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If a model has some behavioral tendency, such as sycophancy or misalignment, and it is trained on its own outputs, will the tendency be amplified in the next generation of models? We study this question by training a series of models where each model is finetuned on data generated by its predecessor, and the initial model is seeded with some persona or belief. We test three settings: supervised finetuning (SFT) on instruct models, synthetic document finetuning (SDF) on base models, and direct preference optimization (DPO). In the SFT and SDF settings, traits mostly decay or remain constant so that further finetuning cycles do nothing. In rare cases when amplification occurs, it generally comes at the cost of coherence. In the DPO setting, trait amplification can reliably occur when a model is continually trained with a preference for its own outputs, but vanishes when models are reinitialized at each cycle. Overall, our results suggest that amplification most likely comes from continual post-training, and limiting this stage may be an effective defense. For non-RL finetuning, trait amplification is rare and very sensitive to data quantity, making it significantly less likely to occ

Translating C programs to safe Rust is challenging owing to significant differences in typing constraints, ownership, and borrowing rules. Interpreter programs are particularly important targets for such translation, as they often handle untrusted inputs and suffer from memory-related vulnerabilities. We present Reboot, a mostly-automatic technique that translates real-world interpreter programs from C to safe Rust. Using Reboot, we have translated six interpreters ranging from 6k to 23k lines of C code to safe Rust, with each translation requiring only 1 to 11 brief user interventions. All translations pass 100% of the provided test suites, and achieve 62%--92% pass rates on separately created validation tests that were never exposed to the system. A security case study on mujs shows that memory vulnerabilities such as heap buffer overflows and use-after-free present in C are eliminated in the safe Rust translation. Two ideas underpin Reboot. First, feature reduction decomposes the translation by program features, creating a sequence of milestones where each is a complete, testable program; the translation starts from the simplest version and incrementally restores features, with

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of (fully and partially) quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. One can perform $Z$ or entangling gates on trapped ions mostly quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Passive lasers control these gates, as well as the Rydberg-atom gates, quantum-autonomously. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical

We introduce the notion of \emph{mostly nonuniform sectional expanding} (MNUSE) for singular flows which encompasses the notions of sectional hyperbolicity, asymptotically sectional and multisingular hyperbolicity. We exhibit an example of a vector field of class $C^r, r > 1$, whose flow exhibits a nonuniformly sectional hyperbolic set satisfying MNUSE, which is neither sectional hyperbolic nor asymptotically sectional hyperbolic. We obtain sufficient conditions for the existence of physical/SRB measures for asymptotically sectionally hyperbolic attracting sets with any finite co-dimension, extending the co-dimension two case. We provide examples of such attractors, either with non-sectional hyperbolic equilibria, or with sectional-hyperbolic equilibria of mixed type, i.e., with a Lorenz-like singularity together with a Rovella-like singularity in a transitive set. These are higher-dimensional versions of contracting Lorenz-like attractors (also known as Rovella-like attractors) to which we apply our criteria to obtain a physical/SRB measure with full ergodic basin. We also adapt the previous examples to obtain higher co-dimensional (i.e. with central direction of dimension grea

The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We prove that for mostly expanding partially hyperbolic diffeomorphisms with minimal strong stable foliation and one-dimensional center bundle, there exists a $C^1$-open neighborhood of them, in which the topological entropy varies continuously and the intermediate entropy property holds. To prove that, we show that each non-hyperbolic ergodic measure is approached by horseshoes in entropy and in weak$*$-topology.

In recent years, the techniques of analytic combinatorics in several variables (ACSV) have been applied to determine asymptotics for several families of lattice path models restricted to the orthant $\mathbb{N}^d$ and defined by step sets $\mathcal{S}\subset\{-1,0,1\}^d\setminus\{\mathbf{0}\}$. Using the theory of ACSV for smooth singular sets, Melczer and Mishna determined asymptotics for the number of walks in any model whose set of steps $\mathcal{S}$ is "highly symmetric" (symmetric over every axis). Building on this work, Melczer and Wilson determined asymptotics for all models where $\mathcal{S}$ is "mostly symmetric" (symmetric over all but one axis) *except* for models whose set of steps have a vector sum of zero but are not highly symmetric. In this paper we complete the asymptotic classification of the mostly symmetric case by analyzing a family of saddle-point-like integrals whose amplitudes are singular near their saddle points.

Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also prove that the range of the function given by $β(G)=\frac{i(G)}{c(G)}$ is dense in $[0,1]$.

We consider a class of fast-slow $C^4$ partially hyperbolic systems on $\mathbb{T}^2$ given by $ε$-perturbations of maps $F(x,θ)=(f(x,θ),θ)$ where $f(\cdot,θ)$ are $C^{4}$ expanding maps of the circle. For sufficiently small $ε$ and an open set of perturbations we prove existence and uniqueness of a physical measure and exponential decay of correlations for sufficiently smooth observables with explicit almost optimal bounds on the decay rate. Our result complements previous work by De Simoi and Liverani, which studied the case of mostly contracting centre.

We study the complexity of learning $k$-mixtures of Gaussians ($k$-GMMs) on $\mathbb{R}^d$. This task is known to have complexity $d^{Ω(k)}$ in full generality. To circumvent this exponential lower bound on the number of components, research has focused on learning families of GMMs satisfying additional structural properties. A natural assumption posits that the component weights are not exponentially small and that the components have the same unknown covariance. Recent work gave a $d^{O(\log(1/w_{\min}))}$-time algorithm for this class of GMMs, where $w_{\min}$ is the minimum weight. Our first main result is a Statistical Query (SQ) lower bound showing that this quasi-polynomial upper bound is essentially best possible, even for the special case of uniform weights. Specifically, we show that it is SQ-hard to distinguish between such a mixture and the standard Gaussian. We further explore how the distribution of weights affects the complexity of this task. Our second main result is a quasi-polynomial upper bound for the aforementioned testing task when most of the weights are uniform while a small fraction of the weights are potentially arbitrary.

We study the long-term behavior of independent random iterations of Lipschitz transformations on a compact metric space. Such a random map is said to be mostly contracting if all Lyapunov exponents associated with stationary measures are negative. This requires introducing the notion of (maximal) Lyapunov exponent in this general context of Lipschitz transformations on compact metric spaces. We show that this class is open with respect to the appropriate topology and satisfies the strong law of large numbers for non-uniquely ergodic systems, the limit theorem for the law of random iterations, Palis' global conjecture, and that the associated annealed Koopman operator is quasi-compact. This implies many statistical properties such as central limit theorems, large deviations, statistical stability, and the continuity and Hölder continuity of Lyapunov exponents. Examples from this class of random maps include random products of circle diffeomorphisms, interval diffeomorphisms onto their images, and diffeomorphisms of a Cantor set on a line, all considered under the assumption of no common invariant measure. This class also includes projective actions of locally constant linear cocycle

By using the variational approach, we prove the existence of Sinai-Ruelle-Bowen measures for partially hyperbolic $\mathcal C^1$ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting $E\oplus F$, where $\dim E=1$ and $F$ is mostly expanding. When the diffeomorphisms are $\mathcal C^{1+α}$, we prove the basin covering property for both cases.

For the heterochaos baker maps whose central direction is mostly neutral, we prove that correlations for Hölder continuous functions decay at an optimal polynomial rate of order $n^{-3/2}$. Our method of proof relies on a description of the action of a reduced Perron-Frobenius operator by means of a comparison to the symmetric simple random walk with an absorbing wall, aka `gambler's ruin problem'.

Quantum signal processing (QSP) and its extensions are increasingly popular frameworks for developing quantum algorithms. Yet QSP implementations still struggle to complete a classical pre-processing step ('QSP-processing') that determines the set of $SU(2)$ rotation matrices defining the QSP circuit. We introduce a method of QSP-processing for complex polynomials that identifies a solution without optimization or root-finding and verify the success of our methods with polynomials characterized by floating point precision coefficients. We demonstrate the success of our technique for relevant target polynomials and precision regimes, including the Jacobi-Anger expansion used in QSP Hamiltonian Simulation. For popular choices of sign and inverse function approximations, we characterize regimes where all known QSP-processing methods should be expected to struggle without arbitrary precision arithmetic.

