arXiv subjects

Michael Frank

Publications and source records attributed to Michael Frank.

At least 19 recordsLinked to original sources

arXiv2026

On the use of foundation models in cognitive science

A host of recent studies have evaluated the cognitive and developmental alignment of Foundation Models (FMs). These investigations include evaluations of their correspondence to adult performance across a range of cognitive domains, as well as whether aspects of model training track children's cognitive development. However, using FMs as candidate cognitive models poses significant methodological and conceptual challenges. A key question underlies this effort: under what conditions does behavioral alignment justify treating FMs as explanatory models of cognition? In this paper, we articulate a four-stage inferential framework for evaluating FMs as cognitive and developmental models: adapting human experimental tasks to model-compatible formats, specifying linking hypotheses that map model outputs to human measures, evaluating behavioral correspondence, and comparing across candidate models or manipulations. We clarify the role of linking hypotheses in mapping model outputs to human behavioral measures, identify challenges that constrain alignment claims, and propose principles for theory-driven and comparative evaluation. Throughout, we argue that behavioral fit alone is insufficient. Alignment becomes scientifically meaningful only when embedded within explicit theoretical commitments, theory-diagnostic tasks, and systematic contrastive evaluation across candidate models.

cs.CL↗

arXiv2026

Extremal representations of functions of matrices and applications to multivariate prediction

Motivated by two seminal results of multivariate prediction theory by Helson and Lowdenslager and by Wiener and Masani we prove extremal representations of functions of matrices and derive their prediction-theoretic consequences. We also sketch a way to obtain matricial inequalities from our results. The main goal of the paper is the computation of the infimum of a set of values of the form $tr(A \Delta A^*)$, where $\Delta$ is a given non-negative Hermitian $n \times n$ matrix and the choices for $A$ exhauste a certain set of $n \times n$ matrices. In particular, we focus on norm-bounded unit spheres with certain types of properties of unitary invariance, what allows an application of the theory of majorization.

math.FA↗

arXiv2026

On bounded module functionals and operators on Hilbert C*-modules without biorthogonally complemented kernels

We investigate the structural reasons behind the existence and non-existence of bounded module functionals and bounded module operators on Hilbert C*-modules whose kernels are not orthogonally complemented. The key motivating example was introduced by J. Kaad and M. Skeide in their 2023 paper. Building on their ideas and related developments, we obtain a structural characterization of this class of examples in a more abstract theoretical framework. We also study non-adjointable bounded module operators associated with such module functionals, together with the properties of the corresponding operator algebras and operator spaces. Our results provide a deeper understanding of phenomena beyond the adjointable setting, place several existing partial results into a unified framework, and show how large families of further examples can be constructed systematically.

math.OA↗

arXiv2025

C-submodule preserving module mappings on Hilbert C-modules

Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $\{ X, \langle .,. \rangle \}$ be a full Hilbert $A$-module. Then any bijective bounded module morphism $T$, for which every norm-closed $A$-submodule of $X$ is invariant, is of the form $T=d \cdot {\rm id}_X$ where $d \in Z(M(A))$ is invertible. As an example of a merely injective bounded module operator with that preserver property serves $T =d \cdot {\rm id}_X$ where $|d| \in Z(M(A))$ has a positive spectrum, but not bounded away from zero. The same assertions are true if the restriction on the C*-submodules to be norm-closed is dropped. From a different point of view, for two given strongly Morita equivalent C*-algebras $A$ and $B$ and a Hilbert $B$-$A$ bimodule $\{ X, \langle .,. \rangle \}$ with faithful compact right action of $B$, for any two two-sided norm-closed ideals $I \in A$, $J \in B$, any full compatible norm-closed Hilbert $J$-$I$ subbimodule of $X$ is invariant for any left bounded $B$-module operator and any right bounded $A$-module operator. So these subsets of submodules of $X$ cannot rule out any bounded module operator as a non-preserver of that subset collection, however any single element of this subset collection is preserved by any bounded module operator on $X$. For any $B$-$A$ imprimitivity bimodule both the C*-valued inner product values are always preserved by bijective bounded module operators $T$ on $X$ iff $T= u \cdot {\rm id}_X$ for a unitary element $u\in Z(M(A))$.

