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The Nobel Prize winning Black-Scholes equation for stock options and the heat equation can both be written in the form \[ \frac{\partial u}{\partial t}=P_2(A)u, \] where $P_2(z)=\alpha z^2+ \beta z+\gamma$ is a quadratic polynomial with $\alpha > 0$. In fact, taking $A = x\frac{\partial}{\partial x}$ on functions on $[0,\infty) \times [0,\infty)$ the previous equality reduces to the Black-Scholes equation, while taking $A = \frac{\partial}{\partial x}$ for functions on $\mathbb{R} \times [0,\infty)$ it becomes the heat equation. Here, we ``connect'' the two previous problems by considering the generalized operator $A= x^a\frac{\partial}{\partial x}$ for functions on $[0,\infty) \times [0,\infty)$ with $0

The Projected Augmented Wave (PAW) Method is based on generating a transform between the pseudo wavefunction and all electron wavefunction. For the accuracy of the method, it is important that the local part of the transform (in each atomic sphere $\mathbf{R}$) be over a complete basis set (with deviations from completeness leading to corrections to the total energy not computed within current implementations of PAW). Here we show how to make this basis much closer to complete without significant additional computational work without modifying the transformation in any way by extending the resolution of unity used for the transform to include more wavefunctions and having them transform via the identity., Comment: Comments welcome, V2: Many corrections

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number. In addition to the boost these embeddings provide on their own, we show that this fix enables architectural modifications such as input injection and recurrent layers to improve performance even further. With positions resolved, we can study the logical extrapolation ability of transformers. Can they solve arithmetic problems that are larger and more complex than those in their training data? We find that training on only 20 digit numbers with a single GPU for one day, we can reach state-of-the-art performance, achieving up to 99% accuracy on 100 digit addition problems. Finally, we show that these gains in numeracy also unlock improvements on other multi-step reasoning tasks including sorting and multiplication.

Large vision-language models (LVLMs) have achieved impressive results in various visual question-answering and reasoning tasks through vision instruction tuning on specific datasets. However, there is still significant room for improvement in the alignment between visual and language modalities. Previous methods to enhance this alignment typically require external models or data, heavily depending on their capabilities and quality, which inevitably sets an upper bound on performance. In this paper, we propose SIMA, a framework that enhances visual and language modality alignment through self-improvement, eliminating the needs for external models or data. SIMA leverages prompts from existing vision instruction tuning datasets to self-generate responses and employs an in-context self-critic mechanism to select response pairs for preference tuning. The key innovation is the introduction of three vision metrics during the in-context self-critic process, which can guide the LVLM in selecting responses that enhance image comprehension. Through experiments across 14 hallucination and comprehensive benchmarks, we demonstrate that SIMA not only improves model performance across all benchmarks but also achieves superior modality alignment, outperforming previous approaches., Comment: 15 pages, 8 figures

Cross-domain alignment refers to the task of mapping a concept from one domain to another. For example, ``If a \textit{doctor} were a \textit{color}, what color would it be?''. This seemingly peculiar task is designed to investigate how people represent concrete and abstract concepts through their mappings between categories and their reasoning processes over those mappings. In this paper, we adapt this task from cognitive science to evaluate the conceptualization and reasoning abilities of large language models (LLMs) through a behavioral study. We examine several LLMs by prompting them with a cross-domain mapping task and analyzing their responses at both the population and individual levels. Additionally, we assess the models' ability to reason about their predictions by analyzing and categorizing their explanations for these mappings. The results reveal several similarities between humans' and models' mappings and explanations, suggesting that models represent concepts similarly to humans. This similarity is evident not only in the model representation but also in their behavior. Furthermore, the models mostly provide valid explanations and deploy reasoning paths that are similar to those of humans., Comment: CogSci

