Scientific discoveries often hinge on synthesizing decades of research, a task that potentially outstrips human information processing capacities. Large language models (LLMs) offer a solution. LLMs trained on the vast scientific literature could potentially integrate noisy yet interrelated findings to forecast novel results better than human experts. To evaluate this possibility, we created BrainBench, a forward-looking benchmark for predicting neuroscience results. We find that LLMs surpass experts in predicting experimental outcomes. BrainGPT, an LLM we tuned on the neuroscience literature, performed better yet. Like human experts, when LLMs were confident in their predictions, they were more likely to be correct, which presages a future where humans and LLMs team together to make discoveries. Our approach is not neuroscience-specific and is transferable to other knowledge-intensive endeavors.

In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through numerical simulations, we find that for realistic systems, the envelope function of off-diagonal elements of observables exhibits an exponential decay at large $\Delta E$, while for randomized models, it tends to be flat. We demonstrate that the correlations of chaotic eigenstates, originating from the delicate structures of Hamiltonians, play a crucial role in the non-trivial structure of the envelope function. Furthermore, we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians. Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from RMT predictions. These understandings offer valuable directions for future research.

In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed.

The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by Random Matrix Theory (RMT). To what extent physical operators can be described by RMT, more precisely at which energy scale strict RMT description applies, is however not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible for exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that genuine RMT behavior is absent even for narrow energy windows corresponding to time scales of the order of thermalization time $\tau_\text{th}$ of the respective observables. We also demonstrate that residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.

Investigating deep learning language models has always been a significant research area due to the ``black box" nature of most advanced models. With the recent advancements in pre-trained language models based on transformers and their increasing integration into daily life, addressing this issue has become more pressing. In order to achieve an explainable AI model, it is essential to comprehend the procedural steps involved and compare them with human thought processes. Thus, in this paper, we use simple, well-understood non-language tasks to explore these models' inner workings. Specifically, we apply a pre-trained language model to constrained arithmetic problems with hierarchical structure, to analyze their attention weight scores and hidden states. The investigation reveals promising results, with the model addressing hierarchical problems in a moderately structured manner, similar to human problem-solving strategies. Additionally, by inspecting the attention weights layer by layer, we uncover an unconventional finding that layer 10, rather than the model's final layer, is the optimal layer to unfreeze for the least parameter-intensive approach to fine-tune the model. We support these findings with entropy analysis and token embeddings similarity analysis. The attention analysis allows us to hypothesize that the model can generalize to longer sequences in ListOps dataset, a conclusion later confirmed through testing on sequences longer than those in the training set. Lastly, by utilizing a straightforward task in which the model predicts the winner of a Tic Tac Toe game, we identify limitations in attention analysis, particularly its inability to capture 2D patterns.

Interdisciplinary research is often at the core of scientific progress. This dissertation explores some advantageous synergies between machine learning, cognitive science and neuroscience. In particular, this thesis focuses on vision and images. The human visual system has been widely studied from both behavioural and neuroscientific points of view, as vision is the dominant sense of most people. In turn, machine vision has also been an active area of research, currently dominated by the use of artificial neural networks. This work focuses on learning representations that are more aligned with visual perception and the biological vision. For that purpose, I have studied tools and aspects from cognitive science and computational neuroscience, and attempted to incorporate them into machine learning models of vision. A central subject of this dissertation is data augmentation, a commonly used technique for training artificial neural networks to augment the size of data sets through transformations of the images. Although often overlooked, data augmentation implements transformations that are perceptually plausible, since they correspond to the transformations we see in our visual world -- changes in viewpoint or illumination, for instance. Furthermore, neuroscientists have found that the brain invariantly represents objects under these transformations. Throughout this dissertation, I use these insights to analyse data augmentation as a particularly useful inductive bias, a more effective regularisation method for artificial neural networks, and as the framework to analyse and improve the invariance of vision models to perceptually plausible transformations. Overall, this work aims to shed more light on the properties of data augmentation and demonstrate the potential of interdisciplinary research.

We study integrability breaking and transport in a discrete space-time lattice with a local integrability breaking perturbation. We find a singular distribution of the Lyapunov spectrum where the majority of Lyapunov exponents vanish in the thermodynamic limit. The sub-extensive sequence of nonzero exponents, converging in the thermodynamic limit, correspond to Lyapunov vectors that are exponentially localized with localization lengths proportional to inverse Lyapunov exponents. Moreover, we investigate the transport behavior of the system by considering the spin-spin and current-current spatio-temporal correlation functions. Our results indicate that the overall transport behavior, similarly as in the purely integrable case, conforms to Kardar-Parisi-Zhang scaling in the thermodynamic limit and at vanishing magnetization. The same dynamical exponent $z=3/2$ governs the effect of local perturbation spreading in the bulk.

