@article{jacobs_predicate/state_2016,
series = {The {Thirty}-second {Conference} on the {Mathematical} {Foundations} of {Programming} {Semantics} ({MFPS} {XXXII})},
title = {A {Predicate}/{State} {Transformer} {Semantics} for {Bayesian} {Learning}},
volume = {325},
issn = {1571-0661},
url = {http://www.sciencedirect.com/science/article/pii/S1571066116300883},
doi = {10/ggdgbb},
abstract = {This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These definitions are illustrated in many examples in discrete and continuous probability theory and also in quantum theory.},
language = {en},
urldate = {2019-11-24},
journal = {Electronic Notes in Theoretical Computer Science},
author = {Jacobs, Bart and Zanasi, Fabio},
month = oct,
year = {2016},
note = {ZSCC: 0000030},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Effectus theory, Programming language theory, Semantics},
pages = {185--200}
}
@article{heckerman_tutorial_1995,
title = {A {Tutorial} on {Learning} {With} {Bayesian} {Networks}},
url = {https://www.microsoft.com/en-us/research/publication/a-tutorial-on-learning-with-bayesian-networks/},
abstract = {A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can …},
language = {en-US},
urldate = {2019-11-22},
author = {Heckerman, David},
month = mar,
year = {1995},
note = {ZSCC: 0000058},
keywords = {Bayesianism, Classical ML, Machine learning}
}
@article{kurakin_adversarial_2017,
title = {Adversarial examples in the physical world},
url = {http://arxiv.org/abs/1607.02533},
abstract = {Most existing machine learning classifiers are highly vulnerable to adversarial examples. An adversarial example is a sample of input data which has been modified very slightly in a way that is intended to cause a machine learning classifier to misclassify it. In many cases, these modifications can be so subtle that a human observer does not even notice the modification at all, yet the classifier still makes a mistake. Adversarial examples pose security concerns because they could be used to perform an attack on machine learning systems, even if the adversary has no access to the underlying model. Up to now, all previous work have assumed a threat model in which the adversary can feed data directly into the machine learning classifier. This is not always the case for systems operating in the physical world, for example those which are using signals from cameras and other sensors as an input. This paper shows that even in such physical world scenarios, machine learning systems are vulnerable to adversarial examples. We demonstrate this by feeding adversarial images obtained from cell-phone camera to an ImageNet Inception classifier and measuring the classification accuracy of the system. We find that a large fraction of adversarial examples are classified incorrectly even when perceived through the camera.},
urldate = {2019-11-23},
journal = {arXiv:1607.02533 [cs, stat]},
author = {Kurakin, Alexey and Goodfellow, Ian and Bengio, Samy},
month = feb,
year = {2017},
note = {ZSCC: NoCitationData[s0]
arXiv: 1607.02533},
keywords = {Adversarial attacks, Classical ML, Machine learning}
}
@article{brown_adversarial_2018,
title = {Adversarial {Patch}},
url = {http://arxiv.org/abs/1712.09665},
abstract = {We present a method to create universal, robust, targeted adversarial image patches in the real world. The patches are universal because they can be used to attack any scene, robust because they work under a wide variety of transformations, and targeted because they can cause a classifier to output any target class. These adversarial patches can be printed, added to any scene, photographed, and presented to image classifiers; even when the patches are small, they cause the classifiers to ignore the other items in the scene and report a chosen target class. To reproduce the results from the paper, our code is available at https://github.com/tensorflow/cleverhans/tree/master/examples/adversarial\_patch},
urldate = {2019-11-23},
journal = {arXiv:1712.09665 [cs]},
author = {Brown, Tom B. and Mané, Dandelion and Roy, Aurko and Abadi, Martín and Gilmer, Justin},
month = may,
year = {2018},
note = {ZSCC: NoCitationData[s0]
arXiv: 1712.09665},
keywords = {Adversarial attacks, Classical ML, Machine learning}
}
@misc{murfet_algebra_nodate,
title = {Algebra and {Artiﬁcial} {Intelligence}},
language = {en},
author = {Murfet, Daniel},
note = {ZSCC: NoCitationData[s0]},
keywords = {Algebra, Classical ML, Machine learning, Sketchy}
}
@inproceedings{izbicki_algebraic_2013,
title = {Algebraic classifiers: a generic approach to fast cross-validation, online training, and parallel training},
shorttitle = {Algebraic classifiers},
