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We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound…
A common approach to data analysis involves understanding and manipulating succinct representations of data. In earlier work, we put forward a succinct representation system for relational data called factorised databases and reported on…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
Recent advances with in-memory columnar database techniques have increased the performance of analytical queries on very large databases and data warehouses. At the same time, advances in artificial intelligence (AI) algorithms have…
Value function factorization has achieved great success in multi-agent reinforcement learning by optimizing joint action-value functions through the maximization of factorized per-agent utilities. To ensure Individual-Global-Maximum…
Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are…
Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…
The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…
Sliding window sums are widely used for string indexing, hashing and time series analysis. We have developed a family of the generic vectorized sliding sum algorithms that provide speedup of O(P/w) for window size $w$ and number of…
Performing effective preference-based data retrieval requires detailed and preferentially meaningful structurized information about the current user as well as the items under consideration. A common problem is that representations of items…
Opinion summarization from online product reviews is a challenging task, which involves identifying opinions related to various aspects of the product being reviewed. While previous works require additional human effort to identify relevant…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
In-database machine learning has been very popular, almost being a cliche. However, can we do it the other way around? In this work, we say "yes" by applying plain old SQL to deep learning, in a sense implementing deep learning algorithms…
Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce…
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with…
Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented…
A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional…
Recent work has shown that Transformers' compositional generalization is governed by \emph{complexity control}, initialization scale and weight decay, which steers training toward low-complexity reasoning solutions rather than…
This article presents new alternatives to the similarity function for the TextRank algorithm for automatic summarization of texts. We describe the generalities of the algorithm and the different functions we propose. Some of these variants…
As one of the most well-known artificial feature sampler, the sliding window is widely used in scenarios where spatial and temporal information exists, such as computer vision, natural language process, data stream, and time series. Among…