6,096 research outputs found
Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks
Information fusion is an essential part of numerous engineering systems and
biological functions, e.g., human cognition. Fusion occurs at many levels,
ranging from the low-level combination of signals to the high-level aggregation
of heterogeneous decision-making processes. While the last decade has witnessed
an explosion of research in deep learning, fusion in neural networks has not
observed the same revolution. Specifically, most neural fusion approaches are
ad hoc, are not understood, are distributed versus localized, and/or
explainability is low (if present at all). Herein, we prove that the fuzzy
Choquet integral (ChI), a powerful nonlinear aggregation function, can be
represented as a multi-layer network, referred to hereafter as ChIMP. We also
put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient
descent-based optimization in light of the exponential number of ChI inequality
constraints. An additional benefit of ChIMP/iChIMP is that it enables
eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP
is applied to the fusion of a set of heterogeneous architecture deep models in
remote sensing. We show an improvement in model accuracy and our previously
established XAI indices shed light on the quality of our data, model, and its
decisions.Comment: IEEE Transactions on Fuzzy System
Flow Factorized Representation Learning
A prominent goal of representation learning research is to achieve
representations which are factorized in a useful manner with respect to the
ground truth factors of variation. The fields of disentangled and equivariant
representation learning have approached this ideal from a range of
complimentary perspectives; however, to date, most approaches have proven to
either be ill-specified or insufficiently flexible to effectively separate all
realistic factors of interest in a learned latent space. In this work, we
propose an alternative viewpoint on such structured representation learning
which we call Flow Factorized Representation Learning, and demonstrate it to
learn both more efficient and more usefully structured representations than
existing frameworks. Specifically, we introduce a generative model which
specifies a distinct set of latent probability paths that define different
input transformations. Each latent flow is generated by the gradient field of a
learned potential following dynamic optimal transport. Our novel setup brings
new understandings to both \textit{disentanglement} and \textit{equivariance}.
We show that our model achieves higher likelihoods on standard representation
learning benchmarks while simultaneously being closer to approximately
equivariant models. Furthermore, we demonstrate that the transformations
learned by our model are flexibly composable and can also extrapolate to new
data, implying a degree of robustness and generalizability approaching the
ultimate goal of usefully factorized representation learning.Comment: NeurIPS2
Spatial, environmental and anthropogenic effects on the taxon composition of hybridizing Daphnia
The competitive ability of hybrids, compared with their parental taxa, can cover a wide fitness range from poor to superior. For example communities of the Daphnia galeata–hyalina–cucullata species complex often show hybrid dominance. We tested whether taxa composition of 43 European lakes inhabited by this species complex can be explained by habitat characteristics (e.g. size descriptors, trophy level) or geography. We found that D. galeata occurs more frequently south of the Alps, whereas D. hyalina and D. cucullata are found more in the north. Lakes with D. galeata dominance had higher temperatures whereas D. hyalina dominance could be attributed to low phosphorus loads. The dominance of F1-hybrids, however, was not explainable with current environmental variables. In a subset of 28 lakes, we studied the impact of eutrophication history on F1-hybrid success. Lakes with the highest trophic state in the past tended to be dominated by F1-hybrids. Our data demonstrate that human-mediated habitat disturbance (eutrophication) has facilitated hybrid success and altered the Daphnia taxon composition across lakes. At the same time, specific habitat conditions might provide a refuge from hybridization for native genotypes
Extension of the fuzzy integral for general fuzzy set-valued information