abstract = {We use abstract algebra to derive new algorithms for fast cross-validation, online learning, and parallel learning. To use these algorithms on a classification model, we must show that the model has appropriate algebraic structure. It is easy to give algebraic structure to some models, and we do this explicitly for Bayesian classifiers and a novel variation of decision stumps called HomStumps. But not all classifiers have an obvious structure, so we introduce the Free HomTrainer. This can be used to give a "generic" algebraic structure to any classifier. We use the Free HomTrainer to give algebraic structure to bagging and boosting. In so doing, we derive novel online and parallel algorithms, and present the first fast cross-validation schemes for these classifiers.},
booktitle = {{ICML}},
author = {Izbicki, Michael},
year = {2013},
note = {ZSCC: 0000013},
keywords = {Algebra, Categorical ML, Machine learning}
}
@misc{watanabe_algebraic_2009,
title = {Algebraic {Geometry} and {Statistical} {Learning} {Theory}},
url = {/core/books/algebraic-geometry-and-statistical-learning-theory/9C8FD1BDC817E2FC79117C7F41544A3A},
abstract = {Cambridge Core - Pattern Recognition and Machine Learning - Algebraic Geometry and Statistical Learning Theory - by Sumio Watanabe},
language = {en},
urldate = {2019-11-22},
journal = {Cambridge Core},
author = {Watanabe, Sumio},
month = aug,
year = {2009},
doi = {10.1017/CBO9780511800474},
note = {ZSCC: 0000276 },
keywords = {Algebra, Bayesianism, Purely theoretical, Statistical learning theory}
}
@article{martin-maroto_algebraic_2018,
title = {Algebraic {Machine} {Learning}},
url = {http://arxiv.org/abs/1803.05252},
abstract = {Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to other datasets. To achieve generalization something else is needed, for example a regularization method or stopping the training when error in a validation dataset is minimal. Here we propose a different approach to learning and generalization that is parameter-free, fully discrete and that does not use function minimization. We use the training data to find an algebraic representation with minimal size and maximal freedom, explicitly expressed as a product of irreducible components. This algebraic representation is shown to directly generalize, giving high accuracy in test data, more so the smaller the representation. We prove that the number of generalizing representations can be very large and the algebra only needs to find one. We also derive and test a relationship between compression and error rate. We give results for a simple problem solved step by step, hand-written character recognition, and the Queens Completion problem as an example of unsupervised learning. As an alternative to statistical learning, algebraic learning may offer advantages in combining bottom-up and top-down information, formal concept derivation from data and large-scale parallelization.},
urldate = {2019-10-10},
journal = {arXiv:1803.05252 [cs, math]},
author = {Martin-Maroto, Fernando and de Polavieja, Gonzalo G.},
month = mar,
year = {2018},
note = {arXiv: 1803.05252}
}
@misc{borchert_amzn/milan_2019,
title = {amzn/milan},
copyright = {Apache-2.0},
url = {https://github.com/amzn/milan},
abstract = {Milan is a Scala API and runtime infrastructure for building data-oriented systems, built on top of Apache Flink.},
urldate = {2019-11-27},
publisher = {Amazon},
author = {Borchert, Tom},
month = nov,
year = {2019},
note = {ZSCC: NoCitationData[s0]
original-date: 2019-11-06T22:37:51Z},
keywords = {Implementation, Machine learning, Probabilistic programming}
}
@article{hamrick_analogues_2019,
series = {{SI}: 29: {Artificial} {Intelligence} (2019)},
title = {Analogues of mental simulation and imagination in deep learning},
volume = {29},
issn = {2352-1546},
url = {http://www.sciencedirect.com/science/article/pii/S2352154618301670},
doi = {10.1016/j.cobeha.2018.12.011},
abstract = {Mental simulation—the capacity to imagine what will or what could be—is a salient feature of human cognition, playing a key role in a wide range of cognitive abilities. In artificial intelligence, the last few years have seen the development of methods which are analogous to mental models and mental simulation. This paper outlines recent methods in deep learning for constructing such models from data and learning to use them via reinforcement learning, and compares such approaches to human mental simulation. Model-based methods in deep learning can serve as powerful tools for building and scaling cognitive models. However, a number of challenges remain in matching the capacity of human mental simulation for efficiency, compositionality, generalization, and creativity.},
urldate = {2019-10-10},
journal = {Current Opinion in Behavioral Sciences},