We study two and three-point tree-level amplitudes of open strings. These amplitudes are reduced from higher-point correlation functions by using mostly BRST exact operators for gauge fixing. For simplicity, we focus on an open string tachyon. The two-point amplitude of open string tachyons is reduced from a three-point function of two tachyon vertex operators and one mostly BRST exact operator. Similarly the three-point amplitude is from a four-point function of three tachyon vertex operators and one mostly BRST exact operator. One can also obtain the two-point amplitude from the four-point function of two tachyon vertex operators and two mostly BRST exact operators. In these derivation from four-point functions, moduli integrals are significant. We discuss the overall signs of amplitudes which are indefinite in this formalism.

In this paper we study physical measures for $\C^{1+α}$ partially hyperbolic diffeomorphisms with mostly expanding center. We show that every diffeomorphism with mostly expanding center direction exhibits a geometrical-combinatorial structure, which we call skeleton, that determines the number, basins and supports of the physical measures. Furthermore, the skeleton allows us to describe how physical measures bifurcate as the diffeomorphism changes under $C^1$ topology. Moreover, for each diffeomorphism with mostly expanding center, there exists a $C^1$ neighborhood, such that diffeomorphism among a $C^1$ residual subset of this neighborhood admits finitely many physical measures, whose basins have full volume. We also show that the physical measures for diffeomorphisms with mostly expanding center satisfy exponentially decay of correlation for any Hölder observes.

In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In this article we move beyond dimer covers to trimer covers, introducing plane regions called benzels that play a role analogous to hexagons for rhombus tilings and Aztec diamonds for domino tilings, inasmuch as one finds many (so far mostly conjectural) exact formulas governing the number of tilings.

A careful gauge fixing of the conformal killing group (CKG) on genus zero surfaces in bosonic string theory gives non-vanishing two point amplitudes that match the corresponding field theory expressions arXiv:1906.06051, arXiv:1909.03672 . An important ingredient for gauge fixing two point amplitudes in arXiv:1909.03672 was the mostly BRST (mBRST) exact operator. The utility of this operator in gauge fixing CKG perhaps is not just limited to two point amplitudes - we can insert a mBRST exact operator to fix a conformal killing vector (CKV) instead of fixing the position of a vertex operator in a general tree level bosonic string amplitude arXiv:2108.05628, arXiv:2109.08433. Using the mBRST exact operator, written in the pure spinor variables, we get the expected two point superstring amplitudes arXiv:2012.03802. In this work we explore if it is possible to use this operator for fixing CKG for general tree level amplitudes in superstrings. We find it to be the case by explicitly re-calculating the three gluon amplitude in open strings by making use of this operator. Finally, we show that this operator directly emerges by following a Faddeev-Popov gauge fixing method in bosonic strin

The ACME Spectra project provides absolutely calibrated, mostly empirical spectra of exoplanet host stars for use in analysis of the stars and their planets. Spectra are obtained from ground-based telescopes and are tied directly to calibrated ground- and space-based photometry. The spectra remain only "mostly" empirical because of telluric absorption, but interpolation of stellar models over the gaps in wavelength coverage provides continuous stellar spectra. Among other uses, the spectra are suitable for precisely converting observed secondary eclipses (occultations) into absolute flux units with minimal recourse to models. In this letter I introduce ACME's methods and present a calibrated spectrum of the nearby, super-Earth hosting star 55 Cancri that spans the range from 0.81-5.05 micron. This spectrum is well-suited for interpreting near- and thermal-infrared eclipse observations. With this spectrum I show that the brightness temperature of the small, low-mass transiting planet 55 Cnc e is 1950 +260/-190 K at 4.5 micron (cooler than previously reported), which corresponds to a planetary flux of 0.44 +0.12/-0.08 mJy. This result suggests the planet has some combination of a non

In this work we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such class is $C^r$-open, $r>1$, among the partially hyperbolic diffeomorphisms (in the narrow sense) and we prove that the mostly expanding condition guarantee the existence of physical measures and provide more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on $\mathbb{T}^3$ belongs to this set.