math.OA↗

arXiv2025

Multiplier modules of Hilbert C*-modules revisited

The theory of multiplier modules of Hilbert C*-modules is reconsidered to obtain more properties of these special Hilbert C*-modules. The property of a Hilbert C*-module to be a multiplier C*-module is shown to be an invariant with respect to the consideration as a left or right Hilbert C*-module in the sense of a imprimitivity bimodule in strong Morita equivalence theory. The interrelation of the C*-algebras of ''compact'' operators, the Banach algebras of bounded module operators and the Banach spaces of bounded module operators of a Hilbert C*-module to its C*-dual Banach C*-module, are characterized for pairs of Hilbert C*-modules and their respective multiplier modules. The structures on the latter are always isometrically embedded into the respective structures on the former. Examples are given for which continuation of these kinds of bounded module operators from the initial Hilbert C*-module to its multiplier module fails. However, existing continuations turn out to be always unique. Similarly, bounded modular functionals from both kinds of Hilbert C*-modules to their respective C*-algebras of coefficients are compared, and eventually existing continuations are shown to be unique.

math.OA↗

arXiv2024

Improving Energy Efficiency in Manufacturing: A Novel Expert System Shell

Expert systems are effective tools for automatically identifying energy efficiency potentials in manufacturing, thereby contributing significantly to global climate targets. These systems analyze energy data, pinpoint inefficiencies, and recommend optimizations to reduce energy consumption. Beyond systematic approaches for developing expert systems, there is a pressing need for simple and rapid software implementation solutions. Expert system shells, which facilitate the swift development and deployment of expert systems, are crucial tools in this process. They provide a template that simplifies the creation and integration of expert systems into existing manufacturing processes. This paper provides a comprehensive comparison of existing expert system shells regarding their suitability for improving energy efficiency, highlighting significant gaps and limitations. To address these deficiencies, we introduce a novel expert system shell, implemented in Jupyter Notebook, that provides a flexible and easily integrable solution for expert system development.

cs.AI↗

arXiv2024

A systematic review on expert systems for improving energy efficiency in the manufacturing industry

Against the backdrop of the European Union's commitment to achieve climate neutrality by 2050, efforts to improve energy efficiency are being intensified. The manufacturing industry is a key focal point of these endeavors due to its high final electrical energy demand, while simultaneously facing a growing shortage of skilled workers crucial for meeting established goals. Expert systems (ESs) offer the chance to overcome this challenge by automatically identifying potential energy efficiency improvements and thereby playing a significant role in reducing electricity consumption. This paper systematically reviews state-of-the-art approaches of ESs aimed at improving energy efficiency in industry, with a focus on manufacturing. The literature search yields 1692 results, of which 54 articles published between 1987 and 2023 are analyzed in depth. These publications are classified according to the system boundary, manufacturing type, application perspective, application purpose, ES type, and industry. Furthermore, we examine the structure, implementation, utilization, and development of ESs in this context. Through this analysis, the review reveals research gaps, pointing toward promising topics for future research.

cs.AI↗

arXiv2023

Neural scaling laws for phenotypic drug discovery

Recent breakthroughs by deep neural networks (DNNs) in natural language processing (NLP) and computer vision have been driven by a scale-up of models and data rather than the discovery of novel computing paradigms. Here, we investigate if scale can have a similar impact for models designed to aid small molecule drug discovery. We address this question through a large-scale and systematic analysis of how DNN size, data diet, and learning routines interact to impact accuracy on our Phenotypic Chemistry Arena (Pheno-CA) benchmark: a diverse set of drug development tasks posed on image-based high content screening data. Surprisingly, we find that DNNs explicitly supervised to solve tasks in the Pheno-CA do not continuously improve as their data and model size is scaled-up. To address this issue, we introduce a novel precursor task, the Inverse Biological Process (IBP), which is designed to resemble the causal objective functions that have proven successful for NLP. We indeed find that DNNs first trained with IBP then probed for performance on the Pheno-CA significantly outperform task-supervised DNNs. More importantly, the performance of these IBP-trained DNNs monotonically improves with data and model scale. Our findings reveal that the DNN ingredients needed to accurately solve small molecule drug development tasks are already in our hands, and project how much more experimental data is needed to achieve any desired level of improvement. We release our Pheno-CA benchmark and code to encourage further study of neural scaling laws for small molecule drug discovery.

cs.LG↗

arXiv2023

Tensor Slicing and Optimization for Multicore NPUs

Although code generation for Convolution Neural Network (CNN) models has been extensively studied, performing efficient data slicing and parallelization for highly-constrai\-ned Multicore Neural Processor Units (NPUs) is still a challenging problem. Given the size of convolutions' input/output tensors and the small footprint of NPU on-chip memories, minimizing memory transactions while maximizing parallelism and MAC utilization are central to any effective solution. This paper proposes a TensorFlow XLA/LLVM compiler optimization pass for Multicore NPUs, called Tensor Slicing Optimization (TSO), which: (a) maximizes convolution parallelism and memory usage across NPU cores; and (b) reduces data transfers between host and NPU on-chip memories by using DRAM memory burst time estimates to guide tensor slicing. To evaluate the proposed approach, a set of experiments was performed using the NeuroMorphic Processor (NMP), a multicore NPU containing 32 RISC-V cores extended with novel CNN instructions. Experimental results show that TSO is capable of identifying the best tensor slicing that minimizes execution time for a set of CNN models. Speed-ups of up to 21.7\% result when comparing the TSO burst-based technique to a no-burst data slicing approach. To validate the generality of the TSO approach, the algorithm was also ported to the Glow Machine Learning framework. The performance of the models were measured on both Glow and TensorFlow XLA/LLVM compilers, revealing similar results.

cs.PF↗

arXiv2022

Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals

Considering the deeper reasons of the appearance of a remarkable counterexample by J.~Kaad and M.~Skeide [17] we consider situations in which two Hilbert C*-modules $M \subset N$ with $M^\bot = \{ 0 \}$ over a fixed C*-algebra $A$ of coefficients cannot be separated by a non-trivial bounded $A$-linear functional $r_0: N \to A$ vanishing on $M$. In other words, the uniqueness of extensions of the zero functional from $M$ to $N$ is focussed. We show this uniqueness of extension for any such pairs of Hilbert C*-modules over W*-algebras, over monotone complete C*-algebras and over compact C*-algebras. Moreover, uniqueness of extension takes place also for any one-sided maximal modular ideal of any C*-algebra. Such a non-zero separating bounded $A$-linear functional $r_0$ exist for a given pair of full Hilbert C*-modules $M \subseteq N$ over a given C*-algebra $A$ iff there exists a bounded $A$-linear non-adjointable operator $T_0: N \to N$ such that the kernel of $T_0$ is not biorthogonally closed w.r.t. $N$ and contains $M$. This is a new perspective on properties of bounded modular operators that might appear in Hilbert C*-module theory. By the way, we find a correct proof of [13, Lemma 2.4] in the case of monotone complete and compact C*-algebras, but not in the general C*-case.

math.OA↗

arXiv2021

Stability of trigonometric approximation in $L^p$ and applications to prediction theory