In this work we present a new basis set for electronic structure calculations of crystalline solids using Density Functional theory (DFT) methods. In this construction we take advantage of the fact that most DFT calculations use a convergence loop in order to obtain the eigenstates of a final Khon Sham (KS) Hamiltonian matrix whose eigenstates also give the appropriate electron density needed to obtain the KS potential needed for that KS Hamiltonian matrix. Here we propose that for the basis of each step of the iteration we use the previous eigenstate basis in the interstitial region but augmented inside the MT sphere with the solution to the spherically averaged KS Hamiltonian for the energy window of that eigenstate. To reduce the number of times the KS potential needs to be solved inside the MT spheres it is advantageous to use energy windows and solve the KS Hamiltonian inside the MT region only once per window (at some energy inside the window) so that the KS Hamiltonian needs only be solved a small number of times per iteration, for practical applications on the order of 10 to 100 windows. This method combines the energy dependence of methods such as Projected Augmented Wave functions (PAW) with the ability of the basis set to adjust to the solid state (rather then atomic) environment of basis sets such as Linearized Augmented Plane Waves (LAPW)., Comment: Comments welcome

The transition from subAlfv\'enic to superAlfv\'enic flow in the solar atmosphere is examined by means of Parker Solar Probe (PSP) measurements during solar encounters 8 to 14. Around 220 subAlfv\'enic periods with a duration $\ge$ 10 minutes are identified. The distribution of their durations, heliocentric distances, and Alfv\'en Mach number are analyzed and compared with a global magnetohydrodynamic model of the solar corona and wind, which includes turbulence effects. The results are consistent with a patchy and fragmented morphology, and suggestive of a turbulent Alfv\'en zone within which the transition from subAlfv\'enic to superAlfv\'enic flow occurs over an extended range of helioradii. These results inform and establish context for detailed analyses of subAlfv\'enic coronal plasma that are expected to emerge from PSP's final mission phase, as well as for NASA's planned PUNCH mission.

Current datasets for long-form video understanding often fall short of providing genuine long-form comprehension challenges, as many tasks derived from these datasets can be successfully tackled by analyzing just one or a few random frames from a video. To address this issue, we present a novel dataset and benchmark, CinePile, specifically designed for authentic long-form video understanding. This paper details our innovative approach for creating a question-answer dataset, utilizing advanced LLMs with human-in-the-loop and building upon human-generated raw data. Our comprehensive dataset comprises 305,000 multiple-choice questions (MCQs), covering various visual and multimodal aspects, including temporal comprehension, understanding human-object interactions, and reasoning about events or actions within a scene. Additionally, we fine-tuned open-source Video-LLMs on the training split and evaluated both open-source and proprietary video-centric LLMs on the test split of our dataset. The findings indicate that although current models underperform compared to humans, fine-tuning these models can lead to significant improvements in their performance., Comment: Project page with all the artifacts - https://ruchitrawal.github.io/cinepile/. Updated version with adversarial refinement pipeline and more model evaluations

We develop a methodology for analyzing language model task performance at the individual example level based on training data density estimation. Experiments with paraphrasing as a controlled intervention on finetuning data demonstrate that increasing the support in the training distribution for specific test queries results in a measurable increase in density, which is also a significant predictor of the performance increase caused by the intervention. Experiments with pretraining data demonstrate that we can explain a significant fraction of the variance in model perplexity via density measurements. We conclude that our framework can provide statistical evidence of the dependence of a target model's predictions on subsets of its training data, and can more generally be used to characterize the support (or lack thereof) in the training data for a given test task., Comment: 10 pages in the main body

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and D\"urr [arXiv:1802.07141] presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, is actually not what Bohmian mechanics predicts., Comment: 24 pages LaTeX, 2 figures; v2 appendices added, two paragraphs on page 2 added