author = {Hamrick, Jessica B},
month = oct,
year = {2019},
pages = {8--16}
}
@article{olah_attention_2016,
title = {Attention and {Augmented} {Recurrent} {Neural} {Networks}},
volume = {1},
issn = {2476-0757},
url = {http://distill.pub/2016/augmented-rnns},
doi = {10/gf33sg},
abstract = {A visual overview of neural attention, and the powerful extensions of neural networks being built on top of it.},
language = {en},
number = {9},
urldate = {2019-11-22},
journal = {Distill},
author = {Olah, Chris and Carter, Shan},
month = sep,
year = {2016},
note = {ZSCC: 0000042},
keywords = {Classical ML, Machine learning},
pages = {e1}
}
@article{baydin_automatic_2018,
title = {Automatic differentiation in machine learning: a survey},
shorttitle = {Automatic differentiation in machine learning},
url = {http://arxiv.org/abs/1502.05767},
abstract = {Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.},
urldate = {2019-11-22},
journal = {arXiv:1502.05767 [cs, stat]},
author = {Baydin, Atilim Gunes and Pearlmutter, Barak A. and Radul, Alexey Andreyevich and Siskind, Jeffrey Mark},
month = feb,
year = {2018},
note = {ZSCC: 0000318
arXiv: 1502.05767},
keywords = {Automatic differentiation, Classical ML, Differentiation, Machine learning}
}
@article{fong_backprop_2019,
title = {Backprop as {Functor}: {A} compositional perspective on supervised learning},
shorttitle = {Backprop as {Functor}},
url = {http://arxiv.org/abs/1711.10455},
abstract = {A supervised learning algorithm searches over a set of functions \$A {\textbackslash}to B\$ parametrised by a space \$P\$ to find the best approximation to some ideal function \$f{\textbackslash}colon A {\textbackslash}to B\$. It does this by taking examples \$(a,f(a)) {\textbackslash}in A{\textbackslash}times B\$, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.},
urldate = {2019-11-23},
journal = {arXiv:1711.10455 [cs, math]},
author = {Fong, Brendan and Spivak, David I. and Tuyéras, Rémy},
month = may,
year = {2019},
note = {ZSCC: 0000015
arXiv: 1711.10455},
keywords = {Categorical ML, Machine learning, Purely theoretical}
}
@article{culbertson_bayesian_2013,
title = {Bayesian machine learning via category theory},
url = {http://arxiv.org/abs/1312.1445},
abstract = {From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.},
urldate = {2019-11-22},
journal = {arXiv:1312.1445 [math]},
author = {Culbertson, Jared and Sturtz, Kirk},
month = dec,
year = {2013},
note = {ZSCC: 0000006
arXiv: 1312.1445},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Purely theoretical}
}
@article{jacobs_categorical_2018,
title = {Categorical {Aspects} of {Parameter} {Learning}},
url = {http://arxiv.org/abs/1810.05814},
abstract = {Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known. There are basically two ways of doing so, referred to as maximal likelihood estimation (MLE) and as Bayesian learning. This paper provides a categorical analysis of these two techniques and describes them in terms of basic properties of the multiset monad M, the distribution monad D and the Giry monad G. In essence, learning is about the reltionships between multisets (used for counting) on the one hand and probability distributions on the other. These relationsips will be described as suitable natural transformations.},
urldate = {2019-11-21},
journal = {arXiv:1810.05814 [cs]},
author = {Jacobs, Bart},
month = oct,
year = {2018},
note = {ZSCC: 0000001
arXiv: 1810.05814},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Machine learning}
}
@article{harris_characterizing_2019,
title = {Characterizing the invariances of learning algorithms using category theory},
url = {http://arxiv.org/abs/1905.02072},
abstract = {Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.},
urldate = {2019-10-10},
journal = {arXiv:1905.02072 [cs, math, stat]},
author = {Harris, Kenneth D.},
month = may,
year = {2019},
note = {arXiv: 1905.02072}
}
@article{tran_deep_2017,
title = {Deep {Probabilistic} {Programming}},
url = {http://arxiv.org/abs/1701.03757},
abstract = {We propose Edward, a Turing-complete probabilistic programming language. Edward defines two compositional representations---random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation to variational inference to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks. For efficiency, Edward is integrated into TensorFlow, providing significant speedups over existing probabilistic systems. For example, we show on a benchmark logistic regression task that Edward is at least 35x faster than Stan and 6x faster than PyMC3. Further, Edward incurs no runtime overhead: it is as fast as handwritten TensorFlow.},
urldate = {2019-11-27},
journal = {arXiv:1701.03757 [cs, stat]},
