Related papers: Balancing lists: a proof pearl
Using Machine Learning systems in the real world can often be problematic, with inexplicable black-box models, the assumed certainty of imperfect measurements, or providing a single classification instead of a probability distribution. This…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…
Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of…
Comparing the top $k$ elements between two or more ranked results is a common task in many contexts and settings. A few measures have been proposed to compare top $k$ lists with attractive mathematical properties, but they face a number of…
In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…
In this paper, we investigate the principle that `good explanations are hard to vary' in the context of deep learning. We show that averaging gradients across examples -- akin to a logical OR of patterns -- can favor memorization and…
We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i…
The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…
Often machine learning methods are applied and results reported in cases where there is little to no information concerning accuracy of the output. Simply because a computer program returns a result does not insure its validity. If…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…
Entailment trees have been proposed to simulate the human reasoning process of explanation generation in the context of open--domain textual question answering. However, in practice, manually constructing these explanation trees proves a…
We present an algorithm that, on input $n$, lists every unlabeled tree of order $n$.
We introduce a simple algorithm for reconstructing phylogenies from multiple gene trees in the presence of incomplete lineage sorting, that is, when the topology of the gene trees may differ from that of the species tree. We show that our…
Large language models achieve strong reasoning performance, yet existing decoding strategies either explore blindly (random sampling) or redundantly (independent multi-sampling). We propose Entropy-Tree, a tree-based decoding method that…
Automatically verifying safety properties of programs is hard, and it is even harder if the program acts upon arrays or other forms of maps. Many approaches exist for verifying programs operating upon Boolean and integer values (e.g.…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…
Traditional Quartet Puzzling algorithms use maximum likelihood methods to reconstruct quartet trees, and a puzzling algorithm to combine these quartets into a tree for the full collection of $n$ taxa. We propose a variation of Quartet…