Search

Riddle-solving requires advanced reasoning skills, pushing LLMs to engage in abstract thinking and creative problem-solving, often revealing limitations in their cognitive abilities. In this paper, we examine the riddle-solving capabilities of LLMs using a multiple-choice format, exploring how different prompting techniques impact performance on riddles that demand diverse reasoning skills. To enhance results, we introduce RISCORE (RIddle Solving with COntext REcontruciton) a novel fully automated prompting method that generates and utilizes contextually reconstructed sentence-based puzzles in conjunction with the original examples to create few-shot exemplars. Our experiments demonstrate that RISCORE significantly improves the performance of language models in both vertical and lateral thinking tasks, surpassing traditional exemplar selection strategies across a variety of few-shot settings.

Countable $\mathcal{L}$-structures $\mathcal{N}$ whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerman-Freer-Patel to be precisely those $\mathcal{N}$ which have no algebraicity. Here we characterize those countable $\mathcal{L}$-structure $\mathcal{N}$ whose isomorphism class supports a quasi-invariant probability measure. These turn out to be precisely those $\mathcal{N}$ which are not "highly algebraic" -- we say that $\mathcal{N}$ is highly algebraic if outside of every finite $F$ there is some $b$ and a tuple $\bar{a}$ disjoint from $b$ so that $b$ has a finite orbit under the pointwise stabilizer of $\bar{a}$ in $\mathrm{Aut}(\mathcal{N})$. As a bi-product of our proof we show that whenever the isomorphism class of $\mathcal{N}$ admits a quasi-invariant measure, then it admits one with continuous Radon--Nikodym cocycles.

For each ordinal $\alpha<\omega_1$, we introduce the class of $\alpha$-balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish groups admitting a two-side-invariant metric (TSI) and the class of Polish groups admitting a complete left-invariant metric (CLI). We establish various closure properties, provide connections to model theory, and we develop a boundedness principle for CLI groups by showing that $\alpha$-balancedness is an initial segment of a regular coanalytic rank. In the spirit of Hjorth's turbulence theory we also introduce "generic $\alpha$-unbalancedness": a new dynamical condition for Polish $G$-spaces which serves as an obstruction to classification by actions of $\alpha$-balanced Polish groups. We use this to provide, for each $\alpha<\omega_1$, an action of an $\alpha$-balanced Polish group whose orbit equivalence relation is strongly generically ergodic against actions of any $\beta$-balanced Polish group with $\beta<\alpha$.

Fast feedforward networks (FFFs) are a class of neural networks that exploit the observation that different regions of the input space activate distinct subsets of neurons in wide networks. FFFs partition the input space into separate sections using a differentiable binary tree of neurons and during inference descend the binary tree in order to improve computational efficiency. Inspired by Mixture of Experts (MoE) research, we propose the incorporation of load balancing and Master Leaf techniques into the FFF architecture to improve performance and simplify the training process. We reproduce experiments found in literature and present results on FFF models enhanced using these techniques. The proposed architecture and training recipe achieves up to 16.3% and 3% absolute classification accuracy increase in training and test accuracy, respectively, compared to the original FFF architecture. Additionally, we observe a smaller variance in the results compared to those reported in prior research. These findings demonstrate the potential of integrating MoE-inspired techniques into FFFs for developing more accurate and efficient models.

Monte Carlo simulations in the grand canonical ensemble were used to obtain critical parameters and conditions leading to microphase separation for block copolymers with solvophilic and solvophobic segments. Solvent selectivity was systematically varied to distinguish between systems that undergo macrophase separation to ones that microphase separate in the dilute phase, prior to macrophase separating. Finite-size scaling was used to obtain the critical parameters. Interestingly, corrections to scaling increase significantly for systems that form finite aggregates. The threshold value of solvent selectivity for aggregation was determined for symmetric diblock chains of varying length. The results indicate that long diblock copolymers form micelles in the dilute phase prior to macrophase separation, even in marginally selective solvents. The dependence of critical temperature on solvent selectivity was obtained for triblock, multiblock, and alternating chains. For highly selective solvents, strong structuring of both dilute and dense phases makes it harder to reach equilibrium.