We suggest a new NLG task in the context of the discourse generation pipeline of computational storytelling systems. This task, textual embellishment, is defined by taking a text as input and generating a semantically equivalent output with increased lexical and syntactic complexity. Ideally, this would allow the authors of computational storytellers to implement just lightweight NLG systems and use a domain-independent embellishment module to translate its output into more literary text. We present promising first results on this task using LSTM Encoder-Decoder networks trained on the WikiLarge dataset. Furthermore, we introduce "Compiled Computer Tales", a corpus of computationally generated stories, that can be used to test the capabilities of embellishment algorithms.

In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely represent point and curvilinear singularities, respectively. Our methodology is based on the very recently introduced mathematical theory of geometric separation, which shows that highly precise separation of the morphologically distinct features of points and curves can be achieved by $\ell^1$ minimization. Finally, we present some experimental results showing the effectiveness of our algorithm, in particular, the ability to accurately separate points from curves even if the curvature is relatively large due to the excellent localization property of compactly supported shearlets.

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-$1/2$ chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where a description in terms of spatio-temporal correlation functions has been suggested in the case of weak driving and small system-bath coupling. Because this work has focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: We (i) consider nonintegrable systems, (ii) take into account open boundary conditions and other bath-coupling geometries, and (iii) provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial, due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is an useful alternative to already existing state-of-the-art approaches.

The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which features a constant current and a characteristic density profile. While the Lindblad equation complements other approaches to transport in closed quantum systems, it has become clear that a connection between closed and open systems exists in certain cases. Here, we build on this connection for magnetization transport in the spin-1/2 XXZ chain with and without integrability-breaking perturbations. Specifically, we study the question whether the time evolution of the open quantum system can be described on the basis of classical correlation functions, as generated by the Hamiltonian equations of motion for real vectors. By comparing to exact numerical simulations of the Lindblad equation, we find a good accuracy of such a description for a range of model parameters, which is consistent with previous studies on closed systems. While this agreement is an interesting physical observation, it also suggests that classical mechanics can be used to solve the Lindblad equation for comparatively large system sizes, which lie outside the possibilities of a quantum mechanical treatment. We also point out counterexamples and limitations for the quantitative extraction of transport coefficients. Remarkably, our classical approach to large open systems allows to detect superdiffusion at the isotropic point.

We study the emergence of decoherent histories in isolated systems based on exact numerical integration of the Schr\"odinger equation for a Heisenberg chain. We reveal that the nature of the system, which we switch from (i) chaotic to (ii) interacting integrable to (iii) non-interacting integrable, strongly impacts decoherence \new{of coarse spin observables}. From a finite size scaling law we infer a strong exponential suppression of coherences for (i), a weak exponential suppression for (ii) and no exponential suppression for (iii) on a relevant short (nonequilibrium) time scale. Moreover, for longer times we find stronger decoherence for (i) but the opposite for (ii), hinting even at a possible power-law decay for (ii) at equilibrium time scales. This behaviour is encoded in the multi-time properties of the quantum histories and it can not be explained by environmentally induced decoherence. Our results suggest that chaoticity plays a crucial role in the emergence of classicality in finite size systems.

Through an explicit construction, we assign to any infinite temperature autocorrelation function $C(t)$ a set of functions $\alpha^n(t)$. The construction of $\alpha^n(t)$ from $C(t)$ requires the first $2n$ temporal derivatives of $C(t)$ at times $0$ and $t$. Our focus is on $\alpha^n(t)$ that (almost) monotonously decrease, we call these ``arrows of time functions" (AOTFs). For autocorrelation functions of few body observables we numerically observe the following: An AOTF featuring a low $n$ may always be found unless the the system is in or close to a nonchaotic regime with respect to a variation of some system parameter. All $\alpha^n(t)$ put upper bounds to the respective autocorrelation functions, i.e. $\alpha^n(t) \geq C^2(t)$. Thus the implication of the existence of an AOTF is comparable to that of the H-Theorem, as it indicates a directed approach to equilibrium. We furthermore argue that our numerical finding may to some extent be traced back to the operator growth hypothesis. This argument is laid out in the framework of the so-called recursion method.

Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature magnetization transport has turned out to range from ballistic, over superdiffusive, to diffusive behavior in different parameter regimes of the anisotropy. Since integrability is rather the exception than the rule, a crucial question is the change of transport under integrability-breaking perturbations. This question includes the stability of superdiffusion at the isotropic point and the change of diffusion constants in the easy-axis regime. In our work, we study this change of diffusion constants by a variety of methods and cover both, linear response theory in the closed system and the Lindblad equation in the open system, where we throughout focus on periodic boundary conditions. In the closed system, we compare results from the recursion method to calculations for finite systems and find evidence for a continuous change of diffusion constants over the full range of perturbation strengths. In the open system weakly coupled to baths, we find diffusion constants in quantitative agreement with the ones in the closed system in a range of nonweak perturbations, but disagreement in the limit of weak perturbations. Using a simple model in this limit, we point out the possibility of a diverging diffusion constant in such an open system.

