Negative / Null Result ReportOpen accessComputer Science
Lukas Balles, Cedric Archambeau, Giovanni Zappella · 2023 · arXiv
With increasing scale in model and dataset size, the training of deep neural networks becomes a massive computational burden. One approach to speed up the training process is Selective Backprop. For this approach, we perform a forward pass to obtain a loss value for each data point in a minibatch. The backward pass is then restricted to a subset of that minibatch, prioritizing high-loss examples. We build on this approach, but seek to improve the subset selection mechanism by choosing the (weighted) subset which best matches the mean gradient over the entire minibatch. We use the gradients w.r
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Simon Kuang, Yuezhu Xu, S. Sivaranjani et al. · 2026 · arXiv
The global Lipschitz constant of a neural network is related to robustness and generalization, yet unlike in many classical models, it is not plainly legible from the parameters. This has motivated sophisticated verification algorithms, especially semidefinite programming (SDP) based on incremental quadratic constraints on the activation functions, to improve on the fast but often loose product of layerwise Lipschitz constants (the trivial bound). We ask why Lipschitz verification is a problem in the first place. Our answer is that the difficulty is structural: estimating a network's Lipschitz
View details →Negative / Null Result ReportOpen accessComputer Science
Kamyar Azizzadenesheli, Brandon Yang, Weitang Liu et al. · 2018 · arXiv
While many recent advances in deep reinforcement learning (RL) rely on model-free methods, model-based approaches remain an alluring prospect for their potential to exploit unsupervised data to learn environment model. In this work, we provide an extensive study on the design of deep generative models for RL environments and propose a sample efficient and robust method to learn the model of Atari environments. We deploy this model and propose generative adversarial tree search (GATS) a deep RL algorithm that learns the environment model and implements Monte Carlo tree search (MCTS) on the lear
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Christoph Schultheiss, Peter Bühlmann · 2022 · arXiv
We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.
View details →Failed Experiment ReportOpen accessComputer Science
Antoine Suarez · 2014 · arXiv
A Michelson-Morley-type experiment is described, which exploits two-photon interference between entangled photons instead of classical light interference. In this experimental context, the negative result (no shift in the detection rates) rules out David Bohm's postulate of an infinite-speed time-ordered "quantum potential", and thereby upholds the timeless standard quantum collapse.
View details →Failed Experiment ReportOpen accessMathematics
Saharon Shelah · 2001 · arXiv
David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result for any regular lambda>aleph_1 even demanding adding no new sequence of ordinals of length<lambda.
View details →Negative / Null Result ReportOpen accessPhysics
Valentin Voroshilov · 2014 · arXiv
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase transition in a Hubbard model on a square lattice. An Appendix presents two cases with a negative result.
View details →Negative / Null Result ReportOpen accessMathematics
Takahiro Hasebe · 2013 · arXiv
We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, ultraspherical and many of Student t-distributions have free divisibility indicator 1.
View details →Negative / Null Result ReportOpen accessComputer Science
Samuel R. Bowman, Jennimaria Palomaki, Livio Baldini Soares et al. · 2020 · arXiv
Natural language inference (NLI) data has proven useful in benchmarking and, especially, as pretraining data for tasks requiring language understanding. However, the crowdsourcing protocol that was used to collect this data has known issues and was not explicitly optimized for either of these purposes, so it is likely far from ideal. We propose four alternative protocols, each aimed at improving either the ease with which annotators can produce sound training examples or the quality and diversity of those examples. Using these alternatives and a fifth baseline protocol, we collect and compare
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Michael Joachim, Thomas Schick · 1999 · arXiv
The Gromov-Lawson-Rosenberg-conjecture for a group G states that a closed spin manifold M^n (n>4) with fundamental group G admits a metric with positive scalar curvature if and only if its C^*-index A(M) in KO_n(C^*_r(G)) vanishes. We prove this for groups G with low-dimensional classifying space, provided the assembly map for G is injective. On the other hand, we construct a spin manifold with no metric with scal>0 but so that already its KO-orientation in KO_*(B pi_1(M)) vanishes. Therefore a corresponding weakened version or the GLR-conjecture is wrong. Last we address non-orientable manifo
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Raphaël Berthon, Nathanaël Fijalkow, Emmanuel Filiot et al. · 2020 · arXiv
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this paper we prove a positive and a negative result for the emptiness problem of alternating automata with qualitative semantics. The positive result is the decidability of the emptiness problem for the case of Büchi acceptance condition. An interesting aspect of our approach is that we
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Matthew D. Kvalheim · 2026 · arXiv
We study whether second-order systems can be made to behave like prescribed first-order dynamical systems through feedback control. More precisely, we study whether prescribed vector fields on compact smooth manifolds, viewed geometrically as sections of the tangent bundle, can be asymptotically stabilized in a strong sense by second-order control systems on the base manifold. Our class of second-order systems includes most Lagrangian systems, and we obtain both positive and negative results. The positive result asserts that, for fully actuated systems, the section corresponding to any smooth
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László Csató · 2017 · arXiv
It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.