This paper focuses on the opportunities and the ethical and societal risks posed by advanced AI assistants. We define advanced AI assistants as artificial agents with natural language interfaces, whose function is to plan and execute sequences of actions on behalf of a user, across one or more domains, in line with the user's expectations. The paper starts by considering the technology itself, providing an overview of AI assistants, their technical foundations and potential range of applications. It then explores questions around AI value alignment, well-being, safety and malicious uses. Extending the circle of inquiry further, we next consider the relationship between advanced AI assistants and individual users in more detail, exploring topics such as manipulation and persuasion, anthropomorphism, appropriate relationships, trust and privacy. With this analysis in place, we consider the deployment of advanced assistants at a societal scale, focusing on cooperation, equity and access, misinformation, economic impact, the environment and how best to evaluate advanced AI assistants. Finally, we conclude by providing a range of recommendations for researchers, developers, policymakers and public stakeholders.

In the paper, we address the following problem, often encountered in geometric constructions: having defined an orientation preserving diffeomorphism in a number of `patches' on a manifold $\mathcal{M}$, can we extend it to a diffeomorphism of the whole manifold $\mathcal{M}$? We give a positive answer, provided the `patches' are sufficiently regular. Then, we extend the same result to the case of bi-Lipschitz homeomorphisms and homeomorphisms.

Since their first discovery in the late 1960s, Gamma-ray bursts have attracted an exponentially growing interest from the international community due to their central role in the most highly debated open questions of the modern research of astronomy, astrophysics, cosmology, and fundamental physics. These range from the intimate nuclear composition of high density material within the core of ultra-dense neuron stars, to stellar evolution via the collapse of massive stars, the production and propagation of gravitational waves, as well as the exploration of the early Universe by unveiling first stars and galaxies (assessing also their evolution and cosmic re-ionization). GRBs have stimulated in the past $\sim$50 years the development of cutting-edge technological instruments for observations of high energy celestial sources from space, leading to the launch and successful operations of many different scientific missions (several of them still in data taking mode nowadays). In this review, we provide a brief description of the GRB-dedicated missions from space being designed and developed for the future. The list of these projects, not meant to be exhaustive, shall serve as a reference to interested readers to understand what is likely to come next to lead the further development of GRB research and associated phenomenology., Comment: Accepted for publication on Universe. Invited review, contribution to the Universe Special Issue "Recent Advances in Gamma Ray Astrophysics and Future Perspectives", P. Romano eds. (https://www.mdpi.com/journal/universe/special_issues/7299902Z97)

Thermal equilibrium states of local quantum many-body systems are notorious for their spatially decaying correlations, which place severe restrictions on the types of many-body entanglement structures that may be observed at finite temperatures. These restrictions may however be defied when an out-of-equilibrium steady state is considered instead. In this paper, we study the entanglement properties of free fermions on a one-dimensional lattice that contains a generic charge- and energy-conserving noninteracting impurity, and that is connected at its edges to two reservoirs with different equilibrium energy distributions. These distributions may differ in either temperature, chemical potential, or both, thereby inducing an external bias. We analytically derive exact asymptotic expressions for several quantum information measures -- the mutual information, its R\'enyi generalizations, and the fermionic negativity -- that quantify the correlation and entanglement between two subsystems located on opposite sides of the impurity. We show that all these measures scale (to a leading order) linearly with the overlap between one subsystem and the mirror image of the other (upon reflection of the latter about the impurity), independently of the distance between the subsystems. While a simple proportionality relation between the negativity and R\'enyi versions of the mutual information is observed to hold at zero temperature, it breaks down at finite temperatures, suggesting that these quantities represent strong long-range correlations of different origins. Our results generalize previous findings that were limited to the case of a chemical-potential bias at zero temperature, rigorously demonstrating that the effect of long-range volume-law entanglement is robust at finite temperatures., Comment: 16+4 pages, 4 figures. v2: Published version, 17+4 pages, 5 figures

In this work we make some progress on studying four center integrals for the Coulomb energy for both Hartree Fock (HF) and Density Functional Theory (DFT) calculations for small molecules. We consider basis wave functions of the form of an arbitrary radial wave function multiplied by a spherical harmonic and study four center Coulomb integrals for them. We reformulated these Coulomb four center integrals in terms of some derivatives of integrals of nearly factorable functions which then depend on the Bessel transform of the radial wave functions considered., Comment: Comments welcome

