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Large language models (LLMs) demonstrate surprising capabilities, but we do not understand how they are implemented. One hypothesis suggests that these capabilities are primarily executed by small subnetworks within the LLM, known as circuits. But how can we evaluate this hypothesis? In this paper, we formalize a set of criteria that a circuit is hypothesized to meet and develop a suite of hypothesis tests to evaluate how well circuits satisfy them. The criteria focus on the extent to which the LLM's behavior is preserved, the degree of localization of this behavior, and whether the circuit is minimal. We apply these tests to six circuits described in the research literature. We find that synthetic circuits -- circuits that are hard-coded in the model -- align with the idealized properties. Circuits discovered in Transformer models satisfy the criteria to varying degrees. To facilitate future empirical studies of circuits, we created the \textit{circuitry} package, a wrapper around the \textit{TransformerLens} library, which abstracts away lower-level manipulations of hooks and activations. The software is available at \url{https://github.com/blei-lab/circuitry}., Comment: Code available here: https://github.com/blei-lab/circuitry

Recommender systems aim to estimate the dynamically changing user preferences and sequential dependencies between historical user behaviour and metadata. Although transformer-based models have proven to be effective in sequential recommendations, their state growth is proportional to the length of the sequence that is being processed, which makes them expensive in terms of memory and inference costs. Our research focused on three promising directions in sequential recommendations: enhancing speed through the use of State Space Models (SSM), as they can achieve SOTA results in the sequential recommendations domain with lower latency, memory, and inference costs, as proposed by arXiv:2403.03900 improving the quality of recommendations with Large Language Models (LLMs) via Monolithic Preference Optimization without Reference Model (ORPO); and implementing adaptive batch- and step-size algorithms to reduce costs and accelerate training processes., Comment: arXiv admin note: text overlap with arXiv:2403.07691 by other authors

In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating It^o's formula we first compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find a short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We also show that our results extend easily to Quanto-Inverse options. We apply our general results to the SABR and fractional Bergomi models, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew. Finally, we provide an empirical application using Bitcoin options traded on Debirit to show how our theoretical formulas can be used to model real market data of such options., Comment: arXiv admin note: text overlap with arXiv:2308.15341, arXiv:2208.01353

When modeling nuclear processes which occur in heavy-ion reactions, it is necessary to calculate the potential energy of interaction between two nuclei. One of the main features determining the dynamics of the nucleus-nucleus collision is the Coulomb barrier, the knowledge of which is especially important when low- and intermediate-energy reactions are being studied. Our goal is to establish a parameterization of nucleon density distributions for calculation of the nucleus-nucleus double-folding potential in nuclear reactions. Special attention is paid to the description of the Coulomb barrier. The study analyzes experimental data on charge radii, diffuseness, and neutron skin thickness of atomic nuclei. The nucleus-nucleus potential is calculated in the framework of the double-folding method with the effective nucleon-nucleon interaction taken in the form of the zero-range Migdal potential. Based on this analysis and comparison with the Bass potential, parameters of nucleon density distributions are fitted to reproduce the Coulomb barrier. A method for correcting the parameters of nucleon densities to reproduce the Coulomb barrier with the double-folding potential is proposed. The presented way to correct nucleon densities allows obtaining a satisfactory description of the Coulomb barrier that is important for modeling near-barrier collisions of heavy ions.

