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Recently, large language models (LLMs) have achieved widespread application across various fields. Despite their impressive capabilities, LLMs suffer from a lack of structured reasoning ability, particularly for complex tasks requiring domain-specific best practices, which are often unavailable in the training data. Although multi-step prompting methods incorporating human best practices, such as chain-of-thought and tree-of-thought, have gained popularity, they lack a general mechanism to control LLM behavior. In this paper, we propose SHERPA, a model-driven framework to improve the LLM performance on complex tasks by explicitly incorporating domain-specific best practices into hierarchical state machines. By structuring the LLM execution processes using state machines, SHERPA enables more fine-grained control over their behavior via rules or decisions driven by machine learning-based approaches, including LLMs. We show that SHERPA is applicable to a wide variety of tasks-specifically, code generation, class name generation, and question answering-replicating previously proposed approaches while further improving the performance. We demonstrate the effectiveness of SHERPA for the

We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for training EBM, by replacing Markov Chain Monte Carlo (MCMC) distribution with a trainable sampler, such as a diffusion model. In GCD, the joint training of EBM and a diffusion model is formulated as a minimax problem, which reaches an equilibrium when both models converge to the data distribution. The minimax learning with GCD bears interesting equivalence to inverse reinforcement learning, where the energy corresponds to a negative reward, the diffusion model is a policy, and the real data is expert demonstrations. We present preliminary yet promising results showing that joint training is beneficial for both EBM and a diffusion model. GCD enables EBM training without MCMC while improving the sample quality of a diffusion model.

Dataset distillation reduces the network training cost by synthesizing small and informative datasets from large-scale ones. Despite the success of the recent dataset distillation algorithms, three drawbacks still limit their wider application: i). the synthetic images perform poorly on large architectures; ii). they need to be re-optimized when the distillation ratio changes; iii). the limited diversity restricts the performance when the distillation ratio is large. In this paper, we propose a novel distillation scheme to \textbf{D}istill information of large train sets \textbf{i}nto generative \textbf{M}odels, named DiM. Specifically, DiM learns to use a generative model to store the information of the target dataset. During the distillation phase, we minimize the differences in logits predicted by a models pool between real and generated images. At the deployment stage, the generative model synthesizes various training samples from random noises on the fly. Due to the simple yet effective designs, the trained DiM can be directly applied to different distillation ratios and large architectures without extra cost. We validate the proposed DiM across 4 datasets and achieve state-of

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity $v_{c}$ has been predicted, such that for pulling speeds $v>v_{c}$ it is the module at the pulled end that opens first, whereas for $v<v_{c}$ it is the weakest. Here, we introduce a variant of the model that is closer to the experimental setup, and discuss the robustness of the emergence of the critical velocity and of its dependence on the model parameters. We also propose a possible experiment to test the theoretical predictions of the model, which seems feasible with state-of-art molecular engineering techniques.

The dilute A_3 model is a solvable IRF (interaction-round-a-face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of a critical Ising model in a magnetic field. One therefore expects the scaling limit to be governed by Zamolodchikov's integrable perturbation of the c=1/2 conformal field theory. We perform a detailed numerical investigation of the solutions of the Bethe ansatz equation for the off-critical model. Our results agree perfectly with the predicted values for the lowest masses of the stable particles and support the assumptions on the nature of the Bethe ansatz solutions which enter crucially in a recent thermodynamic Bethe ansatz calculation of the factorized scattering matrix.

These lecture notes discuss several related features of the exactly solvable two-dimensional corner growth model with exponentially distributed weights. A key property of this model is the availability of a fairly explicit stationary version that possesses useful independence properties. With the help of couplings and estimates, we prove the existence of Busemann functions for this model, and the precise values of the longitudinal and transversal fluctuation exponents for the stationary corner growth model. The Busemann functions in turn furnish extremals for variational formulas that describe limiting shape functions.

The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling and analysis. In this paper we clarify relevant continuous macroscopic model equations that describe follower-leader interactions for a swarm where these two populations are fixed. We study the behaviour of the swarm over long and short time scales to shed light on the number of leaders needed to initiate swarm movement, according to the homogeneous or inhomogeneous nature of the interaction (alignment) kernel. The results indicate the crucial role played by the interaction kernel to model transient behaviour.

Quick commerce (q-commerce) is one of the fastest growing sectors in India. It provides informal employment to approximately 4,50,000 workers, and it is estimated to become a USD 200 Billion industry by 2026. A significant portion of this industry deals with perishable goods. (e.g. milk, dosa batter etc.) These are food items which are consumed relatively fresh by the consumers and therefore their order volume is high and repetitive even when the average basket size is relatively small. The fundamental challenge for the retailer is that, increasing selling price would hamper sales and would lead to unsold inventory. On the other hand setting a price less, would lead to forgoing of potential revenue. This paper attempts to propose a mathematical model which formalizes this dilemma. The problem statement is not only important for improving the unit economics of the perennially loss making quick commerce firms, but also would lead to a trickle-down effect in improving the conditions of the gig workers as observed in [4]. The sections below describe the mathematical formulation. The results from the simulation would be published in a follow-up study.

This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The investors are heterogeneous in that they have different beliefs about the stochastic supply. A momentum in the stock price arises from those agents who incorrectly underestimate the signal accuracy, dampening the initial price impact of the signal. A reversal in price occurs because the price reverts to the fundamental value in the long run. An extension of the model to multiple assets case predicts co-movement and lead-lag effect, in addition to cross-sectional momentum and reversal. The heterogeneous beliefs of investors about news demonstrate how the main predictability anomalies arise endogenously in a model of bounded rationality.