The success behind many pseudopotential methods such as Projected Augmented Waves (PAW) and Phillips-Kleinman pseudopotential methods is that these methods are all electron methods in disguise. For the Phillips Kleinman and PAW methods we show that there is an all electron formulation. In the all electron formulation there are regular low wavevector basis wave functions and several, specially chosen, high wavevector basis wave functions that are specialized to the atomic environment. Using this as inspiration here we propose a new, PAW method inspired, basis set for small molecules, where we use the recently introduced LO or lo (Localized orbitals) basis set is paired with a Gaussian basis, Gaussian type orbitals (GTO), for a hybrid basis for small molecules. Contracted Gaussian functions are also possible (CGFs). We also show how to extend this idea to Slater basis set, Slater type orbitals (STO), instead of GTO orbitals combined with LO or lo orbitals., Comment: Comments welcome, V2: Minor typos corrected; V3: Some extensions

We present Eagle (RWKV-5) and Finch (RWKV-6), sequence models improving upon the RWKV (RWKV-4) architecture. Our architectural design advancements include multi-headed matrix-valued states and a dynamic recurrence mechanism that improve expressivity while maintaining the inference efficiency characteristics of RNNs. We introduce a new multilingual corpus with 1.12 trillion tokens and a fast tokenizer based on greedy matching for enhanced multilinguality. We trained four Eagle models, ranging from 0.46 to 7.5 billion parameters, and two Finch models with 1.6 and 3.1 billion parameters and find that they achieve competitive performance across a wide variety of benchmarks. We release all our models on HuggingFace under the Apache 2.0 license. Models at: https://huggingface.co/RWKV Training code at: https://github.com/RWKV/RWKV-LM Inference code at: https://github.com/RWKV/ChatRWKV Time-parallel training code at: https://github.com/RWKV/RWKV-infctx-trainer

We evaluate ChatGPT's ability to solve algorithm problems from the CLRS benchmark suite that is designed for GNNs. The benchmark requires the use of a specified classical algorithm to solve a given problem. We find that ChatGPT outperforms specialist GNN models, using Python to successfully solve these problems. This raises new points in the discussion about learning algorithms with neural networks and how we think about what out of distribution testing looks like with web scale training data.

Generative models are now widely used by graphic designers and artists. Prior works have shown that these models remember and often replicate content from their training data during generation. Hence as their proliferation increases, it has become important to perform a database search to determine whether the properties of the image are attributable to specific training data, every time before a generated image is used for professional purposes. Existing tools for this purpose focus on retrieving images of similar semantic content. Meanwhile, many artists are concerned with style replication in text-to-image models. We present a framework for understanding and extracting style descriptors from images. Our framework comprises a new dataset curated using the insight that style is a subjective property of an image that captures complex yet meaningful interactions of factors including but not limited to colors, textures, shapes, etc. We also propose a method to extract style descriptors that can be used to attribute style of a generated image to the images used in the training dataset of a text-to-image model. We showcase promising results in various style retrieval tasks. We also quantitatively and qualitatively analyze style attribution and matching in the Stable Diffusion model. Code and artifacts are available at https://github.com/learn2phoenix/CSD.

It is commonplace to produce application-specific models by fine-tuning large pre-trained models using a small bespoke dataset. The widespread availability of foundation model checkpoints on the web poses considerable risks, including the vulnerability to backdoor attacks. In this paper, we unveil a new vulnerability: the privacy backdoor attack. This black-box privacy attack aims to amplify the privacy leakage that arises when fine-tuning a model: when a victim fine-tunes a backdoored model, their training data will be leaked at a significantly higher rate than if they had fine-tuned a typical model. We conduct extensive experiments on various datasets and models, including both vision-language models (CLIP) and large language models, demonstrating the broad applicability and effectiveness of such an attack. Additionally, we carry out multiple ablation studies with different fine-tuning methods and inference strategies to thoroughly analyze this new threat. Our findings highlight a critical privacy concern within the machine learning community and call for a reevaluation of safety protocols in the use of open-source pre-trained models.

