As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Cha…
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48 results for “axiom of choice”
RLHF performs well despite violating social choice theory axioms.
problem RLHF's empirical success contradicts social choice theory axioms.
method Showed RLHF satisfies pairwise majority and Condorcet consistency under mild assumptions, and introduced new alignment criteria.
result RLHF satisfies pairwise majority and Condorcet consistency under mild assumptions, explaining its practical success.
Bayesian model eliminates feedback loops in personalization systems.
problem Feedback loops in user choice systems based on limited exposure.
method Bayesian choice model based on Luce axioms, fair and efficient.
result Low regret in learning to present, accurate preference estimates with minimal interactions.
This paper proposes new get-rich-quick schemes that involve trading in a financial security with a non-degenerate price path. For simplicity the interest rate is assumed zero. If the price path is assumed continuous, the trader can become infinitely rich immediately after it becomes non-constant (if it ever does). If i…
The paper classifies extensions of Yang-Mills-type theories, proving maximality and universality are dense properties.
problem Classifying extensions of Yang-Mills-type theories.
method Categorical characterization and dense properties analysis.
result Maximality and universality are dense properties in the one-point compactification of extension classes.
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any notion of metric, similarity or dissimilarity. Our main results then show that for e…
Axiomatic Market Makingq-fin.MF
Axiomatizes the bid-ask market maker's quoting rule
problem Axiomatizing the quoting rule of a market maker
method Eight natural axioms and six environmental assumptions
result A unique three-parameter family emerges
Paper establishes robust no-arbitrage conditions under projective determinacy.
problem Understanding financial models under Knightian uncertainty.
method Adopting a projective framework, treating all model components uniformly in terms of measurability.
result Establishes characterizations of robust no-arbitrage condition under PD.
New Bregman chord divergences simplify distance selection in machine learning.
problem Selecting appropriate distances for machine learning tasks.
method Extend Bregman divergences with two scalar parameters.
result Simplified distance selection with asymptotic generalization of Bregman divergences.
Paper solves a max-min game for complex performance benchmarks.
problem Max-min portfolio game with complex performance benchmarks.
method Solves a max-min game for complex performance benchmarks using the axiom of choice.
result Exact maximin strategy found for arbitrary performance benchmarks.
Unified framework connects two market-making models, revealing their underlying equivalence.
problem Independent calibration of two market-making frameworks (Avellaneda-Stoikov and Cartea-Jaimungal).
method Axiomatic approach to market preference functional, showing equivalence under specific conditions.
result Avellaneda-Stoikov and Cartea-Jaimungal frameworks are equivalent under certain conditions.
A new axiom for Finsler geometry leads to constant flag curvature.
problem Understanding Finslerian manifolds and their properties.
method Proposing and proving an axiom of spheres.
result Finslerian manifolds satisfying the axiom of spheres have constant flag curvature.
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of -spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …
On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornificationgr-qc
In 1969, Choquet-Bruhat and Geroch established the existence of a unique maximal globally hyperbolic Cauchy development of given initial data for the Einstein equations. Their proof, however, has the unsatisfactory feature that it relies crucially on the axiom of choice in the form of Zorn's lemma. In this paper we pre…
PCMC-Net uses neural networks to estimate transition rates in choice models, improving accuracy over traditional methods.
problem Inference limitations of traditional PCMC models when examples are scarce or new alternatives are observed.
method Amortized inference approach embedding PCMC definition into a neural network.
result Neural network outperforms feature engineered and machine learning models in airline booking prediction.
Motivated by the Moore-Segal axioms for an open-closed topological field theory, we consider planar open string topological field theories. We rigorously define a category 2Thick whose objects and morphisms can be thought of as open strings and diffeomorphism classes of planar open string worldsheets. Just as the categ…
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.
A Morse complex for Axiom A flows on smooth manifolds.
problem Constructing a finite-dimensional cohomological complex for Axiom A flows.
method Defining anisotropic Sobolev spaces and spectral projectors.
result The cohomology of the constructed complex is isomorphic to De Rham cohomology.
Study Vassiliev invariants and periodic orbits of Axiom A flows.
problem Calculating Vassiliev invariants and writhe for periodic orbits of Axiom A flows.
method Asymptotic analysis of Vassiliev invariants and writhe.
result Obtained asymptotics for Vassiliev invariants and writhe of periodic orbits.
The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.
Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.
The notion of Courant algebroid was introduced by Liu, Weinstein and Xu in 1997. Its definition consists of five axioms and an assumption for a derivation. It is shown that two of the axioms and the assumption for the derivation follow from the rest of the axioms.
It is known, that if a 2m-dimensional Kahler manifold satisfies the axiom of holomorphic 2n-spheres (1<n<m) or the axiom of antiholomorphic n-spheres (2<n), it is of constant holomorphic sectional curvature. In this paper the same result is obtained under weaker assumptions.
We propose a class of discrete-time stochastic models for the pricing of inflation-linked assets. The paper begins with an axiomatic scheme for asset pricing and interest rate theory in a discrete-time setting. The first axiom introduces a "risk-free" asset, and the second axiom determines the intertemporal pricing rel…
We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic -spheres. We proved that a nearly Kählerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifold of dimension $2m\geq…
New axioms justify ES without NRC, linking it to mean-ES portfolio selection.
problem Economic axioms for portfolio risk assessment and mean-ES portfolio selection.
method Introducing concentration aversion as an alternative to NRC, establishing axiomatic foundations.
result Concentration aversion uniquely characterizes the family of ES and provides new formulas.
The famous theorems of Cartan, related to the axiom of -planes, and Leung-Nomizu about the axiom of -spheres were extended to Kähler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds (-planes) and extrinsic spheres (-spheres) by a wider class of specia…
Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
We provide an axiomatic foundation for the representation of numéraire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under t…
Shapley values criticized for feature selection, leading to new insights.
problem Using Shapley values for feature selection is problematic.
method Introduced and critiqued Shapley values as feature selection tools, using counterexamples and simulations.
result Shapley values may not always align with feature selection goals.
It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.
We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
Study examines how machine learning attribution methods reflect risk in finance.
problem Ensuring machine learning attribution methods accurately reflect underlying risks in finance.
method Examined Shapley value and Integrated Gradients, and derived axioms from asset pricing domain knowledge.
result Neither Shapley value nor Integrated Gradients can satisfy all axioms for reflecting risks accurately.
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…
Caratheodory's axiom limits arbitrage in resource-limited systems.
problem Non-arbitrage constraints in resource-limited financial systems.
method Preserving Caratheodory's axiom in resource-limited systems.
result Exponential family is the necessary geometric structure for both thermodynamics and finance.
Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…
Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Financeq-fin.MF
The paper establishes axioms for AMMs to ensure fair pricing and fee structures.
problem Ensuring fair and efficient pricing in decentralized finance (DeFi) AMMs.
method Formulating axioms on utility functions to characterize swap sizes and pricing oracles.
result Most existing AMMs satisfy the proposed axioms, and a new AMM is proposed with desirable properties.
Enhanced bikei modules distinguish unoriented and non-orientable surface-links.
problem Distinguishing unoriented and non-orientable surface-links.
method Extending biquandle module invariants to unoriented surface-links using bikei modules.
result Enhanced bikei modules are more effective at distinguishing non-orientable surface-links than bikei homset cardinality alone.
New research shows testing IIA in discrete choice is nearly impossible with current sample sizes.
problem Testing the Independence of Irrelevant Alternatives (IIA) in discrete choice models is challenging.
method Combinatorial analysis of Eulerian orientations of cycle decompositions of a bipartite graph.
result Any general test for IIA with low worst-case error requires an exponential number of samples in the number of alternatives.
Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (…
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
Milnor proved two uniqueness theorems for axiomatic (co)homology: one for pairs of compacta (1960) and another, in particular, for pairs of countable simplicial complexes (1961). We obtain their common generalization: the Eilenberg-Steenrod axioms along with Milnor's map excision axiom and a (non-obvious) common genera…
The paper develops axioms for uniquely decomposing functions with real arguments.
problem Decomposing functions with real arguments while preserving their overall structure.
method Developing axioms to uniquely decompose Borel measurable functions.
result Unique decompositions for all Borel measurable functions are achieved.
Defines Alexandrov spaces via axioms, focusing on curvature bounds.
problem Understanding Alexandrov spaces with curvature constraints.
method Formalizes spaces via axioms, distinguishing between curvature above and below.
result Comprehensive structure theory of Alexandrov spaces with curvature bounds.
New axioms for singquandles simplify applications and reveal algebraic aspects.
problem Axiomatizing singular knots and links.
method Presented new axioms for singquandles, simplified existing ones, and reformulated for affine singquandles.
result Simplified applications and revealed new algebraic aspects of singquandles.
Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.
problem Formalizing and proving the von Neumann-Morgenstern utility theorem.
method Implement classical axioms in Lean 4, formalizing preference relations over lotteries.
result Machine-verified proofs of existence and uniqueness of utility representations.
This study redefines probability for finite outcomes using axioms and examples.
problem Defining probability for finite outcomes and preserving information.
method Developed three axioms for relative probability functions and provided examples and a system for their composition.
result Proved the topological closure of the relative probability space, preserving information under limits.
This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to sati…