arXiv research

New derivation shows how a three-factor learning rule is derived from Oja's rule.

Improved convergence speed of principal component analysis through modified learning rules.

Unified quadrature framework for large-scale kernel machines.

Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement …

New method classifies manifold-valued data using Riemannian geometry.

Proposes an alternative method to train RBMs with binary synapses using Bayesian learning rule.

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in-vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in-silico.…

We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using the Freudenthal's f…

Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus …

For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic fibers, we consider the parameterized surface induced by lifting a base geodesic to po…

We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors.

New characterizations of ruled real hypersurfaces in complex projective space found.

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These…

We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rul…

We show that for any Legendrian link $L$ in the $1$-jet space of $S^1$ the $2$-graded ruling polynomial, $R^2_L(z)$, is determined by the Thurston-Bennequin number and the HOMFLY-PT polynomial. Specifically, we recover $R^2_L(z)$ as a coefficient of a particular specialization of the HOMFLY-PT polynomial. Furthermore, …

For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A.…

New scoring rules compare probabilistic top lists in classification.

Paper constructs an example of a non-compact submanifold in a quaternionic Kähler symmetric space.

Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. …

The flow of a torus by inverse mean curvature keeps total curvature bounded until singularity.

Symmetric CNNs improve sequential recommendation and protein structure prediction.

Study on surfaces with constant curvature under a specific connection.

We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric versio…

Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition H^2(M)=(H^+) + (H^-). This implies, for example, that any such metric on a minimal ru…

R2N learns interpretable rules and literals from numerical features.

New foundation for Shapley value immune to coalitional manipulations.

New framework learns interpretable rule ensembles without sacrificing accuracy.

NeuRules learns interpretable rule lists from data without pre-discretization.

DeepCTRL integrates rules into deep learning models, allowing flexible control at inference.

New efficient method for inverse Z-transform reduces complexity significantly.

In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…

New methods prune unpromising rules from KGs, improving scalability and runtime.

New game approximates mean curvature flow evolution.

Paper extends transfer learning for decision rules, improving treatment rule estimation.

Study explores reinforcement learning in a complex game environment, analyzing rule inference and policy learning.

CRL approach improves understanding of heterogeneous treatment effects in complex diseases.

Generative models learn rules at different timescales, revealing a 'innovation window'.

A method for collecting human supervision that combines rules and instance labels.

A new learning rule consistently reduces error over data samples.

Advances rule-based multi-label classification using conformal prediction.

Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeabl…

New method for inferring network topology from partial data.

In a physical neural system, where storage and processing are intimately intertwined, the rules for adjusting the synaptic weights can only depend on variables that are available locally, such as the activity of the pre- and post-synaptic neurons, resulting in local learning rules. A systematic framework for studying t…

A new robust and flexible classification method for non-Gaussian data.

We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1)…

New pivoting strategy improves trace norm contraction in low-rank approximation.

Throughout music history, theorists have identified and documented interpretable rules that capture the decisions of composers. This paper asks, "Can a machine behave like a music theorist?" It presents MUS-ROVER, a self-learning system for automatically discovering rules from symbolic music. MUS-ROVER performs feature…

A new method learns interpretable decision rules using submodular optimization.