Optimal Allocation of Pauli Measurements for Low-rank Quantum State Tomography

The process of reconstructing quantum states from experimental measurements, accomplished through quantum state tomography (QST), plays a crucial role in verifying and benchmarking quantum devices. A key challenge of QST is to find out how the accuracy of the reconstruction depends on the number of state copies used in the measurements. When multiple measurement settings are used, the total number of state copies is determined by multiplying the number of measurement settings with the number of repeated measurements for each setting. Due to statistical noise intrinsic to quantum measurements, a large number of repeated measurements is often used in practice. However, recent studies have shown that even with single-sample measurements--where only one measurement sample is obtained for each measurement setting--high accuracy QST can still be achieved with a sufficiently large number of different measurement settings. In this paper, we establish a theoretical understanding of the trade-off between the number of measurement settings and the number of repeated measurements per setting in QST. Our focus is primarily on low-rank density matrix recovery using Pauli measurements. We delve into the global landscape underlying the low-rank QST problem and demonstrate that the joint consideration of measurement settings and repeated measurements ensures a bounded recovery error for all second-order critical points, to which optimization algorithms tend to converge. This finding suggests the advantage of minimizing the number of repeated measurements per setting when the total number of state copies is held fixed. Additionally, we prove that the Wirtinger gradient descent algorithm can converge to the region of second-order critical points with a linear convergence rate. We have also performed numerical experiments to support our theoretical findings.

Robust Low-rank Tensor Train Recovery

Tensor train (TT) decomposition represents an $N$-order tensor using $O(N)$ matrices (i.e., factors) of small dimensions, achieved through products among these factors. Due to its compact representation, TT decomposition has found wide applications, including various tensor recovery problems in signal processing and quantum information. In this paper, we study the problem of reconstructing a TT format tensor from measurements that are contaminated by outliers with arbitrary values. Given the vulnerability of smooth formulations to corruptions, we use an $\ell_1$ loss function to enhance robustness against outliers. We first establish the $\ell_1/\ell_2$-restricted isometry property (RIP) for Gaussian measurement operators, demonstrating that the information in the TT format tensor can be preserved using a number of measurements that grows linearly with $N$. We also prove the sharpness property for the $\ell_1$ loss function optimized over TT format tensors. Building on the $\ell_1/\ell_2$-RIP and sharpness property, we then propose two complementary methods to recover the TT format tensor from the corrupted measurements: the projected subgradient method (PSubGM), which optimizes over the entire tensor, and the factorized Riemannian subgradient method (FRSubGM), which optimizes directly over the factors. Compared to PSubGM, the factorized approach FRSubGM significantly reduces the memory cost at the expense of a slightly slower convergence rate. Nevertheless, we show that both methods, with diminishing step sizes, converge linearly to the ground-truth tensor given an appropriate initialization, which can be obtained by a truncated spectral method.

Federated Data-Efficient Instruction Tuning for Large Language Models

Instruction tuning helps improve pretrained large language models (LLMs) in terms of the responsiveness to human instructions, which is benefited from diversified instruction data. Federated learning extends the sources of instruction data by exploiting the diversified client-side data, making it increasingly popular for tuning LLMs. Existing approaches of federated LLM tuning typically traverse all local data during local training, bringing excessive computation overhead and posing a risk of overfitting local data. Thus, a federated data-efficient instruction tuning approach, which consumes relatively little data from the entire dataset, is needed. In response, this work introduces an approach of federated data-efficient instruction tuning for LLMs, FedHDS, which utilizes a representative subset of edge-side data, coreset, to tune the LLM. It reduces the redundancy of data samples at both intra-client and inter-client levels through a hierarchical data selection framework performed by jointly selecting a small number of representative data samples for local training without sharing the raw data. Extensive experiments conducted across six scenarios with various LLMs, datasets and data partitions demonstrate that FedHDS significantly reduces the amount of data required for fine-tuning while improving the responsiveness of the instruction-tuned LLMs to unseen tasks.

Integrating Planning into Single-Turn Long-Form Text Generation

Generating high-quality, in-depth textual documents, such as academic papers, news articles, Wikipedia entries, and books, remains a significant challenge for Large Language Models (LLMs). In this paper, we propose to use planning to generate long form content. To achieve our goal, we generate intermediate steps via an auxiliary task that teaches the LLM to plan, reason and structure before generating the final text. Our main novelty lies in a single auxiliary task that does not require multiple rounds of prompting or planning. To overcome the scarcity of training data for these intermediate steps, we leverage LLMs to generate synthetic intermediate writing data such as outlines, key information and summaries from existing full articles. Our experiments demonstrate on two datasets from different domains, namely the scientific news dataset SciNews and Wikipedia datasets in KILT-Wiki and FreshWiki, that LLMs fine-tuned with the auxiliary task generate higher quality documents. We observed +2.5% improvement in ROUGE-Lsum, and a strong 3.60 overall win/loss ratio via human SxS evaluation, with clear wins in organization, relevance, and verifiability.

