arXiv research

Neural networks with integer weights approximate continuous functions efficiently.

Improved RTM uses integer weights to reduce computation and increase interpretability.

Paper develops machine learning algorithms to learn optimal integer weights for clinical risk scores.

The study examines correlations of logarithms of integers at different scalings.

AF improves classification models by adaptively weighting trees.

Abstract: Necessary and sufficient conditions for circle actions on 4-manifolds with discrete fixed points.

Best-of-$\infty$ improves LLM performance by efficiently allocating inference-time computation.

Low bit-width integer weights and activations are very important for efficient inference, especially with respect to lower power consumption. We propose Monte Carlo methods to quantize the weights and activations of pre-trained neural networks without any re-training. By performing importance sampling we obtain quantiz…

The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.

In the theory of finite order knot invariants, the universal $\text{sl}_2$ weight system maps the chord diagrams to polynomials in a single variable with integer coefficients. In this paper, we define a family of polynomials that generalize the Kreweras triangle (known to refine the normalized median Genocchi numbers),…

Conjecturally, the only knots in $S^3$ with non-integer surgeries producing Seifert fibered spaces are torus knots and cables of torus knots. In this paper, we make progress on the associated realization problem. Let $Y$ be a small Seifert fibered space arising by $p/q$-surgery on a knot in $S^3$, where $p/q$ is positi…

ExDBN learns dynamic Bayesian networks using mixed-integer programming.

ReLU networks trained with MILPs match deep learning accuracy.

We prove that if $N\ge 2$ and $α: F_N\to π_1(Γ)$ is a marking on $F_N$, then for any integer $r\ge 2$ and any $F_N$-invariant collection of non-negative integral "weights" associated to all subtrees $K$ of $\widetilde Γ$ of radius $\le r$ satisfying some natural "switch" conditions, there exists a finite cyclically red…

The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.

For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of L_p…

We introduce a new series $R_k$, $k=2,3,4,\dots$, of integer valued weight systems. The value of the weight system $R_k$ on a chord diagram is a signed number of cycles of even length $2k$ in the intersection graph of the diagram. We show that this value depends on the intersection graph only. We check that for small o…

Optimizes experimental design using synthetic controls for better outcomes.

Study on a weighted Suita conjecture for higher derivatives and their geometric properties.

Mixed integer programming identifies critical neurons in neural networks.

Study links K-stability of certain surfaces to binary forms, proving stability and non-stability conditions.

Hardware-accelerated RBM solves large combinatorial problems and integer factorization.

FairWASP optimizes training data to reduce disparities across subgroups.

Study integrates reliability constraints into generation planning models.

The purpose of this paper is twofold. On one hand, we introduce a modification of the dual canonical basis for invariant tensors of the 3-dimensional irreducible representation of $U_q(sl_2)$, given in terms of Jacobi diagrams, a central tool in quantum topology. On the other hand, we use this modified basis to study t…

This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the i…

In this paper we consider the field equations for linearized gravity and other integer spin fields on the Kerr spacetime, and more generally on spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of decoupled field equations for the linearized Weyl scalars for all spin weights and identify the g…

Improved neural quantization reduces accuracy loss to less than 1% with 4-bit weights.

Study of coloured invariants of torus knots using $\mathcal{W}$ algebras.

Solves constant mean curvature Dirichlet problem on catenoids with improved estimates.

The study counts periodic orbits on smooth manifolds, adding ghost orbits for completeness.

We improve deep threshold networks' memorization capacity exponentially.

Let T be a torus of dimension at least k and M a T-manifold. M is a GKM_k-manifold if the action is equivariantly formal, has only isolated fixed points, and any k weights of the isotropy representation in the fixed points are linearly independent. In this paper we compute the cohomology rings with real and integer coe…

Optimizes risk assessment tools using mixed-integer programming.

The paper models and deforms A-infinity structures for bordered knot algebras.

The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series …

This study optimizes cycle representatives in persistent homology using linear programming.

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We…

This paper shows universality in spectrum behavior for random inner-product kernel matrices in polynomial regime.

Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.

In 2006, Fock and Goncharov constructed a nice basis of the ring of regular functions on the moduli space of framed ${\rm PGL}_2$-local systems on a punctured surface $S$. The moduli space is birational to a cluster $\mathcal{X}$-variety, whose positive real points recover the enhanced Teichmüller space of $S$. Their b…

New q-deformed integers help compute Jones polynomials efficiently.

We present a novel optimization strategy for training neural networks which we call "BitNet". The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over all real values. Our key idea is to limit the expressive power of the network by dynamically controlling the range and set of …

Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by non-negative integer weights, 14 for each 3-simplex, that describe how many copies o…

Proposes a method to learn both constraints and objective functions from data.

FleXOR trains fractional quantization for neural networks, improving accuracy and size.

Generalized Steinberg module presentation for Gaussian and Eisenstein integers.

Hybrid LLM and quantum optimization improve CSA collateral management by 9-10%.