Related papers: NEEXP in MIP*
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
Simulating interactions between non-spherical colloidal particles is computationally challenging due to the complex dependency of forces and energies on their geometry. We introduce and evaluate both descriptor-based and end-to-end models…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
In the evaluation of treatment effects, it is of major policy interest to know if the treatment is beneficial for some and harmful for others, a phenomenon known as qualitative interaction. We formulate this question as a multiple testing…
We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…
Neural Theorem Proving (NTP) employs LLMs to automate formal proofs in proof assistants. While LLMs have achieved relatively remarkable success in informal reasoning tasks using natural languages, the transition to mechanized formal theorem…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…
We provide a general framework to remove short advice by formulating the following computational task for a function $f$: given two oracles at least one of which is honest (i.e. correctly computes $f$ on all inputs) as well as an input, the…
Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a…
The LCF tradition of interactive theorem proving, which was started by Milner in the 1970-ies, appears to be tied to the classic READ-EVAL-PRINT-LOOP of sequential and synchronous evaluation of prover commands. We break up this loop and…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for…
The study of interactive proofs in the context of distributed network computing is a novel topic, recently introduced by Kol, Oshman, and Saxena [PODC 2018]. In the spirit of sequential interactive proofs theory, we study the power of…
Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike…
Mixed-integer programming (MIP) research is both mathematically sophisticated and engineering-intensive: testing an algorithmic hypothesis within a branch-and-cut solver requires substantial implementation, debugging, tuning, and…
The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…
World-class human players have been outperformed in a number of complex two person games (Go, Chess, Checkers) by Deep Reinforcement Learning systems. However, owing to tractability considerations minimax regret of a learning system cannot…
We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement…