DOC3 learns from contradictions to improve deep one class classification.
problem Deep one class classification problems.
method Formalizes learning from contradictions for one class large-margin loss, proposes DOC3 algorithm.
result DOC3 incurs lower generalization error compared to traditional inductive learning.
Unified Growth Theory contradicted by African economic data.
problem Contradiction between Unified Growth Theory and African economic growth data.
method Analysis of Galor's data for African countries.
result Data contradicts Unified Growth Theory's claims about economic growth regimes.
Unified Growth Theory disproved by lack of economic takeoffs.
problem The absence of economic takeoffs from stagnation to growth.
method Analysis of historical economic growth data.
result Takeoffs from stagnation to growth never occurred.
Unified Growth Theory contradicted by Latin American economic data.
problem Unified Growth Theory fails to explain Latin American economic growth.
method Analysis of historical economic growth data from Maddison.
result Unified Growth Theory is inconsistent with Latin American data.
Contradiction graphs reveal VC dimension threshold.
problem Determining VC dimension of concept classes.
method Study contradiction graphs of binary concept classes.
result Single contradiction graph Gm(H) determines VC dimension. Unified Growth Theory contradicted by USSR economic data.
problem Unified Growth Theory fails to explain USSR economic growth.
method Analysis of historical USSR economic data.
result USSR economic growth was hyperbolic, not stagnant.
Proves torus sequences can't collapse to intervals under curvature bounds.
problem Proving torus sequences can't collapse to intervals under curvature bounds.
method Contradiction proof using Yamaguchi fibration theorem and covers.
result Proves tori can't collapse to intervals under curvature constraints.
New method resolves bias in recommender learning without needing missing data.
problem Bias in offline recommender learning from explicit ratings.
method Proposes a novel algorithm to minimize generalization error bound via adversarial learning, independent of propensity estimation.
result Demonstrates superior performance in rating prediction and ranking metrics without missing completely at random data.
Unified Growth Theory contradicted by Asian economic data.
problem Unified Growth Theory fails to explain Asian economic growth.
method Analysis of historical economic growth data in Asia.
result Asian economic growth was hyperbolic, not stagnant.
Data interpolation can achieve optimal rates in nonparametric regression and prediction.
problem Achieving optimal rates in nonparametric regression and prediction.
method Interpolating the training data to achieve optimal rates.
result Interpolating the training data can achieve optimal rates for nonparametric regression and prediction.
Paper proves instability of naked singularities in spherical symmetry without contradiction.
problem Stability of naked singularities in spherical symmetry of self-gravitating scalar fields.
method Appropriate a priori estimates for the solution, relaxing original sharp estimates.
result Robust argument proving instability without contradiction.
Mathematical properties of the historical GDP/cap distributions are discussed and explained. These distributions are frequently incorrectly interpreted and the Unified Growth Theory is an outstanding example of such common misconceptions. It is shown here that the fundamental postulates of this theory are contradicted …
New IBOs resolve contradictions in mutual information optimization.
problem Contradictions in mutual information optimization between IBP, PIBP, and recent results.
method Formulated and optimized variational bounds on new IBOs.
result New IBOs account for parameter selection in trained models.
Proves a special knot type is slice.
problem Characterizing slice knots.
method Proof by contradiction and algebraic topology.
result 0-shake slice knots are indeed slice.
Contradicts claims about Poincaré complexes and homology manifolds.
problem Claims about Poincaré complexes and homology manifolds are contradicted.
method Constructs a Poincaré complex with specific properties to contradict the claims.
result A Poincaré complex with vanishing periodic total surgery obstruction is not necessarily homotopy equivalent to a homology manifold.
Pruning improves model generalization in over-parameterized models, contradicting traditional theories.
problem Pruning's effect on generalization in over-parameterized models.
method Empirical study on standard pruning algorithms and additional regularization effects.
result Pruning leads to better training and regularization, improving generalization.
The bias-variance tradeoff doesn't always apply in neural networks, contradicting textbook claims.
problem The bias-variance tradeoff is not universally applicable in neural networks, contradicting textbook teachings.
method Extensive experiments and analysis on neural networks, revisiting Geman et al. (1992) experiments.
result Neural networks do not exhibit a bias-variance tradeoff when increasing network width, contradicting textbook claims.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.
Study proves a criterion for curve diffusion flow blow-up.
problem Analyzing curve diffusion flow with contact angle constraints.
method Contradiction proof using compactness and short time existence.
result Proves blow-up criterion for L2 curvature bound. High subjective discount and risk aversion contradict financial data.
problem Inconsistent asset pricing with financial stylised facts.
method Analyzing capital market equilibrium restrictions.
result Subjective discount and risk aversion cannot be high simultaneously.
New metrics contradicting old conjectures on umbilic points.
problem Contradicting old conjectures about umbilic points.
method Constructing Riemannian metrics arbitrarily close to flat metrics.
result Explicit construction of metrics with isolated umbilic points.
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
Dehn surgery homeomorphic pairs contradict a conjecture.
problem Understanding homeomorphic outcomes of Dehn surgeries on knots.
method Analyzing rational surgeries on knots to find counterexamples.
result Dehn surgery functions are never injective.
Marxism's rate of profit thesis rejected as illogical.
problem Marxism's rate of profit thesis is challenged as illogical.
method Rejects Marx's thesis on the long-term tendency of the rate of profit to fall.
result Marxism's rate of profit thesis is rejected as illogical.