We study the equilibration times $T_\text{eq}$ of local observables in quantum chaotic systems by considering their auto-correlation functions. Based on the recursion method, we suggest a scheme to estimate $T_\text{eq}$ from the corresponding Lanczos coefficients that is expected to hold in the thermodynamic limit. We numerically find that if the observable eventually shows smoothly growing Lanczos coefficients, a finite number of the former is sufficient for a reasonable estimate of the equilibration time. This implies that equilibration occurs on a realistic time scale much shorter than the life of the universe. The numerical findings are further supported by analytical arguments.

Since perturbations are omnipresent in physics, understanding their impact on the dynamics of quantum many-body systems is a vitally important but notoriously difficult question. On the one hand, random-matrix and typicality arguments suggest a rather simple damping in the overwhelming majority of cases, e.g., exponential damping according to Fermi's Golden Rule. On the other hand, counterexamples are known to exist, and it remains unclear how frequent and under which conditions such counterexamples appear. In our work, we consider the spin-1/2 XXZ chain as a paradigmatic example of a quantum many-body system and study the dynamics of the magnetization current in the easy-axis regime. Using numerical simulations based on dynamical quantum typicality, we show that the standard autocorrelation function is damped in a nontrivial way and that only a modified version of this function is damped in a simple manner. Employing projection-operator techniques in addition, we demonstrate that both, the nontrivial and simple damping relation can be understood on perturbative grounds. Our results are in agreement with earlier findings for the particle current in the Hubbard chain.

The absorption features of optically generated, short-lived small bound electron polarons are inspected in congruent lithium tantalate, ${\rm LiTaO}_3$ (LT), in order to address the question whether it is possible to localize electrons at interstitial ${\rm Ta_V}$:${\rm V_{Li}}$ defect pairs by strong, short-range electron-phonon coupling. Solid-state photoabsorption spectroscopy under light exposure and density functional theory are used for an experimental and theoretical access to the spectral features of small bound polaron states and to calculate the binding energies of the small bound ${\rm Ta}_{\rm Li}^{4+}$(antisite) and${\rm Ta}_{\rm V}^{4+}$:${\rm V_{Li}}$ (interstitial site) electron polarons. As a result, two energetically well separated ($\Delta E \approx 0.5\,{\rm eV}$) absorption features with a distinct dependence on the probe light polarization and peaking at $1.6\,{\rm eV}$ and $2.1\,{\rm eV}$ are discovered. We contrast our results to the interpretation of a single small bound ${\rm Ta}_{\rm Li}^{4+}$ electron state with strong anisotropy of the lattice distortion and discuss the optical generation of interstitial ${\rm Ta}_{\rm V}^{4+}$:${\rm V_{Li}}$ small polarons in the framework of optical gating of ${\rm Ta}_{\rm V}^{4+}$:${\rm Ta}_{\rm Ta}^{4+}$ bipolarons. We can conclude that the appearance of carrier localization at $\mathrm{Ta_V}$:${\rm V_{Li}}$ must be considered as additional intermediate state for the 3D hopping transport mechanisms at room temperature in addition to ${\rm Ta_{Li}}$, as well, and, thus, impacts a variety of optical, photoelectrical and electrical applications of LT in nonlinear photonics. Furthermore, it is envisaged that LT represents a promising model system for the further examination of the small-polaron based photogalvanic effect in polar oxides with the unique feature of two, energetically well separated small polaron states.

Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more) morphologically distinct constituents. The key idea is to carefully select representation systems each providing sparse approximations of one of the components. Then the sparsest coefficient vector representing the data within the composed - and therefore highly redundant - representation system is computed by $\ell_1$ minimization or thresholding. This automatically enforces separation. This paper shall serve as an introduction to and a survey about this exciting area of research as well as a reference for the state-of-the-art of this research field. It will appear as a chapter in a book on "Compressed Sensing: Theory and Applications" edited by Yonina Eldar and Gitta Kutyniok.

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by Barbour (1990) and Kasprzak (2020). We demonstrate the applicability of our results by applying it to joint subgraph counts in an Erdős-Renyi random graph model on the one hand and to vectors of weighted, degenerate $U$-processes on the other hand. As a concrete instance of the latter class of examples, we provide a bound for the functional approximation of a vector of success runs of different lengths by a suitable Gaussian process which, even in the situation of just a single run, would be outside the scope of the existing theory.