nils-herrmann/clean_scirepeval huggingface dataset:
Portfolio diversification based on ratios of risk measures

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately relies on the minimization of ratios of convex functions. The latter arises naturally due to our requirements that diversification measures should be leverage invariant and related to the tail properties of the distribution of portfolio returns. This paper introduces this new framework and its relationship to standardized higher order moments of portfolio returns. Moreover, it addresses the main drawbacks of standard diversification methodologies which are based primarily on estimates of covariance matrices. Maximizing portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex with potentially multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate through numerical experiments that the introduced diversification measures possess desired properties as introduced in the portfolio diversification literature.
Automorphisms of categories of schemes

Given two schemes $S$ and $S'$, we prove that every equivalence between $\mathbf{Sch}_S$ and $\mathbf{Sch}_{S'}$ comes from a unique isomorphism between $S$ and $S'$. This eliminates all Noetherian and finite type hypotheses from a result of Mochizuki and fully answers a programme set out by Brandenburg in a series of questions on MathOverflow in 2011.
For Whom the Bell (Curve) Tolls: A to F, Trade Your Grade Based on the Net Present Value of Friendships with Financial Incentives

We discuss a possible solution to an unintended consequence of having grades, certificates, rankings, and other diversions in the act of transferring knowledge, zooming in specifically on the topic of grading on a curve. We conduct a thought experiment, taking a chapter (and some more?) from the financial markets (where we trade pollution, etc.), to create a marketplace, where we can trade our grade, in a structure similar to the interest rate swap. We connect this to broader problems that creep up when we attach ourselves to artificial labels. The policy and philosophical implications of our arguments suggest that all trophies we collect (including certificates, grades, medals, etc.) should be viewed as personal or private equity (borrowing another widely used term in finance) and that we should not use them to determine the outcomes in any selection criteria except those with a cutoff point—not for jobs, higher studies, or financial scholarships, other than for entertainment or spectator sports. We suggest alternate methods for grading and performance assessment and suggest the use of tests similar to the Turing test for intelligence for evaluation of teaching and learning.  Performance measurement, private equity
Early-Universe Simulations of the Cosmological Axion.

Ultracompact dark matter (DM) minihalos at masses at and below 10^{-12}  M_{⊙} arise in axion DM models where the Peccei-Quinn (PQ) symmetry is broken after inflation. The minihalos arise from density perturbations that are generated from the nontrivial axion self-interactions during and shortly after the collapse of the axion-string and domain-wall network. We perform high-resolution simulations of this scenario starting at the epoch before the PQ phase transition and ending at matter-radiation equality. We characterize the spectrum of primordial perturbations that are generated and comment on implications for efforts to detect axion DM. We also measure the DM density at different simulated masses and argue that the correct DM density is obtained for m_{a}=25.2±11.0  μeV.
Exploring the effects of galaxy formation on matter clustering through a library of simulation power spectra

Upcoming weak lensing surveys require a detailed theoretical understanding of the matter power spectrum in order to derive accurate and precise cosmological parameter values. While galaxy formation is known to play an important role, its precise effects are currently unknown. We present a set of 92 matter power spectra from the OWLS, cosmo-OWLS, and BAryons and HAloes of MAssive Systems simulation suites, including different ΛCDM cosmologies, neutrino masses, subgrid prescriptions, and AGN feedback strengths. We conduct a detailed investigation of the dependence of the relative difference between the total matter power spectra in hydrodynamical and collisionless simulations on the effectiveness of stellar and AGN feedback, cosmology, and redshift. The strength of AGN feedback can greatly affect the power on a range of scales, while a lack of stellar feedback can greatly increase the effectiveness of AGN feedback on large scales. We also examine differences in the initial conditions of hydrodynamic and N-body simulations that can lead to an $\sim 1{{\ \rm per\ cent}}$ discrepancy in the large-scale power, and furthermore show our results to be insensitive to cosmic variance. We present an empirical model capable of predicting the effect of galaxy formation on the matter power spectrum at z = 0 to within $1{{\ \rm per\ cent}}$ for $k\lt 1\, h\, \mathrm{Mpc}^{-1}$, given only the mean baryon fraction in galaxy groups. Differences in group baryon fractions can also explain the quantitative disagreement between predictions from the literature. All total and dark matter only power spectra in this library will be made publicly available at powerlib.strw.leidenuniv.nl.
Very light asymmetric dark matter

Very light dark matter is usually taken to consist of uncharged bosons such as axion-like particles or dark photons. Here, we consider the prospect of very light, possibly even sub-eV dark matter carrying a net charge that is (approximately) conserved. By making use of the Affleck-Dine mechanism for its production, we show that a sizable fraction of the energy density can be stored in the asymmetric component. We furthermore argue that there exist regions of parameter space where the energy density contained in symmetric particle-antiparticle pairs without net charge can to some degree be depleted by considering couplings to additional fields. Finally, we make an initial foray into the phenomenology of this scenario by considering the possibility that dark matter is coupled to the visible sector via the Higgs portal.
Low scale type I seesaw model for lepton masses and mixings

In contrast to the original type I seesaw mechanism that requires right-handed Majorana neutrinos at energies much higher than the electroweak scale, the so-called low scale seesaw models allow lighter masses for the additional neutrinos. Here we propose an alternative low scale type I seesaw model, where neither linear nor inverse seesaw mechanisms take place, but the spontaneous breaking of a discrete symmetry at an energy scale much lower than the model cutoff is responsible for the smallness of the light active neutrino masses. In this scenario, the model is defined with minimal particle content, where the right-handed Majorana neutrinos can have masses at the $\ensuremath{\sim}50\text{ }\text{ }\mathrm{GeV}$ scale. The model is predictive in the neutrino sector having only four effective parameters that allow to successfully reproduce the experimental values of the six low energy neutrino observables.
Superheavy Thermal Dark Matter.

We propose a mechanism of elementary thermal dark matter with a mass up to 10^{14}  GeV, within a standard cosmological history, whose relic abundance is determined solely by its interactions with the standard model, without violating the perturbative unitarity bound. The dark matter consists of many nearly degenerate particles which scatter with the standard model bath in a nearest-neighbor chain, and maintain chemical equilibrium with the standard model bath by in-equilibrium decays and inverse decays. The phenomenology includes super heavy elementary dark matter and heavy relics that decay at various epochs in the cosmological history, with implications for the cosmic microwave background, structure formation, and cosmic ray experiments.
Frontal Low-rank Random Tensors for Fine-grained Action Segmentation

Fine-grained action segmentation in long untrimmed videos is an important task for many applications such as surveillance, robotics, and human-computer interaction. To understand subtle and precise actions within a long time period, second-order information (e.g. feature covariance) or higher is reported to be effective in the literature. However, extracting such high-order information is considerably non-trivial. In particular, the dimensionality increases exponentially with the information order, and hence gaining more representation power also increases the computational cost and the risk of overfitting. In this paper, we propose an approach to representing high-order information for temporal action segmentation via a simple yet effective bilinear form. Specifically, our contributions are: (1) From the multilinear perspective, we derive a bilinear form of low complexity, assuming that the three-way tensor has low-rank frontal slices. (2) Rather than learning the tensor entries from data, we sample the entries from different underlying distributions, and prove that the underlying distribution influences the information order. (3) We employed our bilinear form as an intermediate layer in state-of-the-art deep neural networks, enabling to represent high-order information in complex deep models effectively and efficiently. Our experimental results demonstrate that the proposed bilinear form outperforms the previous state-of-the-art methods on the challenging temporal action segmentation task. One can see our project page for data, model and code: \url{this https URL}.
Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems

Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.
Optimal Learning of Mallows Block Model