Endowed with natural topologies, the fundamental group of the Hawaiian earring continuously injects into the inverse limit of free groups. This note shows the injection fails to have a continuous inverse. Such a phenomenon was unexpected and appears to contradict results of another author.
Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lag…
Modern machine learning practices contradict traditional bias-variance theory.
problem Modern machine learning models often fit data perfectly, yet perform well.
method Introducing a 'double descent' curve to reconcile classical and modern practices.
result Increasing model capacity beyond interpolation improves performance.
Proves estimates for Calabi-Yau metrics as Kahler classes shrink.
problem Estimates for Calabi-Yau metrics under shrinking Kahler classes.
method Proves asymptotic expansion in terms of powers of fiber diameter with uniform C^k-estimates.
result Uniform estimates for all orders of derivatives of Calabi-Yau metrics.
We show that a finite type duality group of dimension d>2 is the fundamental group of a (d+3)-manifold with rationally acyclic universal cover. We use this to find closed manifolds with rationally acyclic universal cover and some nonvanishing L2-Betti numbers outside the middle dimension, which contradicts a rat…
This work explores the relationship between expressivity and generalization in GNNs.
problem Understanding the trade-off between expressivity and generalization in GNNs.
method Introducing a novel framework that connects GNN generalization to the variance in graph structures they can capture.
result Theoretical findings align with empirical results, offering a deeper understanding of how expressivity enhances GNN generalization.
We know that any element X of the exceptional Jordan algebra $\gJ$ is transformed to a diagonal form by the compact exceptional Lie group F4. However, its proof is used the method which is reduced a contradiction. In this paper, we give a direct and constructive proof.
The paper proposes a new risk measure, Expected Downside Risk, to explain risk-preference.
problem Contradictory empirical findings between risk and reward.
method Introducing Expected Downside Risk (EDR) as a new risk measure.
result EDR better explains investors' utility perception and can model both positive and negative risk-reward relationships.
Unified definition of hallucinations in language models.
problem Persistent hallucinations despite mitigation efforts.
method Unified definition of hallucination as inaccurate world modeling.
result Unified framework distinguishes hallucinations from other errors.
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.
Test log-likelihood comparisons can be misleading.
problem Misinterpretation of test log-likelihood in model comparison.
method Simple examples of model comparison and forecast accuracy.
result Test log-likelihood does not always correlate with model accuracy.
Paper proposes Universum GANs to improve GANs with limited labeled data.
problem Limited labeled data makes supervised learning challenging.
method Proposes Universum GANs with evolving discriminator loss.
result Improved discriminator accuracy and high quality data generation.
Throwing away data can improve worst-group error in imbalanced datasets.
problem Improving worst-group accuracy in imbalanced datasets.
method Leveraging extreme value theory to analyze the tails of data distributions and their impact on classifier performance.
result Throwing away data restores geometric symmetry in classifiers, improving worst-group generalization.
For the purpose of elucidating the correlation among currencies, we analyze daily and high-resolution data of foreign exchange rates. There is strong correlation for pairs of currencies of geographically near countries. We show that there is a time delay of order less than a minute between two currency markets having a…
We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The lo…
Softmax confidence misrepresents uncertainty in neural networks.
problem Neural networks fail to increase uncertainty on out-of-distribution data.
method Investigates two implicit biases in softmax confidence.
result Softmax confidence correlates with epistemic uncertainty due to decision boundary structure and deep network filtering.
It has been conjectured that the geometric invariant of knots in 3-space called the width is nearly additive. That is, letting w(K) in N denote the width of a knot K in S^3, the conjecture is that w(K # K') = w(K) + w(K') - 2. We give an example of a knot K_1 so that for K_2 any 2-bridge knot, it appears that w(K_1 # K…
Study finds chirally cosmetic surgeries on knots and manifolds, contradicting previous conjectures.
problem Disprove conjectures about chirally cosmetic surgeries and purely cosmetic surgeries.
method Construct infinite families of chirally cosmetic surgeries and purely cosmetic surgeries on specific geometric objects.
result Found chirally cosmetic surgeries and purely cosmetic surgeries that contradict previous conjectures.
We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don't have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first applications of the Kontsevich integral to intrinsically 3-dimensional questions in topolog…
We show that if V3 is a handlebody in R3, with curves J1,...,Jg⊂∂V which are the attaching curves for a Heegaard splitting of a homology sphere, then there exists a homeomorphism h:V→V so that each of the curves h(Ji) bounds an orientable surface in R3−int(V). This lead…
The Round Handle Problem asks if certain links are slice in a 4-manifold.
problem Whether a specific collection of links is slice in a 4-manifold constructed from round handles.
method Analyzes the slice property of links in a 4-manifold constructed by adding round handles.
result A negative answer would contradict major conjectures in 4-manifold theory.
LLMs excel at summarizing and repairing complex models without needing full models.
problem Understanding and repairing complex models like GAMs.
method Hierarchical reasoning and extensive background knowledge.
result LLMs can detect anomalies, describe reasons, and suggest repairs.
New expanders for mean curvature flow contradict genus-reduction conjecture.
problem Contradicting Ilmanen's genus-reduction conjecture for mean curvature flow.
method Construct new expanders asymptotic to cones arising from shrinkers.
result Existence of expanders of arbitrarily large genus.