author = {Tran, Dustin and Hoffman, Matthew D. and Saurous, Rif A. and Brevdo, Eugene and Murphy, Kevin and Blei, David M.},
month = mar,
year = {2017},
note = {ZSCC: 0000108
arXiv: 1701.03757},
keywords = {Bayesian inference, Implementation, Machine learning, Probabilistic programming}
}
@article{murfet_derivatives_2019,
title = {Derivatives of {Turing} machines in {Linear} {Logic}},
url = {http://arxiv.org/abs/1805.11813},
abstract = {We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.},
urldate = {2019-11-21},
journal = {arXiv:1805.11813 [math]},
author = {Murfet, Daniel and Clift, James},
month = jan,
year = {2019},
note = {ZSCC: NoCitationData[s0]
arXiv: 1805.11813},
keywords = {Abstract machines, Categorical ML, Differentiation, Linear logic, Machine learning}
}
@inproceedings{sprunger_differentiable_2019,
address = {Vancouver, BC, Canada},
title = {Differentiable {Causal} {Computations} via {Delayed} {Trace}},
isbn = {978-1-72813-608-0},
url = {https://ieeexplore.ieee.org/document/8785670/},
doi = {10/ggdf98},
abstract = {We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the ﬁrst n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called “delayed trace”, which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee.},
language = {en},
urldate = {2019-11-23},
booktitle = {2019 34th {Annual} {ACM}/{IEEE} {Symposium} on {Logic} in {Computer} {Science} ({LICS})},
publisher = {IEEE},
author = {Sprunger, David and Katsumata, Shin-ya},
month = jun,
year = {2019},
note = {ZSCC: 0000002},
keywords = {Categorical ML, Differentiation},
pages = {1--12}
}
@misc{murfet_dmurfet/2simplicialtransformer_2019,
title = {dmurfet/2simplicialtransformer},
url = {https://github.com/dmurfet/2simplicialtransformer},
abstract = {Code for the 2-simplicial Transformer paper. Contribute to dmurfet/2simplicialtransformer development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = oct,
year = {2019},
note = {ZSCC: NoCitationData[s0]
original-date: 2019-08-29T13:26:13Z},
keywords = {Abstract machines, Algebra, Implementation, Machine learning, Semantics}
}
@misc{murfet_dmurfet/deeplinearlogic_2018,
title = {dmurfet/deeplinearlogic},
url = {https://github.com/dmurfet/deeplinearlogic},
abstract = {Deep learning and linear logic. Contribute to dmurfet/deeplinearlogic development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = jul,
year = {2018},
note = {ZSCC: NoCitationData[s0]
original-date: 2016-11-05T09:17:10Z},
keywords = {Categorical ML, Implementation, Linear logic, Machine learning, Semantics}
}
@misc{murfet_dmurfet/polysemantics_2018,
title = {dmurfet/polysemantics},
url = {https://github.com/dmurfet/polysemantics},
abstract = {Polynomial semantics of linear logic. Contribute to dmurfet/polysemantics development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = apr,
year = {2018},
note = {ZSCC: NoCitationData[s0]
original-date: 2016-02-23T03:29:42Z},
keywords = {Categorical ML, Implementation, Linear logic, Machine learning, Semantics}
}
@article{goodfellow_explaining_2015,
title = {Explaining and {Harnessing} {Adversarial} {Examples}},
url = {http://arxiv.org/abs/1412.6572},
abstract = {Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.},
urldate = {2019-11-23},
journal = {arXiv:1412.6572 [cs, stat]},
author = {Goodfellow, Ian J. and Shlens, Jonathon and Szegedy, Christian},
month = mar,
year = {2015},
note = {ZSCC: 0000015
arXiv: 1412.6572},
keywords = {Adversarial attacks, Classical ML, Machine learning}
}
@article{goodfellow_generative_2014,
title = {Generative {Adversarial} {Networks}},
url = {http://arxiv.org/abs/1406.2661},
abstract = {We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.},
urldate = {2019-11-28},
journal = {arXiv:1406.2661 [cs, stat]},
author = {Goodfellow, Ian J. and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua},
month = jun,
year = {2014},
note = {ZSCC: 0000010
arXiv: 1406.2661},
keywords = {Adversarial attacks, Classical ML, Implementation, Machine learning}
}
@incollection{wermuth_graphical_2001,
address = {Oxford},
title = {Graphical {Models}: {Overview}},
isbn = {978-0-08-043076-8},
shorttitle = {Graphical {Models}},
url = {http://www.sciencedirect.com/science/article/pii/B008043076700440X},
abstract = {Graphical Markov models provide a method of representing possibly complicated multivariate dependencies in such a way that the general qualitative features can be understood, that statistical independencies are highlighted, and that some properties can be derived directly. Variables are represented by the nodes of a graph. Pairs of nodes may be joined by an edge. Edges are directed if one variable is a response to the other variable considered as explanatory, but are undirected if the variables are on an equal footing. Absence of an edge typically implies statistical independence, conditional, or marginal depending on the kind of graph. The need for a number of types of graph arises because it is helpful to represent a number of different kinds of dependence structures. Of special importance are chain graphs in which variables are arranged in a sequence or chain of blocks, the variables in any one block being on an equal footing, some being possibly joint responses to variables in the past and some being jointly explanatory to variables in the future of the block considered. Some main properties of such systems are outlined, and recent research results are sketched. Suggestions for further reading are given. As an illustrative example, some analysis of data on the treatment of chronic pain is presented.},
language = {en},
urldate = {2019-11-22},
booktitle = {International {Encyclopedia} of the {Social} \& {Behavioral} {Sciences}},
publisher = {Pergamon},
author = {Wermuth, N. and Cox, D. R.},
editor = {Smelser, Neil J. and Baltes, Paul B.},
month = jan,
year = {2001},
doi = {10.1016/B0-08-043076-7/00440-X},
note = {ZSCC: NoCitationData[s0] },
keywords = {Bayesianism, Classical ML, Machine learning},
pages = {6379--6386}
}
@article{philipona_is_2003,
title = {Is {There} {Something} {Out} {There}? {Inferring} {Space} from {Sensorimotor} {Dependencies}},
volume = {15},
shorttitle = {Is {There} {Something} {Out} {There}?},
doi = {10/frg7gs},
abstract = {This letter suggests that in biological organisms, the perceived structure of reality, in particular the notions of body, environment, space, object, and attribute, could be a consequence of an effort on the part of brains to account for the dependency between their inputs and their outputs in terms of a small number of parameters. To validate this idea, a procedure is demonstrated whereby the brain of a (simulated) organism with arbitrary input and output connectivity can deduce the dimensionality of the rigid group of the space underlying its input-output relationship, that is, the dimension of what the organism will call physical space.},
journal = {Neural computation},
author = {Philipona, David and O’Regan, J. and Nadal, Jean-Pierre},
month = oct,
year = {2003},
note = {ZSCC: 0000225},
keywords = {Algebra, Neuroscience},
pages = {2029--49}
}
@misc{murfet_linear_nodate,
title = {Linear logic and deep learning},
language = {en},
author = {Murfet, Daniel and Hu, Huiyi},
note = {ZSCC: NoCitationData[s0]},
keywords = {Categorical ML, Linear logic, Machine learning, Semantics}
}
@article{murfet_logic_2019,
title = {Logic and the \$2\$-{Simplicial} {Transformer}},
url = {http://arxiv.org/abs/1909.00668},
abstract = {We introduce the \$2\$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.},
urldate = {2019-11-21},
journal = {arXiv:1909.00668 [cs, stat]},
author = {Murfet, Daniel and Clift, James and Doryn, Dmitry and Wallbridge, James},
month = sep,
year = {2019},
note = {ZSCC: 0000000
arXiv: 1909.00668
version: 1},
keywords = {Abstract machines, Algebra, Machine learning, Semantics}
}
@article{serafini_logic_2016,
title = {Logic {Tensor} {Networks}: {Deep} {Learning} and {Logical} {Reasoning} from {Data} and {Knowledge}},
shorttitle = {Logic {Tensor} {Networks}},
url = {http://arxiv.org/abs/1606.04422},
abstract = {We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and semantics defined concretely on the domain of real numbers. Logical constants are interpreted as feature vectors of real numbers. Real Logic promotes a well-founded integration of deductive reasoning on a knowledge-base and efficient data-driven relational machine learning. We show how Real Logic can be implemented in deep Tensor Neural Networks with the use of Google's tensorflow primitives. The paper concludes with experiments applying Logic Tensor Networks on a simple but representative example of knowledge completion.},
urldate = {2019-11-24},
journal = {arXiv:1606.04422 [cs]},
author = {Serafini, Luciano and Garcez, Artur d'Avila},
month = jul,
year = {2016},
note = {ZSCC: 0000057
arXiv: 1606.04422},
keywords = {Abstract machines, Machine learning, Symbolic logic}
}
@inproceedings{fages_machine_2006,
address = {Berlin, Heidelberg},
series = {Lecture {Notes} in {Computer} {Science}},
title = {Machine {Learning} {Biochemical} {Networks} from {Temporal} {Logic} {Properties}},
isbn = {978-3-540-46236-1},
doi = {10/dd8},