The Mallows model, introduced in the seminal paper of Mallows 1957, is one of the most fundamental ranking distribution over the symmetric group $S_m$. To analyze more complex ranking data, several studies considered the Generalized Mallows model defined by Fligner and Verducci 1986. Despite the significant research interest of ranking distributions, the exact sample complexity of estimating the parameters of a Mallows and a Generalized Mallows Model is not well-understood. The main result of the paper is a tight sample complexity bound for learning Mallows and Generalized Mallows Model. We approach the learning problem by analyzing a more general model which interpolates between the single parameter Mallows Model and the $m$ parameter Mallows model. We call our model Mallows Block Model -- referring to the Block Models that are a popular model in theoretical statistics. Our sample complexity analysis gives tight bound for learning the Mallows Block Model for any number of blocks. We provide essentially matching lower bounds for our sample complexity results. As a corollary of our analysis, it turns out that, if the central ranking is known, one single sample from the Mallows Block Model is sufficient to estimate the spread parameters with error that goes to zero as the size of the permutations goes to infinity. In addition, we calculate the exact rate of the parameter estimation error.
Data Sampling for Graph Based Unsupervised Learning: Convex and Greedy Optimization

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction steps (in contrast to Frank-Wolfe and its variants), a variant of gradient ascent for coreset selection in graphs, that greedily selects a weighted subset of vertices that are deemed most important to sample. Our algorithm estimates the mean of the function by taking a weighted sum only at these vertices, and we provably bound the estimation error in terms of the location and weights of the selected vertices in the graph. In addition, we consider the case where nodes have different selection costs and provide bounds on the quality of the low-cost selected coresets. We demonstrate the benefits of our algorithm on point clouds and structured graphs, as well as sensor placement where the cost of placing sensors depends on the location of the placement. We also elucidate that the empirical convergence of our proposed method is faster than random selection and various clustering methods while still respecting sensor placement cost. The paper concludes with validation of the developed algorithm on both synthetic and real datasets, demonstrating that it performs very well compared to the current state of the art.
Correctness Verification of Neural Networks

We present the first verification that a neural network produces a correct output within a specified tolerance for every input of interest. We define correctness relative to a specification which identifies 1) a state space consisting of all relevant states of the world and 2) an observation process that produces neural network inputs from the states of the world. Tiling the state and input spaces with a finite number of tiles, obtaining ground truth bounds from the state tiles and network output bounds from the input tiles, then comparing the ground truth and network output bounds delivers an upper bound on the network output error for any input of interest. Results from a case study highlight the ability of our technique to deliver tight error bounds for all inputs of interest and show how the error bounds vary over the state and input spaces.
A language-agnostic model for semantic source code labeling

Code search and comprehension have become more difficult in recent years due to the rapid expansion of available source code. Current tools lack a way to label arbitrary code at scale while maintaining up-to-date representations of new programming languages, libraries, and functionalities. Comprehensive labeling of source code enables users to search for documents of interest and obtain a high-level understanding of their contents. We use Stack Overflow code snippets and their tags to train a language-agnostic, deep convolutional neural network to automatically predict semantic labels for source code documents. On Stack Overflow code snippets, we demonstrate a mean area under ROC of 0.957 over a long-tailed list of 4,508 tags. We also manually validate the model outputs on a diverse set of unlabeled source code documents retrieved from Github, and obtain a top-1 accuracy of 86.6%. This strongly indicates that the model successfully transfers its knowledge from Stack Overflow snippets to arbitrary source code documents.
A Perspective on Objects and Systematic Generalization in Model-Based RL

In order to meet the diverse challenges in solving many real-world problems, an intelligent agent has to be able to dynamically construct a model of its environment. Objects facilitate the modular reuse of prior knowledge and the combinatorial construction of such models. In this work, we argue that dynamically bound features (objects) do not simply emerge in connectionist models of the world. We identify several requirements that need to be fulfilled in overcoming this limitation and highlight corresponding inductive biases.
Transforming Complex Sentences into a Semantic Hierarchy

We present an approach for recursively splitting and rephrasing complex English sentences into a novel semantic hierarchy of simplified sentences, with each of them presenting a more regular structure that may facilitate a wide variety of artificial intelligence tasks, such as machine translation (MT) or information extraction (IE). Using a set of hand-crafted transformation rules, input sentences are recursively transformed into a two-layered hierarchical representation in the form of core sentences and accompanying contexts that are linked via rhetorical relations. In this way, the semantic relationship of the decomposed constituents is preserved in the output, maintaining its interpretability for downstream applications. Both a thorough manual analysis and automatic evaluation across three datasets from two different domains demonstrate that the proposed syntactic simplification approach outperforms the state of the art in structural text simplification. Moreover, an extrinsic evaluation shows that when applying our framework as a preprocessing step the performance of state-of-the-art Open IE systems can be improved by up to 346% in precision and 52% in recall. To enable reproducible research, all code is provided online.
A Surprising Density of Illusionable Natural Speech

Recent work on adversarial examples has demonstrated that most natural inputs can be perturbed to fool even state-of-the-art machine learning systems. But does this happen for humans as well? In this work, we investigate: what fraction of natural instances of speech can be turned into "illusions" which either alter humans' perception or result in different people having significantly different perceptions? We first consider the McGurk effect, the phenomenon by which adding a carefully chosen video clip to the audio channel affects the viewer's perception of what is said (McGurk and MacDonald, 1976). We obtain empirical estimates that a significant fraction of both words and sentences occurring in natural speech have some susceptibility to this effect. We also learn models for predicting McGurk illusionability. Finally we demonstrate that the Yanny or Laurel auditory illusion (Pressnitzer et al., 2018) is not an isolated occurrence by generating several very different new instances. We believe that the surprising density of illusionable natural speech warrants further investigation, from the perspectives of both security and cognitive science. Supplementary videos are available at: .
Cores and Other Dense Structures in Complex Networks

Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world phenomena. Despite the keen interest in a variety of problems, algorithms, and analysis methods for these types of network, the problem of extracting cores and dense structures still has unexplored facets. In this work, we present advancements to the state of the art by the introduction of novel definitions and algorithms for the extraction of dense structures from complex networks, mainly cores. At first, we define core decomposition in multilayer networks together with a series of applications built on top of it, i.e., the extraction of maximal multilayer cores only, densest subgraph in multilayer networks, the speed-up of the extraction of frequent cross-graph quasi-cliques, and the generalization of community search to the multilayer setting. Then, we introduce the concept of core decomposition in temporal networks; also in this case, we are interested in the extraction of maximal temporal cores only. Finally, in the context of discovering polarization in large-scale online data, we study the problem of identifying polarized communities in signed networks. The proposed methodologies are evaluated on a large variety of real-world networks against naïve approaches, non-trivial baselines, and competing methods. In all cases, they show effectiveness, efficiency, and scalability. Moreover, we showcase the usefulness of our definitions in concrete applications and case studies, i.e., the temporal analysis of contact networks, and the identification of polarization in debate networks.
Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy

We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for clustering noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of the unitary group to introduce additional redundancy into the representation of the transport data, extending and outperforming the previous class averaging algorithm of Hadani and Singer [, pp. 589--616 (2011)] that uses only a single representation. The formal algebraic model and representation theoretic patterns of the proposed MFCA algorithm extend the framework of Hadani and Singer to arbitrary irreducible representations of the unitary group. We conceptually establish the consistency and stability of MFCA by inspecting the spectral properties of a generalized localized parallel transport operator on the two-dimensional unit sphere through the lens of Wigner matrices. We demonstrate the efficacy of the proposed algorithm with numerical experiments.
MelNet: A Generative Model for Audio in the Frequency Domain

Capturing high-level structure in audio waveforms is challenging because a single second of audio spans tens of thousands of timesteps. While long-range dependencies are difficult to model directly in the time domain, we show that they can be more tractably modelled in two-dimensional time-frequency representations such as spectrograms. By leveraging this representational advantage, in conjunction with a highly expressive probabilistic model and a multiscale generation procedure, we design a model capable of generating high-fidelity audio samples which capture structure at timescales that time-domain models have yet to achieve. We apply our model to a variety of audio generation tasks, including unconditional speech generation, music generation, and text-to-speech synthesis---showing improvements over previous approaches in both density estimates and human judgments.
Do place cells dream of conditional probabilities? Learning Neural Nyström representations

We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nystrom kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.