Histogram-reweighting grand canonical Monte Carlo simulations are used to obtain the critical properties of lattice chains composed of solvophilic and solvophobic monomers. The model is a modification of one proposed by Larson \emph{et al.} [J. Chem. Phys. 83, 2411 (1985)], lowering the ``contrast'' between beads of different type to prevent aggregation into finite-size micelles that would mask true phase separation between bulk high- and low-density phases. Oligomeric chains of length between 5 and 24 beads are studied. Mixed-field finite-size scaling methods are used to obtain the critical properties with typical relative accuracies of better than $10^{-4}$ for the critical temperature and $10^{-3}$ for the critical volume fraction. Diblock chains are found to have lower critical temperatures and volume fractions relative to the corresponding homopolymers. Addition of solvophilic blocks of increasing length to a fixed-length solvophobic segment results in a decrease of both critical temperature and critical volume fraction, with an eventual slow asymptotic approach to the long-chain limiting behavior. Moving a single solvophobic or solvophilic bead along a chain leads to a minimum or maximum in the critical temperature, with no change in critical volume fraction. Chains of identical length and composition have a significant spread in their critical properties, depending on their precise sequence. The present study has implications on understanding biomolecular phase separation and for developing design rules for synthetic polymers with specific phase separation properties. It also provides data potentially useful for the further development of theoretical models for polymer and surfactant phase behavior.

In this paper, we outline our submission for the SemEval-2024 Task 9 competition: 'BRAINTEASER: A Novel Task Defying Common Sense'. We engage in both sub-tasks: Sub-task A-Sentence Puzzle and Sub-task B-Word Puzzle. We evaluate a plethora of pre-trained transformer-based language models of different sizes through fine-tuning. Subsequently, we undertake an analysis of their scores and responses to aid future researchers in understanding and utilizing these models effectively. Our top-performing approaches secured competitive positions on the competition leaderboard across both sub-tasks. In the evaluation phase, our best submission attained an average accuracy score of 81.7% in the Sentence Puzzle, and 85.4% in the Word Puzzle, significantly outperforming the best neural baseline (ChatGPT) by more than 20% and 30% respectively., Comment: SemEval-2024

We show that the homeomorphisms of the Sierpi\'nski carpet are not classifiable, up to conjugacy, using isomorphism types of countable structures as invariants., Comment: 13 pages, 6 figures

Large Language Models (LLMs) exhibit impressive performance on a range of NLP tasks, due to the general-purpose linguistic knowledge acquired during pretraining. Existing model interpretability research (Tenney et al., 2019) suggests that a linguistic hierarchy emerges in the LLM layers, with lower layers better suited to solving syntactic tasks and higher layers employed for semantic processing. Yet, little is known about how encodings of different linguistic phenomena interact within the models and to what extent processing of linguistically-related categories relies on the same, shared model representations. In this paper, we propose a framework for testing the joint encoding of linguistic categories in LLMs. Focusing on syntax, we find evidence of joint encoding both at the same (related part-of-speech (POS) classes) and different (POS classes and related syntactic dependency relations) levels of linguistic hierarchy. Our cross-lingual experiments show that the same patterns hold across languages in multilingual LLMs., Comment: Accepted in EMNLP Findings 2023

Due to its extremely short timescale, the non-equilibrium melting of metals is exceptionally difficult to probe experimentally. The knowledge of melting mechanisms is thus based mainly on the results of theoretical predictions. This work reports on the investigation of ultrafast melting of thin polycrystalline Pd films studied by optical laser pump - X-ray free-electron laser probe experiments and molecular-dynamics simulations. By acquiring X-ray diffraction snapshots with sub-picosecond resolution, we capture the sample's atomic structure during its transition from the crystalline to the liquid state. Bridging the timescales of experiments and simulations allows us to formulate a realistic microscopic picture of melting. We demonstrate that the existing models of strongly non-equilibrium melting, developed for systems with relatively weak electron-phonon coupling, remain valid even for ultrafast heating rates achieved in femtosecond laser-excited Pd. Furthermore, we highlight the role of pre-existing and transiently generated crystal defects in the transition to the liquid state., Comment: main manuscript 33 pages, 9 figures; supplemental material 19 pages, 13 figures - all in one file

