{"arxiv_id":"2504.11345","incoming":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"outgoing":{"papers":2,"sentences":3,"groups":[{"kind":"background","label":"Cites as background","papers":2,"sentences":3,"quotes":[{"arxiv_id":"1901.01180","title":"Decomposing tropical rational functions","url":"/paper/1901.01180","section":"Examples of activation functions: ReLUs, evaluation schemes, polynomials, rationals, Nash functions and Pfaffian functio","sentence":"A tropical algebraic rational function is the difference between two tropical polynomials (cf. [ref] and references therein).","intent_p":0.93,"contests_p":null},{"arxiv_id":"1704.03842","title":"Tropical Newton-Puiseux polynomials","url":"/paper/1704.03842","section":"Examples of activation functions: ReLUs, evaluation schemes, polynomials, rationals, Nash functions and Pfaffian functio","sentence":"The class $$ of activation functions is formed by a single function, sometimes denoted as $(·)_+$ (cf. [ref] and references therein): [equation] The class $_∘^(n)[]$ of potentially evaluable functions by a ReLU neural network with $n$ input nodes ${X_1,…, X_n}$ and a single output node is an extension of the class of tropical algebraic rational functions (cf. [ref] , [ref] , [ref] , [ref] or [ref] and references therein for further information) admitting real coefficients.","intent_p":0.89,"contests_p":null}]}],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2504.11345"}}