Inference Scaling for Long-Context Retrieval Augmented Generation

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring strategies beyond simply increasing the quantity of knowledge. We focus on two inference scaling strategies: in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs' ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

Sample-Optimal Quantum State Tomography for Structured Quantum States in One Dimension

Quantum state tomography (QST) remains the gold standard for benchmarking and verifying quantum devices. A recent study has proved that, with Haar random projective measurements, only a $O(n^3)$ number of state copies is required to guarantee bounded recovery error of an matrix product operator (MPO) state of qubits $n$. While this result provides a formal evidence that quantum states with an efficient classical representation can be reconstructed with an efficient number of state copies, the number of state copies required is still significantly larger than the number of independent parameters in the classical representation. In this paper, we attempt to narrow this gap and study whether the number of state copies can saturate the information theoretic bound (i.e., $O(n)$, the number of parameters in the MPOs) using physical quantum measurements. We answer this question affirmatively by using a class of Informationally Complete Positive Operator-Valued Measures (IC-POVMs), including symmetric IC-POVMs (SIC-POVMs) and spherical $t$-designs. For SIC-POVMs and (approximate) spherical 2-designs, we show that the number of state copies to guarantee bounded recovery error of an MPO state with a constrained least-squares estimator depends on the probability distribution of the MPO under the POVM but scales only linearly with $n$ when the distribution is approximately uniform. For spherical $t$-designs with $t\ge3$, we prove that only a number of state copies proportional to the number of independent parameters in the MPO is needed for a guaranteed recovery of any state represented by an MPO. Moreover, we propose a projected gradient descent (PGD) algorithm to solve the constrained least-squares problem and show that it can efficiently find an estimate with bounded recovery error when appropriately initialized.

Building Math Agents with Multi-Turn Iterative Preference Learning

Recent studies have shown that large language models' (LLMs) mathematical problem-solving capabilities can be enhanced by integrating external tools, such as code interpreters, and employing multi-turn Chain-of-Thought (CoT) reasoning. While current methods focus on synthetic data generation and Supervised Fine-Tuning (SFT), this paper studies the complementary direct preference learning approach to further improve model performance. However, existing direct preference learning algorithms are originally designed for the single-turn chat task, and do not fully address the complexities of multi-turn reasoning and external tool integration required for tool-integrated mathematical reasoning tasks. To fill in this gap, we introduce a multi-turn direct preference learning framework, tailored for this context, that leverages feedback from code interpreters and optimizes trajectory-level preferences. This framework includes multi-turn DPO and multi-turn KTO as specific implementations. The effectiveness of our framework is validated through training of various language models using an augmented prompt set from the GSM8K and MATH datasets. Our results demonstrate substantial improvements: a supervised fine-tuned Gemma-1.1-it-7B model's performance increased from 77.5% to 83.9% on GSM8K and from 46.1% to 51.2% on MATH. Similarly, a Gemma-2-it-9B model improved from 84.1% to 86.3% on GSM8K and from 51.0% to 54.5% on MATH.

LAMPO: Large Language Models as Preference Machines for Few-shot Ordinal Classification

We introduce LAMPO, a novel paradigm that leverages Large Language Models (LLMs) for solving few-shot multi-class ordinal classification tasks. Unlike conventional methods, which concatenate all demonstration examples with the test instance and prompt LLMs to produce the pointwise prediction, our framework uses the LLM as a preference machine that makes a relative comparative decision between the test instance and each demonstration. A self-supervised method is then introduced to aggregate these binary comparisons into the final ordinal decision. LAMPO addresses several limitations inherent in previous methods, including context length constraints, ordering biases, and challenges associated with absolute point-wise estimation. Extensive experiments on seven public datasets demonstrate LAMPO's remarkably competitive performance across a diverse spectrum of applications (e.g., movie review analysis and hate speech detection). Notably, in certain applications, the improvement can be substantial, exceeding 20% in an absolute term. Moreover, we believe LAMPO represents an interesting addition to the non-parametric application layered on top of LLMs, as it supports black-box LLMs without necessitating the outputting of LLM's internal states (e.g., embeddings), as seen in previous approaches.

Multilingual Fine-Grained News Headline Hallucination Detection

The popularity of automated news headline generation has surged with advancements in pre-trained language models. However, these models often suffer from the ``hallucination'' problem, where the generated headline is not fully supported by its source article. Efforts to address this issue have predominantly focused on English, using over-simplistic classification schemes that overlook nuanced hallucination types. In this study, we introduce the first multilingual, fine-grained news headline hallucination detection dataset that contains over 11 thousand pairs in 5 languages, each annotated with detailed hallucination types by experts. We conduct extensive experiments on this dataset under two settings. First, we implement several supervised fine-tuning approaches as preparatory solutions and demonstrate this dataset's challenges and utilities. Second, we test various large language models' in-context learning abilities and propose two novel techniques, language-dependent demonstration selection and coarse-to-fine prompting, to boost the few-shot hallucination detection performance in terms of the example-F1 metric. We release this dataset to foster further research in multilingual, fine-grained headline hallucination detection.

Boosting Reward Model with Preference-Conditional Multi-Aspect Synthetic Data Generation

Reward models (RMs) are crucial for aligning large language models (LLMs) with human preferences. They are trained using preference datasets where each example consists of one input prompt, two responses, and a preference label. As curating a high-quality human labeled preference dataset is both time-consuming and expensive, people often rely on existing powerful LLMs for preference label generation. This can potentially introduce noise and impede RM training. In this work, we present RMBoost, a novel synthetic preference data generation paradigm to boost reward model quality. Unlike traditional methods, which generate two responses before obtaining the preference label, RMBoost first generates one response and selects a preference label, followed by generating the second more (or less) preferred response conditioned on the pre-selected preference label and the first response. This approach offers two main advantages. First, RMBoost reduces labeling noise since preference pairs are constructed intentionally. Second, RMBoost facilitates the creation of more diverse responses by incorporating various quality aspects (e.g., helpfulness, relevance, completeness) into the prompts. We conduct extensive experiments across three diverse datasets and demonstrate that RMBoost outperforms other synthetic preference data generation techniques and significantly boosts the performance of four distinct reward models.