View details →Negative / Null Result ReportOpen accessComputer Science
Maryam Aliakbarpour, Rose Silver, Thomas Steinke et al. · 2023 · arXiv
We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution.
View details →Negative / Null Result ReportOpen accessComputer Science
Hayato Takahashi · 2011 · arXiv
A new negative result for nonparametric distribution estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there is a zero-entropy binary ergodic process that is inconsistent with the class of estimators. Our result is different from other negative results for universal forecasting scheme of ergodic processes. We also introduce a related result by B. Weiss.
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Geivison Ribeiro · 2024 · arXiv
This note presents an extension of a result within the concept of [S]-lineability, originally developed in 2019 by L. Bernal-González, J.A. Conejero, M. Murillo-Arcila, and J.B. Seoane-Sepúlveda . Additionally, we provide a characterization in terms of lineability in the context of complements of unions of closed subspaces in F-spaces, and finally, we present a negative result in both normed spaces and p-Banach spaces. These findings contribute to the understanding of linearity in exotic settings in topological vector spaces.
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Pierre-Étienne Meunier, Matthew J. Patitz, Scott M. Summers et al. · 2013 · arXiv
We prove a negative result on the power of a model of algorithmic self-assembly for which it has been notoriously difficult to find general techniques and results. Specifically, we prove that Winfree's abstract Tile Assembly Model, when restricted to use noncooperative tile binding, is not intrinsically universal. This stands in stark contrast to the recent result that, via cooperative binding, the abstract Tile Assembly Model is indeed intrinsically universal. Noncooperative self-assembly, also known as "temperature 1", is where tiles bind to each other if they match on one or more sides, whe
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Jack Hall, Amnon Neeman, David Rydh · 2014 · arXiv
Let $X$ be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of $X$: (1) $\mathsf{D}_{\mathrm{qc}}(X)$ is compactly generated by perfect complexes and (2) if $X$ is noetherian or has affine diagonal, then the functor $Ψ_X \colon \mathsf{D}(\mathsf{QCoh}(X)) \to \mathsf{D}_{\mathrm{qc}}(X)$ is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.
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Michael Edward Hill · 2021 · arXiv
In a pervious paper Weidmann shows that there a bound on the number of orbits of edges in a tree on which a finitely generated group acts $(k,C)$-acylindrically. In this paper we extend this result to actions which are $k$-acylindrical except on a family of groups with "finite height". We also give an example which gives a negative result to a conjecture of Weidmann from the same paper and produce a sharp bound for groups acting $k$--acylindrically.
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Brian Swingle · 2009 · arXiv
I compute the entanglement entropy of a strongly coupled 2+1d quantum field theory containing fermions at finite density using gauge/gravity duality. The dual geometry is an extremal black hole in 3+1d Einstein-Maxwell theory. This system was recently shown to exhibit non-Fermi liquid behavior, but the leading geometrical contribution to the entanglement entropy does not produce an expected violation of the boundary law. I discuss this negative result in the context of attempts to find highly entangled states of quantum matter.
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Maya Dotan, Saar Tochner · 2020 · arXiv
Many blockchain systems today, including Bitcoin, rely on Proof of Work (PoW). Proof of work is crucial to the liveness and security of cryptocurrencies. The assumption when using PoW is that a lot of trial and error is required on average before a valid block is generated. One of the main concerns raised with regard to this kind of system is the inherent need to "waste" energy on "meaningless" problems. In fact, the Bitcoin system is believed to consume more electricity than several small countries. In this work we formally define three properties that are necessary for wasteless PoW systems:
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Bjørn Kjos-Hanssen · 2026 · arXiv
Carmo and Jones have presented a sequence of candidate axiom systems for conditional obligation between 1997 and 2022. For their most recent system we demonstrate a limited form of deontic explosion: given that a student does not get the highest possible grade on a test, any other passing grade is acceptable. In addition to that negative result, we give a positive one: revisiting the strongest version of Carmo and Jones' 1997 system, we provide a surprising classification of all satisfying models in terms of a single forbidden possible world.