The (classical) zero bias is a transformation of centered, finite variance probability distributions, often expressed in terms of random variables $X\mapsto X^\ast$, characterized by the functional equation \[ E[Xf(X)] = \sigma^2 E[f'(X^\ast)] \quad \text{for all }\; f\in C_c^\infty(\mathbb{R}) \] where $\sigma^2$ is the variance of $X$. The zero bias distribution is always absolutely continuous, and supported on the convex hull of the support of $X$. It is related to Stein's method, and has many applications throughout probability and statistics, most recently finding new characterization of infinite divisiblity and relation to the L\'evy--Khintchine formula. In this paper, we define a free probability analogue, the {\em free zero bias} transform $X\mapsto X^\circ$ acting on centered $L^2$ random variables, characterized by the functional equation \[ E[Xf(X)] = \sigma^2 E[\partial f(X^\circ)] \quad \text{for all }\; f\in C_c^\infty(\mathbb{R}) \] where $\partial f$ denotes the free difference quotient. We prove existence of this transform, and show that it has comparable smoothness and support properties to the classical zero bias. Our main theorem is an analogous characterization of free infinite divisibility in terms of the free zero bias, and a new understanding of free L\'evy measures. To achieve this, we develop several new operations on Cauchy transforms of probability distributions that are of independent interest., Comment: 45 page, 5 figures

Modern neural networks are often trained on massive datasets that are web scraped with minimal human inspection. As a result of this insecure curation pipeline, an adversary can poison or backdoor the resulting model by uploading malicious data to the internet and waiting for a victim to scrape and train on it. Existing approaches for creating poisons and backdoors start with randomly sampled clean data, called base samples, and then modify those samples to craft poisons. However, some base samples may be significantly more amenable to poisoning than others. As a result, we may be able to craft more potent poisons by carefully choosing the base samples. In this work, we use guided diffusion to synthesize base samples from scratch that lead to significantly more potent poisons and backdoors than previous state-of-the-art attacks. Our Guided Diffusion Poisoning (GDP) base samples can be combined with any downstream poisoning or backdoor attack to boost its effectiveness. Our implementation code is publicly available at: https://github.com/hsouri/GDP .

In this work we present a new basis set for electronic structures (Density Functional Theory (DFT)) calculations. This basis set extends Soler Williams Linearized Augmented Plane Wave (SLAPW) basis sets by allowing variable Muffin Tin (MT) sphere radii for the different angular momentum channels and for different magnitude wave vectors of the augmented plane waves. With the correct choice of MT radius, this allows us to match additional derivatives of the wave function at the MT radius without having to resort to additional higher derivative terms as part of the wave function expansion inside the MT sphere. This should lead to low wave vector basis set and low linearization energy errors, arguably as good as APW basis set size and LAPW basis linearization errors. We call these basis sets SAPWMR and SLAPWMR depending on the number of derivative like wave functions kept inside the MT radii. Similarly local orbital (LO and lo basis wave functions depending on the number of derivative terms in the MT radius) are suggested with a variable radius. that reduces the number of derivative like terms needed to make them continuous or continuously differentiable. As such semi-core states can also be well handled by our methods. Furthermore in the appendix Full Potential Hamiltonian calculations (FLAPW) are extended to FSLAPWMR full potential calculations for Hamiltonian matrix elements. In the Appendix we introduce some further ideas to improve the speed of DFT calculations which are relevant to the basis sets presented here and to other basis sets such as the LAPW basis set., Comment: Comments welcome, V2: Comments and clarifications

