A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Maps between surfaces have degree constraints based on their Euler characteristics.
The entropy-degree theorem applies to Alexandrov spaces with curvature constraints.
We use invariants of Hendricks and Manolescu coming from involutive Heegaard Floer theory to find constraints on possible configurations of singular points of a rational cuspidal curve of odd degree in the projective plane. We show that the results do not carry over to rational cuspidal curves of even degree.
Quantum computing tackles non-convex portfolio optimization with cardinality constraints.
Existing information-theoretic frameworks based on maximum entropy network ensembles are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical framework for networks based on finding an optimal trade-off between the information content of a…
Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to explicitly model such uncertainty through probabilistic constraints over the parameter sp…
In this work, we use the global analysis and degree-theoretic methods introduced by Smale to study the existence and multiplicity of solutions of the vacuum Einstein constraint equations given by the conformal method of Lichnerowicz-Choquet-Bruhat-York. In particular this approach gives a new proof of the existence res…
Unified finetuning of all quantization degrees of freedom achieves state-of-the-art 4-bit quantization.
The paper shows regularization can't always find all optimal solutions in constrained ML.
New computational lower bounds for clustering and related problems.
Improves k-NN for monotonic data with robustness against noise.
Existence of hypersurfaces in warped product manifolds proven.
Constrained clustering has been well-studied for algorithms such as -means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode many constraints is to use spectral clustering, which remains a developing area. I…
New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.
We investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which inc…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the ne…
Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the correlations between the projections are maximized. The solution is invariant to any lin…
New bounds on inscribed triangles in arbitrary planar domains.
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give constraints on the possible mapping degrees of maps between oriented manifolds. …
New algorithms control loss and constraints in uncertain, changing environments.
Analyzes learning dynamics of RNNs under locality constraints.
We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market prices is modeled on a macro-level as the result of the dynamic coupling of two dyn…
Investigates polynomial solutions to minimal surface equation, proving constraints and structure theorems.
Optimizes marketing strategies with practical constraints.
New rigidity result for non-orientable manifolds with scalar curvature constraints.
A lens cluster minimizes perimeter in the plane with given area constraints.
A neural network with a single hidden layer can't represent certain multivariable functions.
Improved machine learning with reduced tensor rank constraints and dropout.
New method controls posterior collapse in VAEs with theoretical guarantees.
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily availa…
In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. Howe…
New method solves Einstein constraint equations for vacuum.
Constructs metrics with zero eigenvalues for Hodge-Laplacian.
Non-negative -approximating polynomials for Gaussian distributions are proven for certain classes of sets.
We study the effect of impairment on stochastic multi-armed bandits and develop new ways to mitigate it. Impairment effect is the phenomena where an agent only accrues reward for an action if they have played it at least a few times in the recent past. It is practically motivated by repetition and recency effects in do…
Study privacy vs. utility in estimating network parameters with aggregated data.
The paper provides a theoretical justification for using stable SSM blocks in deep sequential models.
In recent years, the evaluation of the minimal investment risk of the quenched disordered system of a portfolio optimization problem and the investment concentration of the optimal portfolio has been actively investigated using the analysis methods of statistical mechanical informatics. However, the work to date has no…
Distributed computing offers a high degree of flexibility to accommodate modern learning constraints and the ever increasing size of datasets involved in massive data issues. Drawing inspiration from the theory of distributed computation models developed in the context of gradient-type optimization algorithms, we prese…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allo…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In th…
New algorithm reduces conditional independence tests needed for causal discovery.
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical c…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy and to extend existing work in the literature, which at the moment is only conc…
New method tests causal relationships from data without needing to learn the entire graph.
Computes volumes of metric maps on surfaces, linking to Weil-Petersson volumes.