Related papers: MRA-Wavelet subspace architecture for logic, proba…

More and more evidence has shown that strengthening layer interactions can enhance the representation power of a deep neural network, while self-attention excels at learning interdependencies by retrieving query-activated information.…

Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…

We ask whether multilingual language models trained on unbalanced, English-dominated corpora use English as an internal pivot language -- a question of key importance for understanding how language models function and the origins of…

An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…

We design and conduct a simple experiment to study whether neural networks can perform several steps of approximate reasoning in a fixed dimensional latent space. The set of rewrites (i.e. transformations) that can be successfully performed…

Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied…

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…

Low-Rank Adaptation (LoRA) has emerged as a widely adopted approach for adapting large language models, yet the internal representational changes induced by LoRA fine-tuning remain insufficiently understood. In this work, we investigate the…

The low-rank matrix approximation problem with respect to the component-wise $\ell_1$-norm ($\ell_1$-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine…

Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a…

Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…

Robotic agents should be able to learn from sub-symbolic sensor data, and at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between…

We consider the problem of preprocessing an $n\times n$ matrix $\mathbf{M}$, and supporting queries that, for any vector $v$, returns the matrix-vector product $\mathbf{M} v$. This problem has been extensively studied in both theory and…

The multi-reference alignment (MRA) problem involves reconstructing a signal from multiple noisy observations, each transformed by a random group element. In this paper, we focus on the group \(\mathrm{SO}(2)\) of in-plane rotations and…

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…

Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system…

Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…

Resolving complex information needs that come with multiple constraints should consider enforcing the logical operators encoded in the query (i.e., conjunction, disjunction, negation) on the candidate answer set. Current retrieval systems…

Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory…