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A general theory based upon 6 postulates is introduced. The basical notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From these postulates, the ordinary formalism of quantum theory is derived. The mathematical derivations are not given in this article, but I refer to the recent articles [9, 10]. Three possible applications of the general theory can be given; 1) The variables may decision variables connected to the decisions of a person or of a group of persons. 2) The variables may be statistical parameters or future data, But most importantly here: 3) The variables are physical variables in some context. This last application gives a completely new foundation of quantum mechanics, a foundation which in my opinion is much more easy to understand than the ordinary formalism.The other applications seem also to give interesting consequences of the approach. Socalled paradoxes like that of Schr\"odinger's cat can be clarified under the theory. Explanations of the outcomes of David Bohm's version of the EPR experiment and of the Bell experiment are provided. Finally, references to links towards relativity theory and to quantum field theory are given. The concluding remarks point at further possible developments., Comment: 20 pages

This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R\"udiger Schack on the other side. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection I also sketch some consequences of my approach towards the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation before I give some final remarks., Comment: 28 pages

The growing capabilities of transformer models pave the way for solving increasingly complex NLP tasks. A key to supporting application-specific requirements is the ability to fine-tune. However, compiling a fine-tuning dataset tailored to complex tasks is tedious and results in large datasets, limiting the ability to control transformer output. We present an approach in which complex tasks are divided into simpler subtasks. Multiple transformer models are fine-tuned to one subtask each, and lined up to accomplish the complex task. This simplifies the compilation of fine-tuning datasets and increases overall controllability. Using the example of reducing gender bias as a complex task, we demonstrate our approach and show that it performs better than using a single model., Comment: Proceedings of the Swiss Text Analytics Conference 2023

Quantum decision theory is introduced here, and a new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, and next on arguments for the Born rule, that is, the basis for calculating quantum probabilities. A basic notion behind the quantum theory foundation is that of theoretical variables, that are divided into accessible and inaccessible ones. This is here specialized to decision variables. It is assumed that each accessible variable can be seen as a function of a specific inaccessible variable. Another assumption is that there exist two maximal accessible theoretical variables in the given situation. Two basic assumptions behind the Born rule are 1) the likelihood principle, 2) the actor in question has motivations that can be modeled by a hypothetical perfectly rational higher being. The theory is illustrated by a medical example. Finally, a broad discussion of decision processes is given., Comment: 22 pages. arXiv admin note: text overlap with arXiv:2305.06727

Background: Dental caries diagnosis requires the manual inspection of diagnostic bitewing images of the patient, followed by a visual inspection and probing of the identified dental pieces with potential lesions. Yet the use of artificial intelligence, and in particular deep-learning, has the potential to aid in the diagnosis by providing a quick and informative analysis of the bitewing images. Methods: A dataset of 13,887 bitewings from the HUNT4 Oral Health Study were annotated individually by six different experts, and used to train three different object detection deep-learning architectures: RetinaNet (ResNet50), YOLOv5 (M size), and EfficientDet (D0 and D1 sizes). A consensus dataset of 197 images, annotated jointly by the same six dentist, was used for evaluation. A five-fold cross validation scheme was used to evaluate the performance of the AI models. Results: he trained models show an increase in average precision and F1-score, and decrease of false negative rate, with respect to the dental clinicians. When compared against the dental clinicians, the YOLOv5 model shows the largest improvement, reporting 0.647 mean average precision, 0.548 mean F1-score, and 0.149 mean false negative rate. Whereas the best annotators on each of these metrics reported 0.299, 0.495, and 0.164 respectively. Conclusion: Deep-learning models have shown the potential to assist dental professionals in the diagnosis of caries. Yet, the task remains challenging due to the artifacts natural to the bitewing images., Comment: 24 pages, 5 figure, 7 tables

An alternative approach towards quantum theory is described, and tentative attempts to connect his approach to special and general relativity are discussed. Important concepts are gauge groups and information/entropy connected to some physical systems. Some recent results on information in connection to black holes are touched upon, and it is indicated how expected information can be argued to be conserved. This argument only depends on what happens outside the black hole. Everything connected to the interior of the black hole is inaccessible.

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is indicated here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. In case, this simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The essential use of inaccessible variables can be avoided by basing the approach on some simple category theory.The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations., Comment: 49 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2005.08683

The Bell experiment is discussed in the light of a new approach to the foundation of quantum mechanics. It is concluded from the basic model that the mind of any observer must be limited in some way: In certain contexts, he is simply not able to keep enough variables in his mind when making decisions. This has consequences for Bell's theorem, but it also seems to have wider consequences., Comment: 11 pages

For patients suffering from central nervous system tumors, prognosis estimation, treatment decisions, and postoperative assessments are made from the analysis of a set of magnetic resonance (MR) scans. Currently, the lack of open tools for standardized and automatic tumor segmentation and generation of clinical reports, incorporating relevant tumor characteristics, leads to potential risks from inherent decisions' subjectivity. To tackle this problem, the proposed Raidionics open-source software has been developed, offering both a user-friendly graphical user interface and stable processing backend. The software includes preoperative segmentation models for each of the most common tumor types (i.e., glioblastomas, lower grade gliomas, meningiomas, and metastases), together with one early postoperative glioblastoma segmentation model. Preoperative segmentation performances were quite homogeneous across the four different brain tumor types, with an average Dice around 85% and patient-wise recall and precision around 95%. Postoperatively, performances were lower with an average Dice of 41%. Overall, the generation of a standardized clinical report, including the tumor segmentation and features computation, requires about ten minutes on a regular laptop. The proposed Raidionics software is the first open solution enabling an easy use of state-of-the-art segmentation models for all major tumor types, including preoperative and postsurgical standardized reports., Comment: 11 pages, 3 figures, 3 tables

Extent of resection after surgery is one of the main prognostic factors for patients diagnosed with glioblastoma. To achieve this, accurate segmentation and classification of residual tumor from post-operative MR images is essential. The current standard method for estimating it is subject to high inter- and intra-rater variability, and an automated method for segmentation of residual tumor in early post-operative MRI could lead to a more accurate estimation of extent of resection. In this study, two state-of-the-art neural network architectures for pre-operative segmentation were trained for the task. The models were extensively validated on a multicenter dataset with nearly 1000 patients, from 12 hospitals in Europe and the United States. The best performance achieved was a 61\% Dice score, and the best classification performance was about 80\% balanced accuracy, with a demonstrated ability to generalize across hospitals. In addition, the segmentation performance of the best models was on par with human expert raters. The predicted segmentations can be used to accurately classify the patients into those with residual tumor, and those with gross total resection., Comment: 13 pages, 4 figures, 4 tables

The Nobel prize in physics for 2022 was given for performing Bell experiments with varying degree of sophistication. The interpretation of this experiment is discussed by first recalling Bell's simple argument behind his inequalities, in particular the CHSH inequality. It is argued that any independent observer must have a limitation: He is not able to keep all relevant variables in his mind at the same time when trying to model the experiment. This is contrasted to the solution proposed by Tim Maudlin, where nonlocality is crucial.Maudlin criticizes the Nobel price committee, but this critique is countered. Finally, a related new approach to the foundation of quantum mechanics is briefly sketched, giving references to the relevant literature., Comment: 2 pages

This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions from a quite different, much simpler model. This model is connected to the mind of an observer, or to the joint minds of a group of communicating observers. The model is based upon conceptual variables, and an important aspect is that an observer (a group of observers) must decide on which variable to measure. The model is then linked more generally to a theory of decisions. The results are discussed from several angles. In particular, macroscopic consequences are treated briefly., Comment: 17 pages. arXiv admin note: text overlap with arXiv:2108.12168

The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice's analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind's limitation during a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation., Comment: 22 pages

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different areas of science. In the present article the use of models in statistics is taken as a basis, but links are given to several other areas. Two particular such links are described in some detail here: First the link connected to the chemometrical Partial Least Squares algorithm, a link that now has been generalized to the more sophisticated envelope model. Secondly, statistics, as is well known, relies heavily on making decisions, and it may also in certain cases be connected to a process of taking measurements. A mathematical model for these two activities, connected to the mind of an observer, is introduced. This model is taken further, and shown to be important in a new proposal for a foundation of quantum theory. Quantum mechanics, as seen from this point of view, is described in some detail. The discussion here is close to the discussion in a recent book and in recently published articles by the author., Comment: 14 pages

In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group of observers. These conceptual variables are very often accessible, that is, it is possible to find values of the variables by doing experiments or by making measurements. An important notion is that of maximal accessibility. It is shown here that this new machinery may facilitate the discussion of when a specific quantum state can be given an ontological interpretation, and also the more speculative question whether all states can be given such an interpretation. The discussion here is general, and has implications for the basic problem of how one should look upon information from experiments and measurement, in particularly the question concerning when this information may reflect properties of the real world., Comment: 20 pages

In the book [4] the general problem of reconstructing the Hilbert space formulation in quantum theory is discussed from the point of view of what I called conceptual variables, any variables defined by a person or by a group of persons. These variables may be inaccessible, i.e., impossible to assign numerical value to by experiments or by measurements, or accessible. One basic assumption in [4] and here is that group actions g 2 G are defined on a space where some maximally accessible variable varies, and then accessible functions of these maximal variables are introduced. By using group representation theory the basic Hilbert space formalism is restored under the assumption that the observator or the set of observators has two related maximally accessible variables in his (their) mind(s). The notion of relationship is precisely defined here. Symmetric (self-adjoint) operators are connected to each variable, and in the discrete case the possible values of the variables are given by the eigenvalues of the operators. In this paper the main results from [4] are made more precise and more general. It turns out that the conditions of the main theorem there can be weakened in two essential ways: 1) No measurements need to be assumed, so the result is also applicable to general decision situations; 2) States can have arbitrary phase factors. Some consequences of this approach towards quantum theory are also discussed here., Comment: 12 pages

In this work, we investigate the phenomenon that robust image classifiers have human-recognizable features -- often referred to as interpretability -- as revealed through the input gradients of their score functions and their subsequent adversarial perturbations. In particular, we demonstrate that state-of-the-art methods for adversarial training incorporate two terms -- one that orients the decision boundary via minimizing the expected loss, and another that induces smoothness of the classifier's decision surface by penalizing the local Lipschitz constant. Through this demonstration, we provide a unified discussion of gradient and Jacobian-based regularizers that have been used to encourage adversarial robustness in prior works. Following this discussion, we give qualitative evidence that the coupling of smoothness and orientation of the decision boundary is sufficient to induce the aforementioned human-recognizability phenomenon.

A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical values to them. In an epistemic process, the accessible variables are just ideal observations as observed by an actor or by some communicating actors. Group actions are defined on these variables, and using group representation theory this is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible conceptual variables are derived as a result of the formalism, and in the discrete case it is argued that the possible physical values are the eigenvalues of these operators. The Born formula is derived under specific assumptions. The whole discussion here is a supplement to the author's book [1]. The interpretation of quantum states (or eigenvector spaces) implied by this approach is as focused questions to nature together with sharp answers to those questions. Resolutions if the identity are then connected to the questions themselves; these may be complementary in the sense defined by Bohr. This interpretation may be called a general epistemic interpretation of quantum theory. It is similar to Zwirn's recent Convival Solipsism, and also to QBism, and more generally, can be seen as a concrete implementation of Rovelli's Relational Quantum Mechanics. The focus in the present paper is, however, as much on foundation as on interpretation. But the simple consequences of an epistemic interpretation for some so called quantum paradoxes are discussed. Connections to statistical inference theory are discussed in a preliminary way, both through an example and through a brief discussion of quantum measurement theory., Comment: 37 pages. arXiv admin note: text overlap with arXiv:1905.06590