Let $\Gamma$ be an LCA group and $(\mu_n)$ be a sequence of bounded regular Borel measures on $\Gamma$ tending to a measure $\mu_0$. Let $G$ be the dual group of $\Gamma$, $S$ be a non-empty subset of $G \setminus \{ 0 \}$, and $[{\mathcal T}(S)]_{\mu_n,p}$ the subspace of $L^p(\mu_n)$, $p \in (0,\infty)$, spanned by the characters of $\Gamma$ which are generated by the elements of $S$. The limit behaviour of the sequence of metric projections of the function $1$ onto $[{\mathcal T}(S)]_{\mu_n,p}$ as well as of the sequence of the corresponding approximation errors are studied. The results are applied to obtain stability theorems for prediction of weakly stationary or harmonizable symmetric $p$-stable stochastic processes. Along with the general problem the particular cases of linear interpolation or extrapolation as well as of a finite or periodic observation set are studied in detail and compared to each other.

math.ST↗

arXiv2020

B-spline interpolation problem in Hilbert C*-modules

We introduce the $B$-spline interpolation problem corresponding to a $C^*$-valued sesquilinear form on a Hilbert $C^*$-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when the Hilbert $C^*$-module is self-dual. Extending a bounded $C^*$-valued sesquilinear form on a Hilbert $C^*$-module to a sesquilinear form on its second dual, we then provide some necessary and sufficient conditions for the $B$-spline interpolation problem to have a solution. Passing to the setting of Hilbert $W^*$-modules, we present our main result by characterizing when the spline interpolation problem for the extended $C^*$-valued sesquilinear to the dual $\mathscr{X}'$ of the Hilbert $W^*$-module $\mathscr{X}$ has a solution. As a consequence, we give a sufficient condition that for an orthogonally complemented submodule of a self-dual Hilbert $W^*$-module $\mathscr{X}$ is orthogonally complemented with respect to another $C^*$-inner product on $\mathscr{X}$. Finally, solutions of the $B$-spline interpolation problem for Hilbert $C^*$-modules over $C^*$-ideals of $W^*$-algebras are extensively discussed. Several examples are provided to illustrate the existence or lack of a solution for the problem.

math.OA↗

arXiv2019

Thermodynamic Computing

The hardware and software foundations laid in the first half of the 20th Century enabled the computing technologies that have transformed the world, but these foundations are now under siege. The current computing paradigm, which is the foundation of much of the current standards of living that we now enjoy, faces fundamental limitations that are evident from several perspectives. In terms of hardware, devices have become so small that we are struggling to eliminate the effects of thermodynamic fluctuations, which are unavoidable at the nanometer scale. In terms of software, our ability to imagine and program effective computational abstractions and implementations are clearly challenged in complex domains. In terms of systems, currently five percent of the power generated in the US is used to run computing systems - this astonishing figure is neither ecologically sustainable nor economically scalable. Economically, the cost of building next-generation semiconductor fabrication plants has soared past $10 billion. All of these difficulties - device scaling, software complexity, adaptability, energy consumption, and fabrication economics - indicate that the current computing paradigm has matured and that continued improvements along this path will be limited. If technological progress is to continue and corresponding social and economic benefits are to continue to accrue, computing must become much more capable, energy efficient, and affordable. We propose that progress in computing can continue under a united, physically grounded, computational paradigm centered on thermodynamics. Herein we propose a research agenda to extend these thermodynamic foundations into complex, non-equilibrium, self-organizing systems and apply them holistically to future computing systems that will harness nature's innate computational capacity. We call this type of computing "Thermodynamic Computing" or TC.

cs.CY↗

arXiv2017

Orthogonality preserving property for pairs of operators on Hilbert $C^*$-modules

