while retaining its ability to damage the target.
You can probably use deep learning even if your data isn't that big
Over at Simply Stats Jeff Leek posted an article entitled “Don’t use deep learning your data isn’t that big” that I’ll admit, rustled my jimmies a little bit.
To be clear, I don’t think deep learning is a universal panacea and I mostly agree with his central thesis (more on that later), but I think there are several things going on at once, and I’d like to explore a few of those further in this post.
We tried to mirror the original analysis as closely as possible - we did 5-fold cross validation but used the standard MNIST test set for evaluation (about 2,000 validation samples for 0s and 1s).
The MLP used in the original analysis still looks pretty bad for small sample sizes, but our neural nets get essentially perfect accuracy for all sample sizes.
You should always keep this in mind when working on a deep learning model: Model details are very important and you should be wary of blackbox calls to anything the looks like deeplearning() Here are my best guesses at what is going on in the original post: Thankfully, the good folks at RStudio just released an R interface to Keras, so I was able to recreate my python code in pure R.
Finally, I wanted to revisit a point Jeff made in the original post, specifically this statement: The issue is that only a very few places actually have the data to do deep learning […] But I’ve always thought that the major advantage of using deep learning over simpler models is that if you have a massive amount of data you can fit a massive number of parameters.
Many people seem to think of deep learning as a huge black box with a ton of parameters that can learn any function, provided you have enough data (where enough is some where between a million and Graham’s number of samples).
Here’s a quick run down of some reasons why I think they’ve been successful: To sum up, I think the above reasons are good explanations for why deep learning works in practice, more so than the lots of parameters and lots of data hypothesis.
He told Page, who had read an early draft, that he wanted to start a company to develop his ideas about how to build a truly intelligent computer: one that could understand language and then make inferences and decisions on its own.
The basic idea—that software can simulate the neocortex’s large array of neurons in an artificial “neural network”—is decades old, and it has led to as many disappointments as breakthroughs.
Last June, a Google deep-learning system that had been shown 10 million images from YouTube videos proved almost twice as good as any previous image recognition effort at identifying objects such as cats.
In October, Microsoft chief research officer Rick Rashid wowed attendees at a lecture in China with a demonstration of speech software that transcribed his spoken words into English text with an error rate of 7 percent, translated them into Chinese-language text, and then simulated his own voice uttering them in Mandarin.
Hinton, who will split his time between the university and Google, says he plans to “take ideas out of this field and apply them to real problems” such as image recognition, search, and natural-language understanding, he says.
Extending deep learning into applications beyond speech and image recognition will require more conceptual and software breakthroughs, not to mention many more advances in processing power.
Neural networks, developed in the 1950s not long after the dawn of AI research, looked promising because they attempted to simulate the way the brain worked, though in greatly simplified form.
These weights determine how each simulated neuron responds—with a mathematical output between 0 and 1—to a digitized feature such as an edge or a shade of blue in an image, or a particular energy level at one frequency in a phoneme, the individual unit of sound in spoken syllables.
Programmers would train a neural network to detect an object or phoneme by blitzing the network with digitized versions of images containing those objects or sound waves containing those phonemes.
The eventual goal of this training was to get the network to consistently recognize the patterns in speech or sets of images that we humans know as, say, the phoneme “d” or the image of a dog.
This is much the same way a child learns what a dog is by noticing the details of head shape, behavior, and the like in furry, barking animals that other people call dogs.
Once that layer accurately recognizes those features, they’re fed to the next layer, which trains itself to recognize more complex features, like a corner or a combination of speech sounds.
Because the multiple layers of neurons allow for more precise training on the many variants of a sound, the system can recognize scraps of sound more reliably, especially in noisy environments such as subway platforms.
Hawkins, author of On Intelligence, a 2004 book on how the brain works and how it might provide a guide to building intelligent machines, says deep learning fails to account for the concept of time.
Brains process streams of sensory data, he says, and human learning depends on our ability to recall sequences of patterns: when you watch a video of a cat doing something funny, it’s the motion that matters, not a series of still images like those Google used in its experiment.
In high school, he wrote software that enabled a computer to create original music in various classical styles, which he demonstrated in a 1965 appearance on the TV show I’ve Got a Secret.
Since then, his inventions have included several firsts—a print-to-speech reading machine, software that could scan and digitize printed text in any font, music synthesizers that could re-create the sound of orchestral instruments, and a speech recognition system with a large vocabulary.
This isn’t his immediate goal at Google, but it matches that of Google cofounder Sergey Brin, who said in the company’s early days that he wanted to build the equivalent of the sentient computer HAL in 2001: A Space Odyssey—except one that wouldn’t kill people.
“My mandate is to give computers enough understanding of natural language to do useful things—do a better job of search, do a better job of answering questions,” he says.
queries as quirky as “a long, tiresome speech delivered by a frothy pie topping.” (Watson’s correct answer: “What is a meringue harangue?”) Kurzweil isn’t focused solely on deep learning, though he says his approach to speech recognition is based on similar theories about how the brain works.
“That’s not a project I think I’ll ever finish.” Though Kurzweil’s vision is still years from reality, deep learning is likely to spur other applications beyond speech and image recognition in the nearer term.
