Related papers: Cooperation between Top-Down and Bottom-Up Theorem…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

To make progress in learning the underlying fundamental theory, it will be necessary to combine bottom-up phenomenology and top-down analysis -- in particular, top-down is unlikely to succeed alone. Here I elaborate on the role of both, and…

Models of complex systems often consist of multiple interconnected subsystem/component models that are developed by multi-disciplinary teams of engineers or scientists. To ensure that such interconnected models can be applied for the…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Recently, we have proposed two complementary approaches, top-down and bottom-up, to multilevel supervisory control of discrete-event systems. In this paper, we compare and combine these approaches. The combined approach has strong features…

The top-down and bottom-up methods are two mainstreams of referring segmentation, while both methods have their own intrinsic weaknesses. Top-down methods are chiefly disturbed by Polar Negative (PN) errors owing to the lack of fine-grained…

Bottom-up evaluation of Datalog has been studied for a long time, and is standard material in textbooks. However, if one actually wants to develop a deductive database system, it turns out that there are many implementation options. For…

Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…

How to best integrate linguistic and perceptual processing in multi-modal tasks that involve language and vision is an important open problem. In this work, we argue that the common practice of using language in a top-down manner, to direct…

Agentic theorem provers often introduce intermediate lemmas, proof sketches, or subgoal decompositions before returning to tactic-level search. This can look like an expensive detour: if proving lemmas is itself hard, why should a learned…

A key challenge in program synthesis is the astronomical size of the search space the synthesizer has to explore. In response to this challenge, recent work proposed to guide synthesis using learned probabilistic models. Obtaining such a…

Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…

We propose a bottom-up variant of Earley deduction. Bottom-up deduction is preferable to top-down deduction because it allows incremental processing (even for head-driven grammars), it is data-driven, no subsumption check is needed, and…

Traditionally, researchers in decision making have focused on attempting to reach Pareto Optimality using horizontal approaches, where optimality is calculated taking into account every participant at the same time. Sometimes, this may…

Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…

Both bottom-up and top-down strategies have been used for neural transition-based constituent parsing. The parsing strategies differ in terms of the order in which they recognize productions in the derivation tree, where bottom-up…

We seek to design novel multiple testing procedures, which take into account a relevant notion of ''power'' or true discovery on the one hand, and allow computationally efficient test design and application on the other. Towards this end we…

The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

Large Language Models (LLMs) have shown remarkable prowess in text generation, yet producing long-form, factual documents grounded in extensive external knowledge bases remains a significant challenge. Existing "top-down" methods, which…