In this work we analyze two axis twisting in the presence of depolarizing channel dissipation. We find that spin squeezing is only possible if the dissipation is parametrically weaker than the squeezing coupling. Squeezing may be used for meteorologically useful decrease of spin noise but only in the case where the squeezing occurs before measurement, in the case one squeezes as one measures one also squeezes the signal thereby making spin squeezing ineffective for metrological gain. The key mathematical advance made in this work is the observation that TACT in the presence of depolarizing noise is equivalent to TACT with reduced polarization and no noise. We find an exponential gain in signal to noise with the exponent proportional to the ratio between the squeezing strength and the depolarization rate., Comment: comments welcome

Since the Voyager mission flybys in 1979, we have known the moon Io to be both volcanically active and the main source of plasma in the vast magnetosphere of Jupiter. Material lost from Io forms neutral clouds, the Io plasma torus and ultimately the extended plasma sheet. This material is supplied from Io's upper atmosphere and atmospheric loss is likely driven by plasma-interaction effects with possible contributions from thermal escape and photochemistry-driven escape. Direct volcanic escape is negligible. The supply of material to maintain the plasma torus has been estimated from various methods at roughly one ton per second. Most of the time the magnetospheric plasma environment of Io is stable on timescales from days to months. Similarly, Io's atmosphere was found to have a stable average density on the dayside, although it exhibits lateral and temporal variations. There is potential positive feedback in the Io torus supply: collisions of torus plasma with atmospheric neutrals are probably a significant loss process, which increases with torus density. The stability of the torus environment may be maintained by limiting mechanisms of either torus supply from Io or the loss from the torus by centrifugal interchange in the middle magnetosphere. Various observations suggest that occasionally the plasma torus undergoes major transient changes over a period of several weeks, apparently overcoming possible stabilizing mechanisms. Such events are commonly explained by some kind of change in volcanic activity that triggers a chain of reactions which modify the plasma torus state via a net change in supply of new mass. However, it remains unknown what kind of volcanic event (if any) can trigger events in torus and magnetosphere, whether Io's atmosphere undergoes a general change before or during such events, and what processes could enable such a change in the otherwise stable torus.

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of the future system state given its current state. To this end, we leverage the framework of stochastic interpolants, which facilitates the construction of a generative model between an arbitrary base distribution and the target. We design a fictitious, non-physical stochastic dynamics that takes as initial condition the current system state and produces as output a sample from the target conditional distribution in finite time and without bias. This process therefore maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. We prove that the drift coefficient entering the stochastic differential equation (SDE) achieving this task is non-singular, and that it can be learned efficiently by square loss regression over the time-series data. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a F\"ollmer process. We highlight the utility of our approach on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes and video prediction on the KTH and CLEVRER datasets.

In this work we introduce a Linearized version of the Koringa Khon and Rostoker method (LKKR) and show it to be equivalent to the Linearized Muffin Tin Orbitals method (LMTO). We then present higher derivative versions of both methods, e.g. HDKKR and HDMTO and show them to be partially distinct (not equivalent). In particular HDKKR basis set does not have an equivalent ground state for the Khon Sham (KS) Hamiltonian as the HDKKR basis set and has greater variational power than the HDMTO one. Because the KS method, for Density Functional Theory (DFT), is variational HDKKR will give better ground state energies than HDMTO. However HDKKR is much harder to work with then HDMTO requiring much greater computer resources so HDMTO can often be preferred., Comment: Comments welcome

Much of the research and discourse on risks from artificial intelligence (AI) image generators, such as DALL-E and Midjourney, has centered around whether they could be used to inject false information into political discourse. We show that spammers and scammers - seemingly motivated by profit or clout, not ideology - are already using AI-generated images to gain significant traction on Facebook. At times, the Facebook Feed is recommending unlabeled AI-generated images to users who neither follow the Pages posting the images nor realize that the images are AI-generated, highlighting the need for improved transparency and provenance standards as AI models proliferate., Comment: 18 pages, 13 Figures