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Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan · 2025 · arXiv
We construct four Schauder bases for the space $C[0,1]$, one using ReLU functions, another using Softplus functions, and two more using sigmoidal versions of the ReLU and Softplus functions. This establishes the existence of a basis using these functions for the first time, and improves on the universal approximation property associated with them. We also show an $O(\frac{1}{n})$ approximation bound based on our ReLU basis, and a negative result on constructing multivariate functions using finite combinations of ReLU functions.
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Brieuc Pinon, Raphaël Jungers, Jean-Charles Delvenne · 2025 · arXiv
Reinforcement Learning algorithms designed for high-dimensional spaces often enforce the Bellman equation on a sampled subset of states, relying on generalization to propagate knowledge across the state space. In this paper, we identify and formalize a fundamental limitation of this common approach. Specifically, we construct counterexample problems with a simple structure that this approach fails to exploit. Our findings reveal that such algorithms can neglect critical information about the problems, leading to inefficiencies. Furthermore, we extend this negative result to another approach fr
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Ali Mozaffari · 2011 · arXiv
Building on previous work, we re-examine the possibility of testing MOdified Newtonian Dynamics near the saddle points of gravitational potentials in the Solar System, through an extension of the forthcoming LISA Pathfinder mission. We extend present analysis to include quasi-linear formulations of these theories, resulting from fully relativistic modified gravity theories. Using similar quantitative and qualitative tools, we demonstrate that in general, both the instrumental response and typical Signal to Noise Ratios for such a test will be different. Finally we investigate constraints from
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Andreas Nordvall Lagerås · 2007 · arXiv
Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $Λ$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{ö}hle (2007).
View details →Negative / Null Result ReportOpen accessEngineering
Daniele Gerosa, Thomas Eriksson · 2026 · arXiv
Motivated by recent developments in stochastic modeling of clock jitter in Analog-to-Digital Converters (ADCs) as autoregressive processes of order one (AR(1)), we study the density and stability properties of AR(1)-jittered sampling sets for Paley-Wiener signals. We show that, despite having the correct asymptotic density both on average and almost surely, such sets almost surely fail to be stable sampling sets. We complement this negative result with a finite-dimensional analysis, showing that the corresponding jittered sinc matrices are nonetheless well-conditioned with high probability.
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Yemon Choi · 2015 · arXiv
We show that, given a compact Hausdorff space $Ω$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $Ω$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(Ω)$ is a complete quotient map of operator spaces. In particular, this shows that there exist compact groups which contain infinite cb-Helson subsets, answering a question raised in [Choi--Samei, Proc. AMS 2013; cf. http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also improved.
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Angelos Assos, Yuval Dagan, Constantinos Daskalakis · 2024 · arXiv
Learning algorithms are often used to make decisions in sequential decision-making environments. In multi-agent settings, the decisions of each agent can affect the utilities/losses of the other agents. Therefore, if an agent is good at anticipating the behavior of the other agents, in particular how they will make decisions in each round as a function of their experience that far, it could try to judiciously make its own decisions over the rounds of the interaction so as to influence the other agents to behave in a way that ultimately benefits its own utility. In this paper, we study repeated
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S. M. Bilenky, M. D. Mateev, S. T. Petcov · 2006 · arXiv
We discuss the physics potential of future tritium beta-decay experiments having a sensitivity to a neutrino mass ~\sqrt{|Δm^{2}_{23}|}~5x10^{-2} eV. The case of three-neutrino mixing is analised. A negative result of such an experiment would imply that the neutrino mass spectrum is of normal hierarchical type. The interpretation of a positive result would depend on the value of the lightest neutrino mass; if the lightest neutrino mass satisfies the inequality min(m_j) << \sqrt{|Δm^{2}_{23}|}, it would imply that the neutrino mass spectrum is of the inverted hierarchical type.
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