abstract = {One central issue in systems biology is the definition of formal languages for describing complex biochemical systems and their behavior at different levels. The biochemical abstract machine BIOCHAM is based on two formal languages, one rule-based language used for modeling biochemical networks, at three abstraction levels corresponding to three semantics: boolean, concentration and population; and one temporal logic language used for formalizing the biological properties of the system. In this paper, we show how the temporal logic language can be turned into a specification language. We describe two algorithms for inferring reaction rules and kinetic parameter values from a temporal specification formalizing the biological data. Then, with an example of the cell cycle control, we illustrate how these machine learning techniques may be useful to the modeler.},
language = {en},
booktitle = {Transactions on {Computational} {Systems} {Biology} {VI}},
publisher = {Springer},
author = {Fages, François and Calzone, Laurence and Chabrier-Rivier, Nathalie and Soliman, Sylvain},
editor = {Priami, Corrado and Plotkin, Gordon},
year = {2006},
note = {ZSCC: NoCitationData[s0]},
keywords = {Abstract machines, Biology, Classical ML, Machine learning, Symbolic logic, Systems biology},
pages = {68--94}
}
@misc{murfet_mathematics_nodate,
title = {Mathematics of {AlphaGo}},
author = {Murfet, Daniel},
note = {ZSCC: NoCitationData[s0]},
keywords = {Classical ML, Machine learning}
}
@book{winn_model-based_2019,
title = {Model-{Based} {Machine} {Learning}},
isbn = {978-1-4987-5681-5},
abstract = {This book is unusual for a machine learning text book in that the authors do not review dozens of different algorithms. Instead they introduce all of the key ideas through a series of case studies involving real-world applications. Case studies play a central role because it is only in the context of applications that it makes sense to discuss modelling assumptions. Each chapter therefore introduces one case study which is drawn from a real-world application that has been solved using a model-based approach.},
language = {en},
publisher = {Taylor \& Francis Incorporated},
author = {Winn, John Michael},
month = jun,
year = {2019},
note = {ZSCC: NoCitationData[s1]
Google-Books-ID: 84KRtgEACAAJ},
keywords = {Bayesian inference, Classical ML, Implementation}
}
@article{dong_neural_2019,
title = {Neural {Logic} {Machines}},
url = {http://arxiv.org/abs/1904.11694},
abstract = {We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.},
urldate = {2019-11-24},
journal = {arXiv:1904.11694 [cs, stat]},
author = {Dong, Honghua and Mao, Jiayuan and Lin, Tian and Wang, Chong and Li, Lihong and Zhou, Denny},
month = apr,
year = {2019},
note = {ZSCC: 0000008
arXiv: 1904.11694},
keywords = {Abstract machines, Machine learning, Symbolic logic}
}
@article{jacobs_neural_2018,
title = {Neural {Nets} via {Forward} {State} {Transformation} and {Backward} {Loss} {Transformation}},
url = {http://arxiv.org/abs/1803.09356},
abstract = {This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program semantics. The common two-pass neural network training algorithms make this viewpoint particularly fitting. In the forward direction, neural networks act as state transformers. In the reverse direction, however, neural networks change losses of outputs to losses of inputs, thereby acting like a (real-valued) predicate transformer. In this way, backpropagation is functorial by construction, as shown earlier in recent other work. We illustrate this perspective by training a simple instance of a neural network.},
urldate = {2019-11-21},
journal = {arXiv:1803.09356 [cs]},
author = {Jacobs, Bart and Sprunger, David},
month = mar,
year = {2018},
note = {ZSCC: 0000001
arXiv: 1803.09356},
keywords = {Categorical ML, Effectus theory, Machine learning}
}
@inproceedings{healy_neural_2004,
title = {Neural {Networks}, {Knowledge} and {Cognition}: {A} {Mathematical} {Semantic} {Model} {Based} upon {Category} {Theory}},
shorttitle = {Neural {Networks}, {Knowledge} and {Cognition}},
abstract = {Category theory can be applied to mathematically model the semantics of cognitive neural systems. We discuss semantics as a hierarchy of concepts, or symbolic descriptions of items sensed and represented in the connection weights distributed throughout a neural network. The hierarchy expresses subconcept relationships, and in a neural network it becomes represented incrementally through a Hebbian-like learning process. The categorical semantic model described here explains the learning process as the derivation of colimits and limits in a concept category. It explains the representation of the concept hierarchy in a neural network at each stage of learning as a system of functors and natural transformations, expressing knowledge coherence across the regions of a multi-regional network equipped with multiple sensors. The model yields design principles that constrain neural network designs capable of the most important aspects of cognitive behavior.},