Ultrathin, solution-processed emerging solar cells with high power-per-weight (PPW) outputs demonstrate unique potential for applications where low weight, high power output, and flexibility are indispensable. The following perspective explores the literature of emerging PVs and highlights the maximum reported PPW values of Perovskite Solar Cells (PSCs) 29.4 W/g, Organic Solar Cells (OSCs) 32.07 W/g and Quantum Dot Solar Cells (QDSC) 15.02 W/g, respectively. The record PPW values of OSCs and PSCs are approximately one order of magnitude higher compared to their inorganic ultrathin solar cells counterparts (approx. 3.2 W/g for CIGS and a-Si). This consists emerging PVs, very attractive for a variety of applications where the PPW is the key parameter. In particular, both OSCs and PSCs can be implemented in different scenarios of applications (indoor and biocompatible applications for OSCs and outdoor and high-energy radiation conversion conditions for the PSCs) due to their unique optoelectronic and physiochemical properties. Finally, our theoretical optical and electrical simulation and optimization study for the most promising and well-suited PV technologies, showed an impressive maximum realistic theoretical PPW limit of 74.3 and 93.7 W/g for PSCs and OSCs, respectively. Our finding shows that the literature PSCs and OSCs towards high PPW outputs, is not quite close to the theoretical maximum and thus more work needs to be done to further increase the PPW output of these promising PV technologies., Comment: 41 pages, 20 figues

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters., Comment: has accepted by Physical Review Letters

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water at deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 1 nm from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30,000 atoms. Future work will be directed towards the calculation of nucleation free energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces on ice nucleation., Comment: 12 pages, 6 figures

The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable on rich enough collections of spacetimes is Borel definable. In fact, we show that it is consistent with the Zermelo-Fraenkel and Dependent Choice axioms that no complete observable for rich collections of spacetimes exists whatsoever. In a nutshell, this implies that the Problem of Observables is to 'analysis' what the Delian Problem was to 'straightedge and compass'. Our results remain true even after restricting the space of solutions to vacuum solutions. In other words, the issue can be traced to the presence of local degrees of freedom. We discuss the next steps in a research program that aims to further uncover this novel connection between theoretical physics and descriptive set theory., Comment: 5 pages, 2 figures

The lack of interpretability of the Vision Transformer may hinder its use in critical real-world applications despite its effectiveness. To overcome this issue, we propose a post-hoc interpretability method called VISION DIFFMASK, which uses the activations of the model's hidden layers to predict the relevant parts of the input that contribute to its final predictions. Our approach uses a gating mechanism to identify the minimal subset of the original input that preserves the predicted distribution over classes. We demonstrate the faithfulness of our method, by introducing a faithfulness task, and comparing it to other state-of-the-art attribution methods on CIFAR-10 and ImageNet-1K, achieving compelling results. To aid reproducibility and further extension of our work, we open source our implementation: https://github.com/AngelosNal/Vision-DiffMask, Comment: Accepted in the XAI4CV Workshop at CVPR 2023

This article focuses on phase and aggregation behavior for linear chains composed of blocks of hydrophilic and hydrophobic segments. Phase and conformational transitions of patterned chains are relevant for understanding liquid-liquid separation of biomolecular condensates, which play a prominent role in cellular biophysics, but also for surfactant and polymer applications. Previous studies of simple models for multiblock chains have shown that, depending on the sequence pattern and chain length, such systems can fall into one of two categories: displaying either phase separation or aggregation into finite-size clusters. The key new result of the present study is that both formation of finite-size aggregates and phase separation can be observed for certain chain architectures at appropriate conditions of temperature and concentration. For such systems, a bulk dense liquid condenses from a dilute phase that already contains multi-chain finite-size aggregates. The computational approach involves several distinct steps using histogram-reweighting grand canonical Monte Carlo simulations, which are described here in some level of detail., Comment: 9 pages, 11 figures

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here we utilize the Deep Potential methodology -- a machine learning approach -- to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K, and evaluate the Deep Potential model performance against experimental results and the semi-empirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model, due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 $\pm$ 0.008) nm at 296.4 K. Lastly, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point towards the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behaviour is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebraic topology. In it, we show that the \v{C}ech cohomology functors $\check{\mathrm{H}}^n$ on the category of locally compact separable metric spaces each factor into (i) what we term their definable version, a functor $\check{\mathrm{H}}^n_{\mathrm{def}}$ taking values in the category $\mathsf{GPC}$ of groups with a Polish cover (a category first introduced in this work's predecessor), followed by (ii) a forgetful functor from $\mathsf{GPC}$ to the category of groups. These definable cohomology functors powerfully refine their classical counterparts: we show that they are complete invariants, for example, of the homotopy types of mapping telescopes of $d$-spheres or $d$-tori for any $d\geq 1$, and, in contrast, that there exist uncountable families of pairwise homotopy inequivalent mapping telescopes of either sort on which the classical cohomology functors are constant. We then apply the functors $\check{\mathrm{H}}^n_{\mathrm{def}}$ to show that a seminal problem in the development of algebraic topology, namely Borsuk and Eilenberg's 1936 problem of classifying, up to homotopy, the maps from a solenoid complement $S^3\backslash\Sigma$ to the $2$-sphere, is essentially hyperfinite but not smooth. In the course of this work, we record Borel definable versions of a number of classical results bearing on both the combinatorial and homotopical formulations of \v{C}ech cohomology; in aggregate, this work may be regarded as laying foundations for the descriptive set theoretic study of the homotopy relation on the space of maps from a locally compact Polish space to a polyhedron, a relation which embodies a substantial variety of classification problems arising throughout mathematics., Comment: 63 pages; revised and accepted to Forum of Mathematics, Pi