In this work we study One Axis Twisting (OAT) spin squeezing for metrology in the presence of decoherence. We study Linbladian evolution in the presence of both T_1 and T_2 (longitudinal and transverse relaxation processes). We show that spin squeezing can be an effective way to improve metrological accuracy even in the presence of decoherence for OAT squeezing. We show our results are not sensitive to inhomogeneity of the squeezing strength of the many spin OAT Hamiltonian and that very general squeezed states do not have entanglement enhanced decoherence. We also extend the Kitagawa-Ueda OAT squeezing formula to finite polarization., Comment: Comments welcome, V2:Added clarifying appendix

In this work we study STM signal in the presence of Coulomb assisted hopping. We perform an extended two site Hubbard model analysis between the atom on the tip and the atom in the sample nearest to each other. We show that in the presence of Coulomb assisted hopping the STM signal depends on several spectral functions thereby complicating its interpretation. Furthermore in the broadband tip limit there are now three different competing rates for the total current (instead of one for the usual two site Hubbard model analysis used in the literature so far). We find an exact (within the Fermi golden rule - that is in the limit of weak coupling between tip and sample) expression for the current as a function of the bias voltage. As an example we apply our calculations to the case of free fermions with a uniform density of states. Even in this simple case there are non-trivial corrections - where the $dI/d\mathcal{V}$ (the rate of change of the current with respect to bias voltage) is not uniform as a two site (non-extended) Hubbard model analysis would predict. We also show that for realistic conditions the corrections predicted here are order one., Comment: Comments welcome. V2: Minor corrections

In this work we extend the notion of what is meant by a meanfield. Meanfields are approximately maps - through some self consistency relation - of a complex, usually manybody, problem to a simpler more readily solvable problem. This mapping can then be solved to represent properties of the complex many body problem using some self consistency relations. Prototypical examples of simpler meanfield problems (meanfield systems) are the single site and free particle problems. Here we propose a new class of simple meanfield systems where the simple problem to be solved is a 1D spin chain. These meanfields are particularly useful for studying quasi-1D models, where there is a 3D system composed of weakly coupled 1D spin chains with the coupling in the transverse direction weaker than in the 1D direction. We illustrate this idea by considering meanfields for the Ising (of any coupling sign) and ferromagnetic Heisenberg models with one direction coupled much more strongly then the other directions (quasi-1D systems) which map at meanfield level onto the 1D Ising and 1D ferromagnetic Heisenberg models. We also consider more exotic models to illustrate other methods of solving 1D systems, namely the $N$-state Potts model. Magnetic phase transition temperatures and are obtained for all three models, we see that they significantly differ from the usual meanfield estimates. Indeed if the 1D direction has coupling $\Gamma$ and the transverse directions have coupling $J$ with $\lambda\sim\frac{\Gamma}{J}\gg1$ then regular meanfield would predict the transition temperature to be $k_{B}T_{c}\sim\Gamma$ for all three models while 1D meanfield predicts temperatures of $k_{B}T_{c}\sim\frac{\Gamma}{\log\left(\lambda\right)}$ for the Ising and Potts models and $k_{B}T_{c}\sim\frac{\Gamma}{\sqrt{\lambda}}$ for the ferromagnetic Heisenberg model. Cluster 1D meanfield extensions are also proposed., Comment: Comments welcome, V2: Some clarifications and further examples

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time $t$, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time $t$. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells $\Delta_\alpha$. The initial and final macrostates of the system are equilibrium states in volumes $V$ and $2V$, with the same energy $E$ and particle number $N$. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the $\Delta_\alpha$. The intermediate (non-equilibrium) entropy does however depend on the size of the cells $\Delta_\alpha$. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining $\Delta v$: it produces entropy at a rate proportional to $\Delta v$. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of $\Delta v$ and is given by the Boltzmann equation for the limit $\Delta v\rightarrow 0$. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes., Comment: (20 pages, 8 figures)

