nils-herrmann/clean_scirepeval huggingface dataset:
Fast Sigmoidal N etworks v ia Spiking Neurons

We show that networks of relatively realistic mathematical models for biological neurons in principle can simulate arbitrary feedfornard sigmoidal neural neb in away that has previoudv not been considered. This new approach is based on temporal coding b;single spikes (mspectively bv the timine of svnchmnous firin= in ~oals of neurons) rather than on ., 2 -. the traditional interpretation of analog variables in terms of firing rates. Ihe resulting new simulation is subrtantially faster and hence more consistent withexperimental resulbabout Ihemuimalspeedof information processing in cortical neural systems. Asa consequence wecan show that networks of noisy spiking neurons are "universal soomximators" in the sense that thev can a~oroximate . . , .. with regard to temporal coding any givencontinuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. This new proposal for the possible organization of computations in nehvorks of spiking neurons systems has some interesting consequences for the type of learning rules that would be needed to explain the selforganization of such networks. Finally, the fast and noise-robust implementation of sigmoidal neural nets by temporal coding points to possible new ways of implementing feedforward and recurrent sigmoidal neural neb with pulse stream VLSI.
Eecient Learning with Virtual Threshold Gates

We reduce learning simple geometric concept classes to learning disjunctions over exponentially many variables. We then apply an on-line algorithm called Winnow whose number of prediction mistakes grows only logarithmically with the number of variables. The hypotheses of Winnow are linear threshold functions with one weight per variable. We nd ways to keep the exponentially many weights of Winnow implicitly so that the time for the algorithm to compute a prediction and update its \virtual" weights is polynomial. Our method can be used to learn d-dimensional axis-parallel boxes when d is variable, and unions of d-dimensional axis-parallel boxes when d is constant. The worst-case number of mistakes of our algorithms for the above classes is optimal to within a constant factor, and our algorithms inherit the noise robustness of Winnow. We think that other on-line algorithms with multiplicative weight updates whose loss bounds grow logarithmically with the dimension are amenable to our methods.
Towards a Computational Semantics of Pathrelations

We present an idea how to provide a computational semantics for path relations like along, through or around. Since the shape of the trajectory of a path relation is bounded by the shapes of the reference objects, an extended notion of geometrical approximations is suggested to take into account detailed shape information. Furthermore we discuss a set of features that are the building blocks of the semantics of path relations. In particular geometric features of several reference objects are evaluated to generate a single integrated reference object. As an example a procedural description of the semantics for along is presented.
On the Complexity of Learning for Spiking Neurons with Temporal Coding

Spiking neurons are models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal patterns of their activity. In a network of spiking neurons a new set of parameters becomes relevant which has no counterpart in traditional neural network models: the time that a pulse needs to travel through a connection between two neurons (also known as delay of a connection). It is known that these delays are tuned in biological neural systems through a variety of mechanisms. In this article we consider the arguably most simple model for a spiking neuron, which can also easily be implemented in pulsed VLSI. We investigate the Vapnik–Chervonenkis (VC) dimension of networks of spiking neurons, where the delays are viewed as programmable parameters and we prove tight bounds for this VC dimension. Thus, we get quantitative estimates for the diversity of functions that a network with fixed architecture can compute with different settings of its delays. In particular, it turns out that a network of spiking neurons with k adjustable delays is able to compute a much richer class of functions than a threshold circuit with k adjustable weights. The results also yield bounds for the number of training examples that an algorithm needs for tuning the delays of a network of spiking neurons. Results about the computational complexity of such algorithms are also given.
Fast Sigmoidal Networks via Spiking Neurons

We show that networks of relatively realistic mathematical models for biological neurons in principle can simulate arbitrary feedforward sigmoidal neural nets in a way that has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous firing in pools of neurons) rather than on the traditional interpretation of analog variables in terms of firing rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are universal approximators in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. This new proposal for the possible organization of computations in networks of spiking neurons systems has some interesting consequences for the type of learning rules that would be needed to explain the self-organization of such networks. Finally, the fast and noise-robust implementation of sigmoidal neural nets by temporal coding points to possible new ways of implementing feedforward and recurrent sigmoidal neural nets with pulse stream VLSI.
Networks of spiking neurons can emulate arbitrary Hopfield nets in temporal coding

A theoretical model for analogue computation in networks of spiking neurons with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analogue computations via the timing of single spikes in networks of detailed compartmental neuron models.In this way, one arrives at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. We also show that it suffices to store these patterns in the efficacies of excitatory synapses.A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different stable firing patterns for different inputs.
Lower Bounds for the Computational Power of Networks of Spiking Neurons

We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phase differences between spike-trains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network of spiking neurons. We construct networks of spiking neurons that simulate arbitrary threshold circuits, Turing machines, and a certain type of random access machines with real valued inputs. We also show that relatively weak basic assumptions about the response and threshold functions of the spiking neurons are sufficient to employ them for such computations.
The Computational Power of Spiking Neurons Depends on the Shape of the Postsynaptic Potentials

Recently one has started to investigate the computational power of spiking neurons (also called \integrate and re neurons"). These are neuron models that are substantially more realistic from the biological point of view than the ones which are traditionally employed in arti cial neural nets. It has turned out that the computational power of networks of spiking neurons is quite large. In particular they have the ability to communicate and manipulate analog variables in spatio-temporal coding, i.e. encoded in the time points when speci c neurons \ re" (and thus send a \spike" to other neurons). These preceding results have motivated the question which details of the ring mechanism of spiking neurons are essential for their computational power, and which details are \accidental" aspects of their realization in biological \wetware". Obviously this question becomes important if one wants to capture some of the advantages of computing and learning with spatio-temporal coding in a new generation of arti cial neural nets, such as for example pulse stream VLSI. The ring mechanism of spiking neurons is de ned in terms of their postsynaptic potentials or \response functions", which describe the change in their electric membrane potential as a result of the ring of another neuron. We consider in this article the case where the response functions of spiking neurons are assumed to be of the mathematically most elementary type: they are assumed to be step-functions (i.e. piecewise constant functions). This happens to be the functional form which has so far been adapted most frequently in pulse stream VLSI as the form of potential changes (\pulses") that mimic the role of postsynaptic potentials in biological neural systems. We prove the rather surprising result that in models without noise the computational power of networks of spiking neurons with arbitrary piecewise constant response functions is strictly weaker than that of networks where the response functions of neurons also contain short segments where they increase respectively decrease in a linear fashion (which is in fact biologically more realistic). More precisely we show for example that an addition of analog numbers is impossible for a network of spiking neurons with piecewise constant response functions (with any bounded number of computation steps, i.e. spikes), whereas addition of analog numbers is easy if the response functions have linearly increasing segments.
How visual salience influences natural language descriptions

The model presented is part of a larger project called VITRA (visual translator), where we investigate aspects at the interaction of vision and language. A particular interest lies on the information flow from the analysis of visual data to language generation. We focus on how visual information can be used for grounding descriptions in the environment. In cooperation with the visual perception group of the IIFB at the Fraunhofer Institute at the University of Karlsruhe, we have shown how real world visual data in dynamic environments can be used in natural language descriptions. A model based approach is used for automatically generating 3D representations of the environment. Our current work is related to problems which occur if an agent moves through real or synthetic environments. The agent's task during its movement is to incrementally describe a route from a starting point to a destination by refering to visually obtained objects. In general, the whole complexity of AI research is involved, e.g. control laws for movement, early vision processing, high level vision, naive physics, temporal and spatial reasoning, knowledge representation, planning and language processing. In a first approach, we have implemented a software agent called MOSES who describes a path in a synthetic 3D environment. MOSES can only refer to visually obtained objects (landmarks) in the current situation. Information about the path is extracted from a map by using an incremental path finding procedure.
An E cient Implementation of Sigmoidal Neural Nets in Temporal Coding with Noisy Spiking Neurons

We show that networks of relatively realistic mathematical models for biological neurons can in principle simulate arbitrary feedforward sigmoidal neural nets in a way which has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous ring in pools of neurons), rather than on the traditional interpretation of analog variables in terms of ring rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are "universal approximators" in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by ring times of spiking neurons. Our new proposal for the possible organization of computations in networks of spiking neurons systems has some interesting consequences for the type of learning rules that would be needed to explain the self-organization of such networks. Finally, our fast and noise-robust implementation of sigmoidal neural nets via temporal coding points to possible new ways of implementing feedforward and recurrent sigmoidal neural nets with pulse stream VLSI.
How Spatial Information Connects Visual Perception and Natural Language Generation in Dynamic Environments: Towards a Computational Model