A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles., Comment: 14 pages, 3 figures. Supplemental material contains 11 pages, 8 figures

Let $E$ be a countable Borel equivalence relation on the space $\mathcal{E}_{\infty}$ of all infinite partitions of the natural numbers. We show that $E$ coincides with equality below a Carlson-Simpson generic element of $\mathcal{E}_{\infty}$. In contrast, we show that there is a hypersmooth equivalence relation on $\mathcal{E}_{\infty}$ which is Borel bireducible with $E_1$ on every Carlson-Simpson cube. Our arguments are classical and require no background in forcing.

Although machine learning (ML) has shown promise in numerous domains, there are concerns about generalizability to out-of-sample data. This is currently addressed by centrally sharing ample, and importantly diverse, data from multiple sites. However, such centralization is challenging to scale (or even not feasible) due to various limitations. Federated ML (FL) provides an alternative to train accurate and generalizable ML models, by only sharing numerical model updates. Here we present findings from the largest FL study to-date, involving data from 71 healthcare institutions across 6 continents, to generate an automatic tumor boundary detector for the rare disease of glioblastoma, utilizing the largest dataset of such patients ever used in the literature (25,256 MRI scans from 6,314 patients). We demonstrate a 33% improvement over a publicly trained model to delineate the surgically targetable tumor, and 23% improvement over the tumor's entire extent. We anticipate our study to: 1) enable more studies in healthcare informed by large and diverse data, ensuring meaningful results for rare diseases and underrepresented populations, 2) facilitate further quantitative analyses for glioblastoma via performance optimization of our consensus model for eventual public release, and 3) demonstrate the effectiveness of FL at such scale and task complexity as a paradigm shift for multi-site collaborations, alleviating the need for data sharing., Comment: federated learning, deep learning, convolutional neural network, segmentation, brain tumor, glioma, glioblastoma, FeTS, BraTS

This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the potential viability of the underlying feedback control techniques in an experiment. In contrast to previous experimental studies that used iterative root-finding methods on the feedback control targets, we propose a feedback control law that is inherently non-invasive. That is, the control discovers the location of equilibria and stabilizes them simultaneously. We call the proposed control zero-in-equilibrium feedback control and we prove that it is able to stabilize branches of equilibria, except at singularities of codimension n+1, where n is the number of state space dimensions the feedback can depend on. We apply the method to a simulated evacuation scenario were pedestrians have to reach an exit after maneuvering left or right around an obstacle. The scenario shows a hysteresis phenomenon with bistability and tipping between two possible steady pedestrian flows in microscopic simulations. We demonstrate for the evacuation scenario that the proposed control law is able to uniformly discover and stabilize steady flows along the entire branch, including points where other non-invasive approaches to feedback control become singular., Comment: submitted (34 pages 12 figures)

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine learning model trained on density-functional theory (DFT) energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation) which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates., Comment: 20 pages, 5 figures

Salt water is ubiquitous, playing crucial roles in geological and physiological processes. Despite centuries of investigations, whether or not water's structure is drastically changed by dissolved ions is still debated. Based on density functional theory, we employ machine learning based molecular dynamics to model sodium chloride, potassium chloride, and sodium bromide solutions at different concentrations. The resulting reciprocal-space structure factors agree quantitatively with neutron diffraction data. Here we provide clear evidence that the ions in salt water do not distort the structure of water in the same way as neat water responds to elevated pressure. Rather, the computed structural changes are restricted to the ionic first solvation shells intruding into the hydrogen bond network, beyond which the oxygen radial-distribution function does not undergo major change relative to neat water. Our findings suggest that the widely cited pressure-like effect on the solvent in Hofmeister series ionic solutions should be carefully revisited., Comment: 22 pages, 4 figures