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Luigi Scorzato

Publications and source records attributed to Luigi Scorzato.

At least 19 recordsLinked to original sources
arXiv2026

A not-too-simple solution to Goodman's New Riddle of induction

I review the works of Gärdenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a solution: understanding that philosophy of science is a science itself, with the same limitations and strengths as other scientific disciplines; (2) understanding that the concept of complexity of a model's assumptions and the concept of direct measurements must be characterized together. Although both measurements and complexity have been the subject of a vast literature, within the philosophy of science, essentially no other attempt has been made to combine them. The widespread expectation, among modern philosophers, that Goodman's new riddle cannot be solved is not defensible without a serious exploration of such a natural approach. A clarification of this riddle has always been very important, but it has become even more crucial in the age of AI.

physics.hist-ph↗
arXiv2024

Reliability and Interpretability in Science and Deep Learning

In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these studies have applied standard error analysis to ML models, and in particular Deep Neural Network (DNN) models, which represent a rather significant departure from standard scientific modelling. It is therefore necessary to integrate the standard error analysis with a deeper epistemological analysis of the possible differences between DNN models and standard scientific modelling and the possible implications of these differences in the assessment of reliability. This article offers several contributions. First, it emphasises the ubiquitous role of model assumptions (both in ML and traditional Science) against the illusion of theory-free science. Secondly, model assumptions are analysed from the point of view of their (epistemic) complexity, which is shown to be language-independent. It is argued that the high epistemic complexity of DNN models hinders the estimate of their reliability and also their prospect of long-term progress. Some potential ways forward are suggested. Thirdly, this article identifies the close relation between a model's epistemic complexity and its interpretability, as introduced in the context of responsible AI. This clarifies in which sense, and to what extent, the lack of understanding of a model (black-box problem) impacts its interpretability in a way that is independent of individual skills. It also clarifies how interpretability is a precondition for assessing the reliability of any model, which cannot be based on statistical analysis alone. This article focuses on the comparison between traditional scientific models and DNN models. But, Random Forest and Logistic Regression models are also briefly considered.

cs.AI↗
arXiv2016

A simple model of scientific progress - with examples

One of the main goals of scientific research is to provide a description of the empirical data which is as accurate and comprehensive as possible, while relying on as few and simple assumptions as possible. In this paper, I propose a definition of the notion of "few and simple assumptions" that is not affected by known problems. This leads to the introduction of a simple model of scientific progress that is based only on empirical accuracy and conciseness. An essential point in this task is the understanding of the role played by "measurability" in the formulation of a scientific theory. This is the key to prevent artificially concise formulations. The model is confronted here with many possible objections and with challenging cases of real progress. Although I cannot exclude that the model might have some limitations, it includes all the cases of genuine progress examined here, and no spurious one. In this model, I stress the role of the "state of the art", which is the collection of all the theories that are the only legitimate source of scientific predictions. Progress is a global upgrade of the state of the art.

physics.hist-ph↗
arXiv2016

Science and Illusions

It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful demarcation between science and pseudo-science, because ad-hoc assumptions are always able to save any theory that conflicts with the empirical data (a.k.a. the Duhem-Quine problem), and a characterization of ad-hoc assumptions is lacking. Moreover, adding some testable predictions is not very difficult. It should be emphasized that these problems do not simply make Popper's demarcation approximate (if it were so, all our problems would be solved!), they make it totally useless. More in general, no philosophical criterion of demarcation is presently able to rule out even some of the most blatant cases of pseudo-science, not even approximatively (in any well defined sense of approximation). This is in sharp contrast with our firm belief that some theories are clearly not scientific. Where does this belief come from? In this paper I argue that it is necessary and possible to recognize the notion of syntactic simplicity that is able to tell the difference between empirically equivalent scientific and non-scientific theories, with a confidence that is adequate to many important practical purposes, and it fully agrees with the judgments generally held in the scientific community.

physics.hist-ph↗
arXiv2015

The Lefschetz thimble and the sign problem

In this talk I review the proposal to formulate quantum field theories (QFTs) on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations of lattice QFTs affected by sign problem. First I will review the theoretical justification of the approach, and comment on some open issues. Then, I will review the algorithms that have been proposed and are being tested to represent and simulate a lattice QFT on a Lefschetz thimble. In particular, I will review the lessons from the very first models of QFTs that have been studied with this approach.

hep-lat↗
arXiv2015

High density QCD on a Lefschetz thimble?

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but - quite surprisingly - most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.

hep-lat↗
arXiv2014

On the role of simplicity in science

Simple assumptions represent a decisive reason to prefer one theory to another in everyday scientific praxis. But this praxis has little philosophical justification, since there exist many notions of simplicity, and those that can be defined precisely strongly depend on the language in which the theory is formulated. The language dependence is a natural feature - to some extent - but it is also believed to be a fatal problem, because, according to a common general argument, the simplicity of a theory is always trivial in a suitably chosen language. But, this trivialization argument is typically either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. This paper shows that the trivialization argument fails, when one considers realistic theories and requires their empirical content to be preserved. In fact, the concepts that enable a very simple formulation, are not necessarily measurable, in general. Moreover, the inspection of a theory describing a chaotic billiard shows that precisely those concepts that naturally make the theory extremely simple are provably not measurable. This suggests that - whenever a theory possesses sufficiently complex consequences - the constraint of measurability prevents too simple formulations in any language. This explains why the scientists often regard their assessments of simplicity as largely unambiguous. In order to reveal a cultural bias in the scientists' assessment, one should explicitly identify different characterizations of simplicity of the assumptions that lead to different theory selections. General arguments are not sufficient.

physics.hist-ph↗
arXiv2013

Recent developments in the tmLQCD software suite

We present an overview of recent developments in the tmLQCD software suite. We summarise the features of the code, including actions and operators implemented. In particular, we discuss the optimisation efforts for modern architectures using the Blue Gene/Q system as an example.

hep-lat↗
arXiv2013

Monte Carlo simulations on the Lefschetz thimble: taming the sign problem

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to 8^4 using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that - at least in the case of the relativistic Bose gas - the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability - in principle - of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.

hep-lat↗
arXiv2013

Study of the a_0(980) on the lattice

We present lattice results for the a_0(980) state using a variational approach with a variety of creation operators: quark-antiquark, mesonic molecule, diquark-antidiquark as well as two-meson type. Focus is put on recent technical advances, in particular the computation of singly disconnected diagrams.

hep-lat↗
arXiv2013

Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model

We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem.

physics.comp-ph↗
arXiv2013

Scalar mesons and tetraquarks from twisted mass lattice QCD

We study light scalar mesons with particular focus on the a_0(980) using lattice QCD with 2+1+1 dynamical quark flavors. To investigate the structure of these scalar mesons and to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquark-antidiquark, mesonic molecule and two-meson operators. We find that the low-lying states overlap essentially exclusively with two-meson states. This indicates that in the channels investigated no tightly bound four-quark states of either molecular or diquark-antidiquark type exist.

hep-lat↗
arXiv2012

Scalar mesons and tetraquarks by means of lattice QCD

We study the light scalar mesons a_0(980) and kappa using N_f = 2+1+1 flavor lattice QCD. In order to probe the internal structure of these scalar mesons, and in particular to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquark-antidiquark, mesonic molecule and two-meson operators. The inclusion of disconnected diagrams, which are technically rather challenging, but which would allow us to extend our work to e.g. the f_0(980) meson, is introduced and discussed.

hep-lat↗
arXiv2012

Lattice investigation of the scalar mesons a_0(980) and κ using four-quark operators

We carry out an exploratory study of the isospin one a0(980) and the isospin one-half kappa scalar mesons using Nf=2+1+1 Wilson twisted mass fermions at one lattice spacing. The valence strange quark is included as an Osterwalder-Seiler fermion with mass tuned so that the kaon mass matches the corresponding mass in the unitary Nf=2+1+1 theory. We investigate the internal structure of these mesons by using a basis of four-quark interpolating fields. We construct diquark-diquark and molecular-typecinterpolating fields and analyse the resulting correlation matrices keeping only connected contributions. For both channels, the low-lying spectrum is found to be consistent with two-particle scattering states. Therefore, our analysis shows no evidence for an additional state that can be interpreted as either a tetraquark or a tightly-bound molecular state.

hep-lat↗
arXiv2012

Lattice investigation of the tetraquark candidates a0(980) and kappa

It is a long discussed issue whether light scalar mesons have sizeable four-quark components. We present an exploratory study of this question using N_f=2+1+1 twisted mass lattice QCD. A mixed action approach ignoring disconnected contributions is used to calculate correlator matrices consisting of mesonic molecule, diquark-antidiquark and two-meson interpolating operators with quantum numbers of the scalar mesons a0(980) (1(0^++)) and kappa (1/2(0+)). The correlation matrices are analyzed by solving the generalized eigenvalue problem. The theoretically expected free two-particle scattering states are identified, while no additional low lying states are observed. We do not observe indications for bound four-quark states in the channels investigated.

hep-lat↗
arXiv2012

The sign problem and the Lefschetz thimble

Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with the sign problem that hinders Monte Carlo simulations of many quantum field theories (QFTs). The approach consists in formulating the QFT on a Lefschetz thimble. In this paper we concentrate on the application to a scalar field theory with a sign problem. In particular, we review the formulation and the justification of the approach, and we also describe the Aurora Monte Carlo algorithm that we are currently testing.

hep-lat↗
arXiv2007

Results from overlap valence quarks on a twisted mass sea

We present results of lattice computations using overlap fermions on a twisted mass background. $N_f=2$ full QCD gauge configurations have been produced by the ETM Collaboration with very light pions (down to less than 300 MeV), with small lattice spacing ($a \approx 0.09$ fm) and large volumes ($V/a^4=24^3\times 48$). By profiting of the good chiral properties of the overlap operator for the valence quarks, it is also possible to have a precise (and unquenched) determination of those physical quantities where the chiral properties are crucial. In order to have unquenched results, we match the valence quark mass with the sea quark mass. We also perform computations with different quark masses in order to simulate (partially quenched) Strange and Charm quarks. A typical application is the computation of $B_K$, for which we present first results.

hep-lat↗