Recent literature highlights a significant cross-impact between transfer learning and cybersecurity. Many studies have been conducted on using transfer learning to enhance security, leading to various applications in different cybersecurity tasks. However, previous research is focused on specific areas of cybersecurity. This paper presents a comprehensive survey of transfer learning applications in cybersecurity by covering a wide range of domains, identifying current trends, and shedding light on under-explored areas. The survey highlights the significance of transfer learning in addressing critical issues in cybersecurity, such as improving detection accuracy, reducing training time, handling data imbalance, and enhancing privacy preservation. Additional insights are provided on the common problems solved using transfer learning, such as the lack of labeled data, different data distributions, and privacy concerns. The paper identifies future research directions and challenges that require community attention, including the need for privacy-preserving models, automatic tools for knowledge transfer, metrics for measuring domain relatedness, and enhanced privacy preservation mechanisms. The insights and roadmap presented in this paper will guide researchers in further advancing transfer learning in cybersecurity, fostering the development of robust and efficient cybersecurity systems to counter emerging threats and protect sensitive information. To the best of our knowledge, this paper is the first of its kind to present a comprehensive taxonomy of all areas of cybersecurity that benefited from transfer learning and propose a detailed future roadmap to shape the possible research direction in this area.

In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating It\^o's formula we first compute the level of the implied volatility when the maturity converges to zero. Then, we find a short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We apply our general results to the SABR and fractional Bergomi models, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew., Comment: arXiv admin note: text overlap with arXiv:2208.01353

Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free samples from the two distributions of interest are available.We relax this assumption and study the estimation of the MMD under $\epsilon$-contamination, where a possibly non-random $\epsilon$ proportion of one distribution is erroneously grouped with the other. We show that under $\epsilon$-contamination, the typical estimate of the MMD is unreliable. Instead, we study partial identification of the MMD, and characterize sharp upper and lower bounds that contain the true, unknown MMD. We propose a method to estimate these bounds, and show that it gives estimates that converge to the sharpest possible bounds on the MMD as sample size increases, with a convergence rate that is faster than alternative approaches. Using three datasets, we empirically validate that our approach is superior to the alternatives: it gives tight bounds with a low false coverage rate.

The Veronese subalgebra $A_0$ of degree $d\geq 2$ of the polynomial algebra $A=K[x_1,x_2,\ldots,x_n]$ over a field $K$ in the variables $x_1,x_2,\ldots,x_n$ is the subalgebra of $A$ generated by all monomials of degree $d$ and the Veronese subalgebra $P_0$ of degree $d\geq 2$ of the free Poisson algebra $P=P\langle x_1,x_2,\ldots,x_n\rangle$ is the subalgebra spanned by all homogeneous elements of degree $kd$, where $k\geq 0$. If $n\geq 2$ then every derivation and every locally nilpotent derivation of $A_0$ and $P_0$ over a field $K$ of characteristic zero is induced by a derivation and a locally nilpotent derivation of $A$ and $P$, respectively. Moreover, we prove that every automorphism of $A_0$ and $P_0$ over a field $K$ closed with respect to taking all $d$-roots of elements is induced by an automorphism of $A$ and $P$, respectively., Comment: 13 pages

Given a similarity metric, contrastive methods learn a representation in which examples that are similar are pushed together and examples that are dissimilar are pulled apart. Contrastive learning techniques have been utilized extensively to learn representations for tasks ranging from image classification to caption generation. However, existing contrastive learning approaches can fail to generalize because they do not take into account the possibility of different similarity relations. In this paper, we propose a novel multi-similarity contrastive loss (MSCon), that learns generalizable embeddings by jointly utilizing supervision from multiple metrics of similarity. Our method automatically learns contrastive similarity weightings based on the uncertainty in the corresponding similarity, down-weighting uncertain tasks and leading to better out-of-domain generalization to new tasks. We show empirically that networks trained with MSCon outperform state-of-the-art baselines on in-domain and out-of-domain settings.