author = {Healy, Michael J. and Caudell, Thomas P.},
year = {2004}
}
@article{graves_neural_2014,
title = {Neural {Turing} {Machines}},
url = {http://arxiv.org/abs/1410.5401},
abstract = {We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.},
urldate = {2019-11-21},
journal = {arXiv:1410.5401 [cs]},
author = {Graves, Alex and Wayne, Greg and Danihelka, Ivo},
month = dec,
year = {2014},
note = {ZSCC: 0001222
arXiv: 1410.5401},
keywords = {Abstract machines, Classical ML, Machine learning}
}
@article{siegelmann_computational_1995,
title = {On the {Computational} {Power} of {Neural} {Nets}},
volume = {50},
issn = {0022-0000},
url = {http://www.sciencedirect.com/science/article/pii/S0022000085710136},
doi = {10/dvwtc3},
abstract = {This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a linear combination of the previous states of all units. We prove that one may simulate all Turing machines by such nets. In particular, one can simulate any multi-stack Turing machine in real time, and there is a net made up of 886 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Non-deterministic Turing machines can be simulated by non-deterministic rational nets, also in real time. The simulation result has many consequences regarding the decidability, or more generally the complexity, of questions about recursive nets.},
language = {en},
number = {1},
urldate = {2019-11-28},
journal = {Journal of Computer and System Sciences},
author = {Siegelmann, H. T. and Sontag, E. D.},
month = feb,
year = {1995},
note = {ZSCC: 0000002},
keywords = {Classical ML, Machine learning},
pages = {132--150}
}
@article{ghahramani_probabilistic_2015,
title = {Probabilistic machine learning and artificial intelligence},
volume = {521},
issn = {0028-0836, 1476-4687},
url = {http://www.nature.com/articles/nature14541},
doi = {10/gdxwhq},
language = {en},
number = {7553},
urldate = {2019-11-28},
journal = {Nature},
author = {Ghahramani, Zoubin},
month = may,
year = {2015},
note = {ZSCC: 0000611},
keywords = {Bayesian inference, Classical ML, Machine learning, Probabilistic programming},
pages = {452--459}
}
@article{battaglia_relational_2018,
title = {Relational inductive biases, deep learning, and graph networks},
url = {http://arxiv.org/abs/1806.01261},
abstract = {Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.},
urldate = {2019-10-10},
journal = {arXiv:1806.01261 [cs, stat]},
author = {Battaglia, Peter W. and Hamrick, Jessica B. and Bapst, Victor and Sanchez-Gonzalez, Alvaro and Zambaldi, Vinicius and Malinowski, Mateusz and Tacchetti, Andrea and Raposo, David and Santoro, Adam and Faulkner, Ryan and Gulcehre, Caglar and Song, Francis and Ballard, Andrew and Gilmer, Justin and Dahl, George and Vaswani, Ashish and Allen, Kelsey and Nash, Charles and Langston, Victoria and Dyer, Chris and Heess, Nicolas and Wierstra, Daan and Kohli, Pushmeet and Botvinick, Matt and Vinyals, Oriol and Li, Yujia and Pascanu, Razvan},
month = jun,
year = {2018},
note = {arXiv: 1806.01261}
}
@article{eykholt_robust_2018,
title = {Robust {Physical}-{World} {Attacks} on {Deep} {Learning} {Models}},
url = {http://arxiv.org/abs/1707.08945},
abstract = {Recent studies show that the state-of-the-art deep neural networks (DNNs) are vulnerable to adversarial examples, resulting from small-magnitude perturbations added to the input. Given that that emerging physical systems are using DNNs in safety-critical situations, adversarial examples could mislead these systems and cause dangerous situations.Therefore, understanding adversarial examples in the physical world is an important step towards developing resilient learning algorithms. We propose a general attack algorithm,Robust Physical Perturbations (RP2), to generate robust visual adversarial perturbations under different physical conditions. Using the real-world case of road sign classification, we show that adversarial examples generated using RP2 achieve high targeted misclassification rates against standard-architecture road sign classifiers in the physical world under various environmental conditions, including viewpoints. Due to the current lack of a standardized testing method, we propose a two-stage evaluation methodology for robust physical adversarial examples consisting of lab and field tests. Using this methodology, we evaluate the efficacy of physical adversarial manipulations on real objects. Witha perturbation in the form of only black and white stickers,we attack a real stop sign, causing targeted misclassification in 100\% of the images obtained in lab settings, and in 84.8\%of the captured video frames obtained on a moving vehicle(field test) for the target classifier.},
urldate = {2019-11-23},