The purpose was to assess the clinical value of a novel DropOut model for detecting and segmenting brain metastases, in which a neural network is trained on four distinct MRI sequences using an input dropout layer, thus simulating the scenario of missing MRI data by training on the full set and all possible subsets of the input data. This retrospective, multi-center study, evaluated 165 patients with brain metastases. A deep learning based segmentation model for automatic segmentation of brain metastases, named DropOut, was trained on multi-sequence MRI from 100 patients, and validated/tested on 10/55 patients. The segmentation results were compared with the performance of a state-of-the-art DeepLabV3 model. The MR sequences in the training set included pre- and post-gadolinium (Gd) T1-weighted 3D fast spin echo, post-Gd T1-weighted inversion recovery (IR) prepped fast spoiled gradient echo, and 3D fluid attenuated inversion recovery (FLAIR), whereas the test set did not include the IR prepped image-series. The ground truth were established by experienced neuroradiologists. The results were evaluated using precision, recall, Dice score, and receiver operating characteristics (ROC) curve statistics, while the Wilcoxon rank sum test was used to compare the performance of the two neural networks. The area under the ROC curve (AUC), averaged across all test cases, was 0.989+-0.029 for the DropOut model and 0.989+-0.023 for the DeepLabV3 model (p=0.62). The DropOut model showed a significantly higher Dice score compared to the DeepLabV3 model (0.795+-0.105 vs. 0.774+-0.104, p=0.017), and a significantly lower average false positive rate of 3.6/patient vs. 7.0/patient (p<0.001) using a 10mm3 lesion-size limit. The DropOut model may facilitate accurate detection and segmentation of brain metastases on a multi-center basis, even when the test cohort is missing MRI input data.

Magnetic resonance (MR) imaging is an essential diagnostic tool in clinical medicine. Recently, a variety of deep learning methods have been applied to segmentation tasks in medical images, with promising results for computer-aided diagnosis. For MR images, effectively integrating different pulse sequences is important to optimize performance. However, the best way to integrate different pulse sequences remains unclear. In this study, we evaluate multiple architectural features and characterize their effects in the task of metastasis segmentation. Specifically, we consider (1) different pulse sequence integration schemas, (2) different modes of weight sharing for parallel network branches, and (3) a new approach for enabling robustness to missing pulse sequences. We find that levels of integration and modes of weight sharing that favor low variance work best in our regime of small data (n = 100). By adding an input-level dropout layer, we could preserve the overall performance of these networks while allowing for inference on inputs with missing pulse sequence. We illustrate not only the generalizability of the network but also the utility of this robustness when applying the trained model to data from a different center, which does not use the same pulse sequences. Finally, we apply network visualization methods to better understand which input features are most important for network performance. Together, these results provide a framework for building networks with enhanced robustness to missing data while maintaining comparable performance in medical imaging applications., Comment: In the IEEE transactions format for submission to IEEE-TMI

A general question is posed to the quantum community. Partial results are formulated in a self-contained way. In particular, the title question is answered affirmatorily in two cases: 1) The case of spin/ angular momentum of a partcle; 2) A general symmetry situation under certain technical assumptions., Comment: 10 pages. arXiv admin note: text overlap with arXiv:1905.06592, arXiv:1507.07701

The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical inference theory. The approach can be said to have an intuitive basis: The quantum states of a physical system are under certain conditions in one-to-one correspondence with the following: 1. Focus on a concrete question to nature and then 2. Give a definite answer to this question. This foundation implies an epistemic interpretation, depending upon the observer, but the objective world is restored when all observers agree on their observations on some variables. The article contains a survey of parts of the authors books on epistemic processes, which give more details about the theory. At the same time, the article extends some of the discussion in the books, and at places makes it more precise., Comment: 6 pages

A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given time. An example may be the spin vector of a particle; another example may be the vector (position, momentum). In this paper, a space of inaccessible conceptual variables is defined, and group actions are defined on this space. Accessible functions are then defined on the same space. Assuming this structure, the basic Hilbert space structure of quantum theory is derived: Operators on a Hilbert space corresponding to the accessible variables are introduced; when these operators have a discrete spectrum, a natural model reduction implies a new model in which the values of the accessible variables are the eigenvalues of the operator. The principle behind this model reduction demands that a group action may also be defined also on the accessible variables; this is possible if the corresponding functions are permissible, a term that is precisely defined. The following recent principle from statistics is assumed: every model reduction should be to an orbit or to a set of orbits of the group. From this derivation, a new interpretation of quantum theory is briefly discussed: I argue that a state vector may be interpreted as connected to a focused question posed to nature together with a definite answer to this question. Further discussion of these topics is provided in a recent book published by the author of this paper.