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Current-induced spin generations are of significant importance for electrically controllable magnetization. Due to symmetry constraints, linear spin generation is absent in centrosymmetric magnets and nonlinear contributions become crucial. However, nonlinear spin generations have few examples in centrosymmetric compensated magnets with opposite-spin sublattices, which hinders electric control of associated magnetization. Here, we study nonlinear spin generations in altermagnets with opposite-spin sublattices. In a square altermagnetic model, both staggered and uniform nonlinear spin generations appear at opposite-spin sublattices. They vary as the magnetization direction rotates, with emerging out-of-plane components that can be utilized in perpendicular magnetization switching of high-density storage devices. By first-principles calculations, out-of-plane, staggered nonlinear spin generations are found to be considerable in a typical altermagnet, Fe$_2$Se$_2$O monolayer. Our findings provide opportunities for electrically manipulating magnetization and designing energy-efficient magnetic devices based on compensated magnets.

Language models (LMs) may lead their users to make suboptimal downstream decisions when they confidently hallucinate. This issue can be mitigated by having the LM verbally convey the probability that its claims are correct, but existing models cannot produce long-form text with calibrated confidence statements. Through the lens of decision-making, we define linguistic calibration for long-form generations: an LM is linguistically calibrated if its generations enable its users to make calibrated probabilistic predictions. This definition enables a training framework where a supervised finetuning step bootstraps an LM to emit long-form generations with confidence statements such as "I estimate a 30% chance of..." or "I am certain that...", followed by a reinforcement learning step which rewards generations that enable a user to provide calibrated answers to related questions. We linguistically calibrate Llama 2 7B and find in automated and human evaluations of long-form generations that it is significantly more calibrated than strong finetuned factuality baselines with comparable accuracy. These findings generalize under significant domain shifts to scientific and biomedical question

We develop an overlapping generations model where each agent observes a verifiable private signal about the state and, with positive probability, also receives signals disclosed by his predecessor. The agent then takes an action and decides which signals to pass on. Each agent's action has a positive externality on his predecessor and his optimal action increases in his belief about the state. We show that as the probability that messages reach the next generation approaches one, agents become increasingly selective in disclosing information. In the limit, all signals except for the most favorable ones will be concealed.

In open-ended generative tasks like narrative writing or dialogue, large language models often exhibit cultural biases, showing limited knowledge and generating templated outputs for less prevalent cultures. Recent works show that these biases may stem from uneven cultural representation in pretraining corpora. This work investigates how pretraining leads to biased culture-conditioned generations by analyzing how models associate entities with cultures based on pretraining data patterns. We propose the MEMOed framework (MEMOrization from pretraining document) to determine whether a generation for a culture arises from memorization. Using MEMOed on culture-conditioned generations about food and clothing for 110 cultures, we find that high-frequency cultures in pretraining data yield more generations with memorized symbols, while some low-frequency cultures produce none. Additionally, the model favors generating entities with extraordinarily high frequency regardless of the conditioned culture, reflecting biases toward frequent pretraining terms irrespective of relevance. We hope that the MEMOed framework and our insights will inspire more works on attributing model performance on pr

Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8%-5.1%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 39% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

As the demand for high-quality training data escalates, researchers have increasingly turned to generative models to create synthetic data, addressing data scarcity and enabling continuous model improvement. However, reliance on self-generated data introduces a critical question: Will this practice amplify bias in future models? While most research has focused on overall performance, the impact on model bias, particularly subgroup bias, remains underexplored. In this work, we investigate the effects of the generated data on image classification tasks, with a specific focus on bias. We develop a practical simulation environment that integrates a self-consuming loop, where the generative model and classification model are trained synergistically. Hundreds of experiments are conducted on Colorized MNIST, CIFAR-20/100, and Hard ImageNet datasets to reveal changes in fairness metrics across generations. In addition, we provide a conjecture to explain the bias dynamics when training models on continuously augmented datasets across generations. Our findings contribute to the ongoing debate on the implications of synthetic data for fairness in real-world applications.

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

Large Language Models (LLMs) can exhibit considerable variation in the quality of their sampled outputs. Reranking and selecting the best generation from the sampled set is a popular way of obtaining strong gains in generation quality. In this paper, we present a novel approach for reranking LLM generations. Unlike other techniques that might involve additional inferences or training a specialized reranker, our approach relies on easy to compute pairwise statistics between the generations that have minimal compute overhead. We show that our approach can be formalized as an extension of self-consistency and analyze its performance in that framework, theoretically as well as via simulations. We show strong improvements for selecting the best k generations for code generation tasks as well as robust improvements for the best generation for the tasks of autoformalization, summarization, and translation. While our approach only assumes black-box access to LLMs, we show that additional access to token probabilities can improve performance even further.

We investigate high-order harmonic generations (HHGs) under the comparison of Weyl cones in two types. Due to the hyperboloidal electron pocket structure, strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at frequency zero. Such remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition. Under weak pulse electric field , the linear optical response of a non-tilted Weyl cone is consistent with the Kubo theory. With more numerical simulations, we conclude the non-zero chemical potential can enhance the even-order generations, from the slightly tilted system to the over-tilted systems. In consideration of dynamical symmetries, type-I and -II Weyl cones also show different selective responses under the circularly polarized light. Finally, using a more realistic model containing two pairs of Weyl points, we demonstrate the paired Weyl points with opposite chirality could suppress the overall even-order generations.

It is shown that additional chiral generations are not excluded by the latest electroweak precision data if one assumes that there is no mixing with the known three generations. In the case of ``heavy extra generations'', when all four new particles are heavier than $Z$ boson, quality of the fit for the one new generation is as good as for zero new generations (Standard Model). In the case of neutral leptons with masses around 50 GeV (``partially heavy extra generations'') the minimum of $χ^2$ is between one and two extra generations.

