Building and Interpreting Deep Similarity Models

Abstract

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on distances or similarities. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation. We develop BiLRP, a scalable and theoretically founded method to systematically decompose the output of an already trained deep similarity model on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear models. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.

Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications

“…Taylor expansions are a well-known mathematical framework to decompose a function into a series of terms associated with different degrees and combinations of input variables. Unlike Shapley values that evaluate the function f (x) multiple times, the Taylor expansion framework for explaining an ML model [13], [19], [42] evaluates the function once at some reference point x and assigns feature contributions by locally extracting the gradient (and higher order derivatives). Specifically, the Taylor expansion of some smooth and differentiable function f : R d → R at some reference point x is given by where ∇f and ∇ 2 f denote the gradient and the Hessian, respectively, and .…”

“…For illustration, we present the BiLRP method [42], which assumes that we have a similarity model built as a dot product on some hidden…”

“…Let us use for this the Adience benchmark data set [44], providing 26 580 images captured "in the wild" and labeled into eight ordinal groups of age ranges {(0-2), (4-6), (8)(9)(10)(11)(12)(13), (15)(16)(17)(18)(19)(20), (25)(26)(27)(28)(29)(30)(31)(32), (38)(39)(40)(41)(42)(43), (48)(49)(50)(51)(52)(53), (60+)}.…”

“…In the neurosciences, von der Malsburg [192] has coined the concept of "binding" for neural strategies that allow sets of variables (neurons) to synchronize collectively by learning. While steps have already been taken in XAI to identify interacting variables [34], [42], [115], [162], [188], it will be necessary for a broader usage to generalize the approach, e.g., to extract "mathematical formulas" that first build the needed collective variables and use them to explain, concisely but deeply, the ML predictions.…”

Evolution and transformation of early modern cosmological knowledge: a network study

“…The next step in our analysis will be to consider the how socioeconomic factors that determined the production and distribution of those treatises may have altered the path of knowledge transmission. In addition to this contextual data, we will also use machine learning techniques to expand the dataset to include other "knowledge atoms, " specifically scientific images and computational astronomic tables extracted from the same textbooks 41 .…”