Suppose that you are required to describe a route step-by-step to somebody who does not know the environment. A major question in this context is what kind of spatial information must be integrated in a route description. This task generally refers to two cognitive abilities: Visual perception and natural language. In this domain, a computational model for the generation of incremental route descriptions is presented. Central to this model is a distinction into a visual, a linguistic, and a conceptual-spatial level. Basing on these different levels a software agent, called MOSES, is introduced who moves through a simulated 3D environment from a starting-point to a destination. He selects visuo-spatial information and generates appropriate route descriptions. It is shown how MOSES adopts his linguistic behavior to spatial and temporal constraints. The generation process is based on a corpus of incremental route descriptions which were collected by field experiments. The agent and the 3D environment are entirely implemented.
On the Computational Power of Noisy Spiking Neurons

It has remained unknown whether one can in principle carry out reliable digital computations with networks of biologically realistic models for neurons. This article presents rigorous constructions for simulating in real-time arbitrary given boolean circuits and finite automata with arbitrarily high reliability by networks of noisy spiking neurons. 
 
In addition we show that with the help of "shunting inhibition" even networks of very unreliable spiking neurons can simulate in real-time any McCulloch-Pitts neuron (or "threshold gate"), and therefore any multilayer perceptron (or "threshold circuit") in a reliable manner. These constructions provide a possible explanation for the fact that biological neural systems can carry out quite complex computations within 100 msec. 
 
It turns out that the assumption that these constructions require about the shape of the EPSP's and the behaviour of the noise are surprisingly weak.
Fast Identification of Geometric Objects with Membership Queries

We investigate the number of membership queries that are needed to identify polygons (i.e., intersections of halfplanes) over a two dimensional grid {0, ..., n ? 1}2. We exhibit a learning algorithm that learns 100% correctly, while requiring no random examples and not more membership queries than previous algorithms needed in addition to their random examples for probably almost correctly learning (even for moderate values of ?, ?). Furthermore, the learning algorithm in this paper uses only grid points for its membership queries. This appears to be appropriate in situations where the probing device has only a limited resolution, and for applications to the set of pixels on a two-dimensional screen. The learning algorithm that is described in this paper overcomes a fundamental obstacle related to the zigzag borderline that is generated by a halfplane over a discrete grid. This obstacle had thwarted previous attempts to show that, in Angluin?s model for on-line learning with equivalence and membership queries, one can learn in an efficient manner even those classes of geometric objects which cannot be learnt fast by equivalence queries alone (such as rectangles in general position).
Fast Rates for Support Vector Machines

We establish learning rates to the Bayes risk for support vector machines (SVMs) using a regularization sequence λ n = n -α , where a ∈ (0,1) is arbitrary. Under a noise condition recently proposed by Tsybakov these rates can become faster than n -1/2 . In order to deal with the approximation error we present a general concept called the approximation error function which describes how well the infinite sample versions of the considered SVMs approximate the data-generating distribution. In addition we discuss in some detail the relation between the classical approximation error and the approximation error function. Finally, for distributions satisfying a geometric noise assumption we establish some learning rates when the used RKHS is a Sobolev space.
A Classification Framework for Anomaly Detection

One way to describe anomalies is by saying that anomalies are not concentrated. This leads to the problem of finding level sets for the data generating density. We interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem. In particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem. This allows us to compare different anomaly detection algorithms empirically, i.e. with the help of a test set. Furthermore, by the above interpretation we can give a strong justification for the well-known heuristic of artificially sampling "labeled" samples, provided that the sampling plan is well chosen. In particular this enables us to propose a support vector machine (SVM) for anomaly detection for which we can easily establish universal consistency. Finally, we report some experiments which compare our SVM to other commonly used methods including the standard one-class SVM.
2 . Detecting Density Levels is a Classification Problem