Microsoft’s Peter Lee says there’s promising early research on potential uses of deep learning in machine vision—technologies that use imaging for applications such as industrial inspection and robot guidance.
A Beginner's Guide to Neural Networks and Deep Learning
Contents Neural networks are a set of algorithms, modeled loosely after the human brain, that are designed to recognize patterns.
so you can think of deep neural networks as components of larger machine-learning applications involving algorithms for reinforcement learning, classification and regression.) What kind of problems does deep learning solve, and more importantly, can it solve yours?
It is known as a “universal approximator”, because it can learn to approximate an unknown function f(x) = y between any input x and any output y, assuming they are related at all (by correlation or causation, for example).
In the process of learning, a neural network finds the right f, or the correct manner of transforming x into y, whether that be f(x) = 3x + 12 or f(x) = 9x - 0.1.
A node combines input from the data with a set of coefficients, or weights, that either amplify or dampen that input, thereby assigning significance to inputs for the task the algorithm is trying to learn.
(For example, which input is most helpful is classifying data without error?) These input-weight products are summed and the sum is passed through a node’s so-called activation function, to determine whether and to what extent that signal progresses further through the network to affect the ultimate outcome, say, an act of classification.
Therefore, one of the problems deep learning solves best is in processing and clustering the world’s raw, unlabeled media, discerning similarities and anomalies in data that no human has organized in a relational database or ever put a name to.
For example, deep learning can take a million images, and cluster them according to their similarities: cats in one corner, ice breakers in another, and in a third all the photos of your grandmother.
Given that feature extraction is a task that can take teams of data scientists years to accomplish, deep learning is a way to circumvent the chokepoint of limited experts.
When training on unlabeled data, each node layer in a deep network learns features automatically by repeatedly trying to reconstruct the input from which it draws its samples, attempting to minimize the difference between the network’s guesses and the probability distribution of the input data itself.
In the process, these networks learn to recognize correlations between certain relevant features and optimal results – they draw connections between feature signals and what those features represent, whether it be a full reconstruction, or with labeled data.
(Bad algorithms trained on lots of data can outperform good algorithms trained on very little.) Deep learning’s ability to process and learn from huge quantities of unlabeled data give it a distinct advantage over previous algorithms.
The starting line for the race is the state in which our weights are initialized, and the finish line is the state of those parameters when they are capable of producing accurate classifications and predictions.
collection of weights, whether they are in their start or end state, is also called a model, because it is an attempt to model data’s relationship to ground-truth labels, to grasp the data’s structure.
(You can think of a neural network as a miniature enactment of the scientific method, testing hypotheses and trying again – only it is the scientific method with a blindfold on.) Here is a simple explanation of what happens during learning with a feedforward neural network, the simplest architecture to explain.
The neural then takes its guess and compares it to a ground-truth about the data, effectively asking an expert “Did I get this right?” The difference between the network’s guess and the ground truth is its error.
The three pseudo-mathematical formulas above account for the three key functions of neural networks: scoring input, calculating loss and applying an update to the model – to begin the three-step process over again.
In its simplest form, linear regression is expressed as where Y_hat is the estimated output, X is the input, b is the slope and a is the intercept of a line on the vertical axis of a two-dimensional graph.
It’s typically expressed like this: (To extend the crop example above, you might add the amount of sunlight and rainfall in a growing season to the fertilizer variable, with all three affecting Y_hat.) Now, that form of multiple linear regression is happening at every node of a neural network.
The output of all nodes, each squashed into an s-shaped space between 0 and 1, is then passed as input to the next layer in a feed forward neural network, and so on until the signal reaches the final layer of the net, where decisions are made.
The name for one commonly used optimization function that adjusts weights according to the error they caused is called “gradient descent.” Gradient is another word for slope, and slope, in its typical form on an x-y graph, represents how two variables relate to each other: rise over run, the change in money over the change in time, etc.
the signal of the weight passes through activations and sums over several layers, so we use the chain rule of calculus to march back through the networks activations and outputs and finally arrive at the weight in question, and its relationship to overall error.
That is, given two variables, Error and weight, that are mediated by a third variable, activation, through which the weight is passed, you can calculate how a change in weight affects a change in Error by first calculating how a change in activation affects a change in Error, and how a change in weight affects a change in activation.
(We’re 120% sure of that.) As the input x that triggers a label grows, the expression e to the x shrinks toward zero, leaving us with the fraction 1/1, or 100%, which means we approach (without ever quite reaching) absolute certainty that the label applies.
Input that correlates negatively with your output will have its value flipped by the negative sign on e’s exponent, and as that negative signal grows, the quantity e to the x becomes larger, pushing the entire fraction ever closer to zero.
You can set different thresholds as you prefer – a low threshold will increase the number of false positives, and a higher one will increase the number of false negatives – depending on which side you would like to err.
That said, gradient descent is not recombining every weight with every other to find the best match – its method of pathfinding shrinks the relevant weight space, and therefore the number of updates and required computation, by many orders of magnitude.
- On 7. marts 2021
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