By adopting empirical estimates of the Helium enhancement (Delta Y) between consecutive stellar generations for a sample of Galactic globular clusters (GGC), we uniquely constraint the star formation efficiency of each stellar generation in these stellar systems. In our approach, the star formation efficiency is the central factor that links stellar generations as it defines both their stellar mass and the remaining mass available for further star formation, fixing also the amount of matter required to contaminate the next stellar generation. In this way, the star formation efficiency is here shown to be fully defined by the He enhancement between successive stellar generations in a GC. Our approach has also an impact on the evolution of clusters and thus considers the possible loss of stars through evaporation, tidal interactions and stellar evolution. We focus on the present mass ratio between consecutive stellar generations and the present total mass of Galactic globular clusters. Such considerations suffice to determine the relative proportion of stars of consecutive generations that remain today in globular clusters. The latter is also shown to directly depend on the values of

Possible existence of "hot-sector generations" above the well known 3 generation bound is investigated on the basis of a model of leptons and quarks, which is based on the Harari and Shupe's one. Our model predicts the existence of {\bf3 + 1} generations above the ordinary "cold-sector" 3 generations. Majorana neutrinos are introduced to realize the heavy neutrino masses in hot-sector generations. Properties of heavy neutrinos are also discussed.

Coding over subsets (known as generations) rather than over all content blocks in P2P distribution networks and other applications is necessary for a number of practical reasons such as computational complexity. A penalty for coding only within generations is an overall throughput reduction. It has been previously shown that allowing contiguous generations to overlap in a head-to-toe manner improves the throughput. We here propose and study a scheme, referred to as the {\it random annex code}, that creates shared packets between any two generations at random rather than only the neighboring ones. By optimizing very few design parameters, we obtain a simple scheme that outperforms both the non-overlapping and the head-to-toe overlapping schemes of comparable computational complexity, both in the expected throughput and in the rate of convergence of the probability of decoding failure to zero. We provide a practical algorithm for accurate analysis of the expected throughput of the random annex code for finite-length information. This algorithm enables us to quantify the throughput vs.computational complexity tradeoff, which is necessary for optimal selection of the scheme parameters.

We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety for multiple generations of Standard Model matter and Higgs doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric signatures which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for right-handed neutrinos. We speculate as to why three generations is special.

The data from collider experiments and cosmic observatories indicates the existence of three light matter generations. In some classes of string compactifications the number of generations is related to a topological quantity, the Euler characteristic. However, these do not explain the existence of three generations. In a class of free fermionic string models, related to the Z2 X Z2 orbifold compactification, the existence of three generations is correlated with the existence of three twisted sectors in this class of compactifications. However, the three generation models are constructed in the free fermionic formulation and their geometrical correspondence is not readily available. In this paper we classify quotients of the Z2 X Z2 orbifold by additional symmetric shifts on the three complex tori. We show that three generation vacua are not obtained in this manner, indicating that the geometrical structures underlying the free fermionic models are more esoteric.

New dynamical mechanism of quark mass generations and mixing is demonstrated in the examples of three and four generations. In the framework of the new mixing pattern, called the coherent mixing, the CKM elements are predicted compatible with experimental data for three generations, and are strongly constrained for four generations.

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms of several generations of such processes. Applications of our main result include a functional central limit theorem (CLT), a Darling-Erdös result, and an extremal process result. The limiting process for our functional CLT is an infinite dimensional Brownian motion with sample paths in the infinite product space $(C_0[0,1])^{\infty}$, with the product topology, or in Banach subspaces of $(C_0[0,1])^{\infty}$ determined by norms related to the distribution of the population size of the branching process. As an application of this CLT we obtain a central limit theorem for ratios of weighted sums of generations of a branching processes, and also to various maximums of these generations. The Darling-Erdös result and the application to extremal distributions also include infinite dimensional limit laws. Some branching process examples where the CLT fails are also included.

Let $(ξ_k,η_k)_{k\in\mathbb{N}}$ be independent identically distributed random vectors with arbitrarily dependent positive components. We call a (globally) perturbed random walk a random sequence $(T_k)_{k\in\mathbb{N}}$ defined by $T_k:=ξ_1+\cdots+ξ_{k-1}+η_k$ for $k\in\mathbb{N}$. Further, by an iterated perturbed random walk is meant the sequence of point processes defining the birth times of individuals in subsequent generations of a general branching process provided that the birth times of the first generation individuals are given by a perturbed random walk. For $j\in\mathbb{N}$ and $t\geq 0$, denote by $N_j(t)$ the number of the $j$th generation individuals with birth times $\leq t$. In this article we prove counterparts of the classical renewal-theoretic results (the elementary renewal theorem, Blackwell's theorem and the key renewal theorem) for $N_j(t)$ under the assumption that $j=j(t)\to\infty$ and $j(t)=o(t^{2/3})$ as $t\to\infty$. According to our terminology, such generations form a subset of the set of intermediate generations.

We propose a model of generations that has exactly three generations. This model has several attractive features: There is a simple mechanism to produce the CKM quark mixings and their neutrino analogs. There are definite predictions for particles of much higher mass than the quarks and leptons of the standard model, including the prediction of two-body decays without missing mass for the higher mass particles. There is a natural dark matter particle. A discussion of masses of the quarks suggests that the large mass differences between the generations could have a qualitative explanation, and there could be a simple way to make the $u$-$d$ mass difference negative, but the $c$-$s$ and $t$-$b$ mass differences positive. The model also suggests a completely new scenario for the production, mass and decays of the Higgs meson that will be analysed in a separate paper.