One way to describe anomalies is by saying that anomalies are not concentrated. This leads to the problem of finding level sets for the data generating density . We interpret this learning problem as a binary classification problem and compare the correspondi ng classification risk with the standard performance measure for the density level problem. In parti cular it turns out that the empirical classification risk can serve as an empirical performance me asur for the anomaly detection problem. This allows us to compare different anomaly detection a lgorithmsempirically, i.e. with the help of a test set. Furthermore, by the above interpretation we can give a strong justification for the well-known heuristic of artificially sampling “labeled” sa mples, provided that the sampling plan is well chosen. In particular this enables us to propose a suppo rt vector machine (SVM) for anomaly detection for which we can easily establish universal consi stency. Finally, we report some experiments which compare our SVM to other commonly used methods in cluding the standard one-class SVM.
Consistency and robustness of kernel based regression

We investigate properties of kernel based regression (KBR) methods which are inspired by the convex risk minimization method of support vector machines. We first describe the relation between the used loss function of the KBR method and the tail of the response variable Y . We then establish a consistency result for KBR and give assumptions for the existence of the influence function. In particular, our results allow to choose the loss function and the kernel to obtain computational tractable and consistent KBR methods having bounded influence functions. Furthermore, bounds for the sensitivity curve which is a finite sample version of the influence function are developed, and some numerical experiments are discussed.
Consistency of support vector machines and other regularized kernel classifiers

It is shown that various classifiers that are based on minimization of a regularized risk are universally consistent, i.e., they can asymptotically learn in every classification task. The role of the loss functions used in these algorithms is considered in detail. As an application of our general framework, several types of support vector machines (SVMs) as well as regularization networks are treated. Our methods combine techniques from stochastics, approximation theory, and functional analysis
On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition

The paper brings together methods from two disciplines: machine learning theory and robust statistics. We argue that robustness is an important aspect and we show that many existing machine learning methods based on the convex risk minimization principle have - besides other good properties - also the advantage of being robust. Robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition. Assumptions are given for the existence of the influence function of the classifiers and for bounds on the influence function. Kernel logistic regression, support vector machines, least squares and the AdaBoost loss function are treated as special cases. Some results on the robustness of such methods are also obtained for the sensitivity curve and the maxbias, which are two other robustness criteria. A sensitivity analysis of the support vector machine is given.
Sparseness of Support Vector Machines

Support vector machines (SVMs) construct decision functions that are linear combinations of kernel evaluations on the training set. The samples with non-vanishing coefficients are called support vectors. In this work we establish lower (asymptotical) bounds on the number of support vectors. On our way we prove several results which are of great importance for the understanding of SVMs. In particular, we describe to which "limit" SVM decision functions tend, discuss the corresponding notion of convergence and provide some results on the stability of SVMs using subdifferential calculus in the associated reproducing kernel Hilbert space.
Sparseness of Support Vector Machines---Some Asymptotically Sharp Bounds

The decision functions constructed by support vector machines (SVM's) usually depend only on a subset of the training set—the so-called support vectors. We derive asymptotically sharp lower and upper bounds on the number of support vectors for several standard types of SVM's. In particular, we show for the Gaussian RBF kernel that the fraction of support vectors tends to twice the Bayes risk for the L1-SVM, to the probability of noise for the L2-SVM, and to 1 for the LS-SVM.
Entropy numbers of convex hulls and an application to learning algorithms

Given a positive sequence $ a = (a_n) \in \ell_{p,q} $, for 0 < p < 2 and $ 0 < q \leq \infty $, and a finite set $ A = \{x_1, \dots , x_m\} \subset \ell_2 $ with $ |x_i| \leq a $ for all $ i = 1, \dots , m $ we prove¶¶$ \|(e_{n}(\textrm{aco}A))\|_{p,q} \leq c_{p,q} \sqrt{\textrm{log}(m + 1)}\,\, q}, $¶¶where $ e_{n}(\textrm{aco}A $ is the nth dyadic entropy number of the absolutely convex hull acoA of A and cp,q > 0 is a suitable constant only depending on p and q. Moreover we show that this is asymptotically optimal in M for the most interesting case $ q = \infty $.¶As an application we give an upper bound for the so-called growth function which is of special interest in the theory of learning algorithms.