journal = {arXiv:1707.08945 [cs]},
author = {Eykholt, Kevin and Evtimov, Ivan and Fernandes, Earlence and Li, Bo and Rahmati, Amir and Xiao, Chaowei and Prakash, Atul and Kohno, Tadayoshi and Song, Dawn},
month = apr,
year = {2018},
note = {ZSCC: 0000005
arXiv: 1707.08945},
keywords = {Adversarial attacks, Classical ML, Machine learning}
}
@book{engeler_combinatory_1995,
series = {Progress in {Theoretical} {Computer} {Science}},
title = {The {Combinatory} {Programme}},
isbn = {978-0-8176-3801-6},
url = {https://www.springer.com/gb/book/9780817638016},
abstract = {Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to create a coherent mathematical view of these foundations. The result of this collaborative work is presented here in the hope that it does justice to the individual contributor and that the reader has a chance of judging the work as a whole. E. Engeler ETH Zurich, April 1994 lCollected in Chapter III, An Algebraization of Algorithmics, in Algorithmic Properties of Structures, Selected Papers of Erwin Engeler, World Scientific PubJ. Co. , Singapore, 1993, pp. 183-257. I Historical and Philosophical Background Erwin Engeler In the fall of 1928 a young American turned up at the Mathematical Institute of Gottingen, a mecca of mathematicians at the time; he was a young man with a dream and his name was H. B. Curry. He felt that he had the tools in hand with which to solve the problem of foundations of mathematics mice and for all. His was an approach that came to be called "formalist" and embodied that later became known as Combinatory Logic.},
language = {en},
urldate = {2019-11-26},
publisher = {Birkhäuser Basel},
author = {Engeler, Erwin},
year = {1995},
doi = {10.1007/978-1-4612-4268-0},
note = {ZSCC: NoCitationData[s1] },
keywords = {Algebra, Programming language theory, Purely theoretical}
}
@incollection{poggio_tomaso_2013,
title = {Tomaso {A}. {Poggio} autobiography},
url = {http://poggio-lab.mit.edu/sites/default/files/cv/tomasopoggio.pdf},
author = {Poggio, Tomaso},
year = {2013},
note = {ZSCC: NoCitationData[s0]},
keywords = {Classical ML, Compendium, Machine learning},
pages = {54}
}
@article{zhang_understanding_2017,
title = {Understanding deep learning requires rethinking generalization},
url = {http://arxiv.org/abs/1611.03530},
abstract = {Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training. Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice. We interpret our experimental findings by comparison with traditional models.},
urldate = {2019-11-22},
journal = {arXiv:1611.03530 [cs]},
author = {Zhang, Chiyuan and Bengio, Samy and Hardt, Moritz and Recht, Benjamin and Vinyals, Oriol},
month = feb,
year = {2017},
note = {ZSCC: NoCitationData[s0]
arXiv: 1611.03530},
keywords = {Classical ML, Machine learning}
}
@article{mccullagh_what_2002,
title = {What is a statistical model?},
volume = {30},
url = {http://projecteuclid.org/euclid.aos/1035844977},
doi = {10/bkts3m},
language = {en},
number = {5},
urldate = {2019-11-22},
journal = {The Annals of Statistics},
author = {McCullagh, Peter},
month = oct,
year = {2002},
note = {ZSCC: 0000230},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Compendium, Purely theoretical, Statistical learning theory},
pages = {1225--1310}
}
@article{paul_why_2015,
title = {Why does {Deep} {Learning} work? - {A} perspective from {Group} {Theory}},
shorttitle = {Why does {Deep} {Learning} work?},
url = {http://arxiv.org/abs/1412.6621},
abstract = {Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step called pre-training: first search for a good generative model for the input samples, and repeat the process one layer at a time. We show deeper implications of this simple principle, by establishing a connection with the interplay of orbits and stabilizers of group actions. Although the neural networks themselves may not form groups, we show the existence of \{{\textbackslash}em shadow\} groups whose elements serve as close approximations. Over the shadow groups, the pre-training step, originally introduced as a mechanism to better initialize a network, becomes equivalent to a search for features with minimal orbits. Intuitively, these features are in a way the \{{\textbackslash}em simplest\}. Which explains why a deep learning network learns simple features first. Next, we show how the same principle, when repeated in the deeper layers, can capture higher order representations, and why representation complexity increases as the layers get deeper.},
urldate = {2019-11-22},
journal = {arXiv:1412.6621 [cs, stat]},
author = {Paul, Arnab and Venkatasubramanian, Suresh},
month = feb,
year = {2015},
note = {ZSCC: NoCitationData[s0]
arXiv: 1412.6621},
keywords = {Classical ML, Machine learning}
}