The fuzzy integral (FI) is an extremely flexible aggregation operator. It is used in numerous applications, such as image processing, multicriteria decision making, skeletal age-at-death estimation, and multisource (e.g., feature, algorithm, sensor, and confidence) fusion. To date, a few works have appeared on the topic of generalizing Sugeno's original real-valued integrand and fuzzy measure (FM) for the case of higher order uncertain information (both integrand and measure). For the most part, these extensions are motivated by, and are consistent with, Zadeh's extension principle (EP). Namely, existing extensions focus on fuzzy number (FN), i.e., convex and normal fuzzy set- (FS) valued integrands. Herein, we put forth a new definition, called the generalized FI (gFI), and efficient algorithm for calculation for FS-valued integrands. In addition, we compare the gFI, numerically and theoretically, with our non-EP-based FI extension called the nondirect FI (NDFI). Examples are investigated in the areas of skeletal age-at-death estimation in forensic anthropology and multisource fusion. These applications help demonstrate the need and benefit of the proposed work. In particular, we show there is not one supreme technique. Instead, multiple extensions are of benefit in different contexts and applications
Self Normalizing Flows
Efficient gradient computation of the Jacobian determinant term is a core
problem in many machine learning settings, and especially so in the normalizing
flow framework. Most proposed flow models therefore either restrict to a
function class with easy evaluation of the Jacobian determinant, or an
efficient estimator thereof. However, these restrictions limit the performance
of such density models, frequently requiring significant depth to reach desired
performance levels. In this work, we propose Self Normalizing Flows, a flexible
framework for training normalizing flows by replacing expensive terms in the
gradient by learned approximate inverses at each layer. This reduces the
computational complexity of each layer's exact update from
to , allowing for the training of flow architectures which
were otherwise computationally infeasible, while also providing efficient
sampling. We show experimentally that such models are remarkably stable and
optimize to similar data likelihood values as their exact gradient
counterparts, while training more quickly and surpassing the performance of
functionally constrained counterparts
Functional Integral Approach to the Single Impurity Anderson Model
Recently, a functional integral representation was proposed by Weller
(Weller, W.: phys.~stat.~sol.~(b) {\bf 162}, 251 (1990)), in which the
fermionic fields strictly satisfy the constraint of no double occupancy at each
lattice site. This is achieved by introducing spin dependent Bose fields. The
functional integral method is applied to the single impurity Anderson model
both in the Kondo and mixed-valence regime. The f-electron Green's function and
susceptibility are calculated using an Ising-like representation for the Bose
fields. We discuss the difficulty to extract a spectral function from the
knowledge of the imaginary time Green's function. The results are compared with
NCA calculations.Comment: 11 pages, LaTeX, figures upon request, preprint No. 93/10/
Adaptive Silhouette Extraction In Dynamic Environments Using Fuzzy Logic
Extracting a human silhouette from an image is the enabling step for many high-level vision processing tasks, such as human tracking and activity analysis. In a
previous paper, we addressed some of the challenges in silhouette extraction and human tracking in a real-world unconstrained environment where the background is complex and dynamic. We extracted features from
image regions, accumulated the feature information over time, fused high-level knowledge with low-level features, and built a time-varying background model. A problem
with our system is that by adapting the background model, objects moved by a human are difficult to handle. In order to reinsert them into the background, we run the risk of cutting off part of the human silhouette, such
as in a quick arm movement. In this paper, we develop a fuzzy logic inference system to detach the silhouette of a moving object from the human body. Our experimental results demonstrate that the fuzzy inference system is
very efficient and robust.The authors are grateful for the support from NSF ITR grant IIS-0428420 and the U.S. Administration on Aging, under grant 90AM3013
Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure
We further develop the numerical algorithm for computing the gauge connection
of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In
particular, recent work on the generalized Donaldson algorithm is extended to
bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the
computation depends only on a one-dimensional ray in the Kahler moduli space,
it can probe slope-stability regardless of the size of h^{1,1}. Suitably
normalized error measures are introduced to quantitatively compare results for
different directions in Kahler moduli space. A significantly improved numerical
integration procedure based on adaptive refinements is described and
implemented. Finally, an efficient numerical check is proposed for determining
whether or not a vector bundle is slope-stable without computing its full
connection.Comment: 38 pages, 10 figure
- …