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product structure of a Hilbert $C^*$-module is determined essentially by the module structure and by the orthogonality structure, pairs of linear and local orthogonality-preserving mappings are investigated, not a priori bounded. The intuition is that most often $C^*$-linearity and boundedness can be derived from the settings under consideration. In particular, we obtain that if $\mathscr{A}$ is a $C^{*}$-algebra and $T, S:\mathscr{E}\longrightarrow \mathscr{F}$ are two bounded ${\mathscr A}$-linear mappings between full Hilbert $\mathscr{A}$-modules, then $\langle x, y\rangle = 0$ implies $\langle T(x), S(y)\rangle = 0$ for all $x, y\in \mathscr{E}$ if and only if there exists an element $\gamma$ of the center $Z(M({\mathscr A}))$ of the multiplier algebra $M({\mathscr A})$ of ${\mathscr A}$ such that $\langle T(x), S(y)\rangle = \gamma \langle x, y\rangle$ for all $x, y\in \mathscr{E}$. In particular, for adjointable operators $S$ we have $T=(S^*)^{-1}$, and any bounded invertible module operator $T$ may appear. Varying the conditions on the mappings $T$ and $S$ we obtain further affirmative results for local operators and for pairs of a bounded and of an unbounded module operator with bounded inverse, among others. Also, unbounded operators with disjoint ranges are considered. The proving techniques give new insights.

math.OA↗

arXiv2017

JetsonLEAP: a Framework to Measure Power on a Heterogeneous System-on-a-Chip Device

Computer science marches towards energy-aware practices. This trend impacts not only the design of computer architectures, but also the design of programs. However, developers still lack affordable and accurate technology to measure energy consumption in computing systems. The goal of this paper is to mitigate such problem. To this end, we introduce JetsonLEAP, a framework that supports the implementation of energy-aware programs. JetsonLEAP consists of an embedded hardware, in our case, the Nvidia Tegra TK1 System-on-a-chip device, a circuit to control the flow of energy, of our own design, plus a library to instrument program parts. We discuss two different circuit setups. The most precise setup lets us reliably measure the energy spent by 225,000 instructions, the least precise, although more affordable setup, gives us a window of 975,000 instructions. To probe the precision of our system, we use it in tandem with a high-precision, high-cost acquisition system, and show that results do not differ in any significant way from those that we get using our simpler apparatus. Our entire infrastructure - board, power meter and both circuits - can be reproduced with about $500.00. To demonstrate the efficacy of our framework, we have used it to measure the energy consumed by programs running on ARM cores, on the GPU, and on a remote server. Furthermore, we have studied the impact of OpenACC directives on the energy efficiency of high-performance applications.

cs.OH↗

arXiv2016

Logic Programming with Graph Automorphism: Integrating naut with Prolog (Tool Description)

This paper presents the plnauty~library, a Prolog interface to the nauty graph-automorphism tool. Adding the capabilities of nauty to Prolog combines the strength of the "generate and prune" approach that is commonly used in logic programming and constraint solving, with the ability to reduce symmetries while reasoning over graph objects. Moreover, it enables the integration of nauty in existing tool-chains, such as SAT-solvers or finite domain constraints compilers which exist for Prolog. The implementation consists of two components: plnauty, an interface connecting \nauty's C library with Prolog, and plgtools, a Prolog framework integrating the software component of nauty, called gtools, with Prolog. The complete tool is available as a SWI-Prolog module. We provide a series of usage examples including two that apply to generate Ramsey graphs. This paper is under consideration for publication in TPLP.

cs.DS↗

arXiv2015

Computing the Ramsey Number R(4,3,3) using Abstraction and Symmetry breaking

The number $R(4,3,3)$ is often presented as the unknown Ramsey number with the best chances of being found "soon". Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on \emph{abstraction} and \emph{symmetry breaking} that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value $R(4,3,3)=30$. Along the way it is required to first compute the previously unknown set ${\cal R}(3,3,3;13)$ consisting of 78{,}892 Ramsey colorings.

cs.AI↗

arXiv2015

When Six Gates are Not Enough

We apply the pigeonhole principle to show that there must exist Boolean functions on 7 inputs with a multiplicative complexity of at least 7, i.e., that cannot be computed with only 6 multiplications in the Galois field with two elements.

cs.CC↗