In this work we write down a classical (not quantum) action for the surface height for the Kardar-Parisi-Zhang (KPZ) equation for surface growth. We do so starting with the regular Martin-Siggia-Rose (MSR) action (which is quantum - contains the constraint field) and integrate out the quantum constraint field exactly. We analyze the classical action, we thereby obtain, within the gaussian and one loop approximations various instabilities to rough surfaces. The gaussian analysis predicts instabilities to rough surfaces below two dimensions while one loop analysis predicts stronger surface stability to roughness and instabilities to roughness below one dimension rather than two dimensions. The one loop analysis shows that the KPZ action is incomplete and that we generate additional terms (not found in the initial classical action) in the action perturbatively. In the supplement we also modify the KPZ equation for growing surfaces to include the effect of surface tilt on the noise (that is have two sources of noise one of which is multiplicatively coupled noise)., Comment: Comments welcome, V2: Important corrections (thank you Davide Venturelli); V3: More corrections, V4: Minor typos corrected, V5:Supplement corrected, V6:Minor typos

In this work we re-examine the Wilson Fisher fixed point. We study Wilsonian momentum space renormalization group (RG) flow for various forms of the cutoff. We show that already at order $\left(4-d\right)^{1}$, where $d$ is the dimension of the $\phi^{4}$ theory, there are changes to the position of the fixed point and the direction of irrelevant coupling parameters. We also show in a multi-flavor $\phi^{4}$ model that symmetries of the Lagrange function can be destroyed if the different flavors have different cutoffs (that is the Lagrangian can flow to a non-symmetric fixed point). Some related comments are made about a similar situation in parquet RG (pRG). In future works we will study Wilsonian RG to order $\left(4-d\right)^{2}$ and find non-universal critical exponents that depend on the cutoff., Comment: Comments welcome, V2:typos corrected

We employ an inversion-based approach to examine CLIP models. Our examination reveals that inverting CLIP models results in the generation of images that exhibit semantic alignment with the specified target prompts. We leverage these inverted images to gain insights into various aspects of CLIP models, such as their ability to blend concepts and inclusion of gender biases. We notably observe instances of NSFW (Not Safe For Work) images during model inversion. This phenomenon occurs even for semantically innocuous prompts, like "a beautiful landscape," as well as for prompts involving the names of celebrities., Comment: Warning: This paper contains sexually explicit images and language, offensive visuals and terminology, discussions on pornography, gender bias, and other potentially unsettling, distressing, and/or offensive content for certain readers

In this work we present a doubled version of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open proposals thereby obtaining time reversal invariant p-wave superconductivity in both 1D and 2D. This construction is much like the Kane-Mele spin Hall model which is a time reversal invariant doubling of the Haldane model. We show that the low energy effective action for these doubled versions of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open models corresponds to a single band p-wave time reversal invariant superconductors with pseudo spin degree of freedom instead of spin degree of freedom. There are Majorana fermions at the ends of wires or in vortex cores of these superconductors. Furthermore these are shown to be stable to small perturbations. In the supplement we present physical realization of the system with cold atoms and show a related "no-go" theorem given in Haim et. al. (2019) has too restrictive assumptions to apply to this proposal., Comment: Comments welcome, V2: minor typos corrected, V3 Minor clarifications

Recent advances in LLMs have sparked a debate on whether they understand text. In this position paper, we argue that opponents in this debate hold different definitions for understanding, and particularly differ in their view on the role of consciousness. To substantiate this claim, we propose a thought experiment involving an open-source chatbot $Z$ which excels on every possible benchmark, seemingly without subjective experience. We ask whether $Z$ is capable of understanding, and show that different schools of thought within seminal AI research seem to answer this question differently, uncovering their terminological disagreement. Moving forward, we propose two distinct working definitions for understanding which explicitly acknowledge the question of consciousness, and draw connections with a rich literature in philosophy, psychology and neuroscience., Comment: Accepted to Findings of ACL (2024)