Many reinforcement learning (RL) applications have combinatorial action spaces, where each action is a composition of sub-actions. A standard RL approach ignores this inherent factorization structure, resulting in a potential failure to make meaningful inferences about rarely observed sub-action combinations; this is particularly problematic for offline settings, where data may be limited. In this work, we propose a form of linear Q-function decomposition induced by factored action spaces. We study the theoretical properties of our approach, identifying scenarios where it is guaranteed to lead to zero bias when used to approximate the Q-function. Outside the regimes with theoretical guarantees, we show that our approach can still be useful because it leads to better sample efficiency without necessarily sacrificing policy optimality, allowing us to achieve a better bias-variance trade-off. Across several offline RL problems using simulators and real-world datasets motivated by healthcare, we demonstrate that incorporating factored action spaces into value-based RL can result in better-performing policies. Our approach can help an agent make more accurate inferences within underexplored regions of the state-action space when applying RL to observational datasets., Comment: 30 pages, 18 figures, 2 tables. NeurIPS 2022. Code available at https://github.com/MLD3/OfflineRL_FactoredActions

Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to poor decisions and poor policies, but also have disastrous effects in critical applications such as healthcare and education. We map out the landscape of offline policy evaluation for confounded MDPs, distinguishing assumptions on confounding based on whether they are memoryless and on their effect on the data-collection policies. We characterize settings where consistent value estimates are provably not achievable, and provide algorithms with guarantees to instead estimate lower bounds on the value. When consistent estimates are achievable, we provide algorithms for value estimation with sample complexity guarantees. We also present new algorithms for offline policy improvement and prove local convergence guarantees. Finally, we experimentally evaluate our algorithms on both a gridworld environment and a simulated healthcare setting of managing sepsis patients. In gridworld, our model-based method provides tighter lower bounds than existing methods, while in the sepsis simulator, our methods significantly outperform confounder-oblivious benchmarks., Comment: Overhauled terminology and presentation, strengthened presentation of results

Robustness to distribution shift and fairness have independently emerged as two important desiderata required of modern machine learning models. While these two desiderata seem related, the connection between them is often unclear in practice. Here, we discuss these connections through a causal lens, focusing on anti-causal prediction tasks, where the input to a classifier (e.g., an image) is assumed to be generated as a function of the target label and the protected attribute. By taking this perspective, we draw explicit connections between a common fairness criterion - separation - and a common notion of robustness - risk invariance. These connections provide new motivation for applying the separation criterion in anticausal settings, and inform old discussions regarding fairness-performance tradeoffs. In addition, our findings suggest that robustness-motivated approaches can be used to enforce separation, and that they often work better in practice than methods designed to directly enforce separation. Using a medical dataset, we empirically validate our findings on the task of detecting pneumonia from X-rays, in a setting where differences in prevalence across sex groups motivates a fairness mitigation. Our findings highlight the importance of considering causal structure when choosing and enforcing fairness criteria.

In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating Ito's formula we first compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find and short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We apply our general results to the SABR model and the rough Bergomi model, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew.

In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst parameter of the volatility process) for rough volatilitites (see Bourgey, De Marco, Friz, and Pigato (2022)), that states that the short-time skew slope of the at-the-money implied volatility is $\frac{1}{H+3/2}$ the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and viceversa, and that this relationship depends on $H$., Comment: 13 pages

The physical autonomy of robots is well understood both theoretically and practically. By contrast, there is almost no research exploring their potential economic autonomy. In this paper, we present the first economically autonomous robot -- a robot able to produce marketable goods while having full control over the use of its generated income. Gaka-chu ("painter" in Japanese) is a 6-axis robot arm that creates paintings of Japanese characters from an autoselected keyword. By using a blockchain-based smart contract, Gaka-chu can autonomously list a painting it made for sale in an online auction. In this transaction, the robot interacts with the human bidders as a peer not as a tool. Using the blockchain-based smart contract, Gaka-chu can then use its income from selling paintings to replenish its resources by autonomously ordering materials from an online art shop. We built the Gaka-chu prototype with an Ethereum-based smart contract and ran a 6-month long experiment, during which the robot created and sold four paintings, simultaneously using its income to purchase supplies and repay initial investors. In this work, we present the results of the experiments conducted and discuss the implications of economically autonomous robots., Comment: Accepted for publication in 2023 IEEE International Conference on Robotics and Automation (ICRA)