arXiv subjects

Aaron Chan

Publications and source records attributed to Aaron Chan.

At least 37 records · Page 2Linked to original sources

arXiv2024

Unconventional Magnetic Oscillations in Kagome Mott Insulators

In metals, electrons in a magnetic field undergo cyclotron motion, leading to oscillations in physical properties called quantum oscillations. This phenomenon has never been seen in a robust insulator because there are no mobile electrons. We report the first exception to this rule. We study a Mott insulator on a kagome lattice which does not order magnetically down to milli-Kelvin temperatures despite antiferromagnetic interactions. We observe a plateau at magnetization equal to 1/9 Bohr magneton per magnetic ion, accompanied by oscillations in the magnetic torque, reminiscent of quantum oscillations in metals. The temperature dependence obeys Fermi distribution. These phenomena are consistent with a quantum spin liquid state whose excitations are fermionic spinons with a Dirac-like spectrum coupled to an emergent gauge field.

cond-mat.str-el↗

arXiv2024

Field tunable BKT and quantum phase transitions in spin-1/2 triangular lattice antiferromagnet

Quantum magnetism is one of the most active fields for exploring exotic phases and phase transitions. The recently synthesized Na2BaCo(PO4)2 (NBCP) is an ideal material incarnation of the spin-1/2 easy axis triangular lattice antiferromagnet (TLAF). Experimental evidence shows that NBCP hosts the spin supersolid state with a giant magnetocaloric effect. It was also proposed that the applied magnetic field B can drive the system through Berezinskii-Kosterlitz-Thouless (BKT) and other richer quantum phase transitions. However, the detection of these transitions is challenging because they onset at extremely low temperature T at around 60 mK, and the measurement of the magnetic susceptibility of these transitions requires high sensitivity. With the help of our newly developed gradient force magnetometer in a dilution refrigerator, we constructed the contour diagram of the magnetic susceptibility in the B-T phase diagram in T as cold as 30 mK. These results provide a more comprehensive and accurate understanding of the several field-tunable quantum phase transitions and BKT melting of the spin supersolidity, which are especially significant when their giant magnetocaloric effects highlight potential applications for sub-Kelvin refrigeration under concerns about global helium shortages.

cond-mat.str-el↗

arXiv2024

Auslander-Reiten's Cohen-Macaulay algebras and contracted preprojective algebras

Auslander and Reiten called a finite dimensional algebra $A$ over a field Cohen-Macaulay if there is an $A$-bimodule $W$ which gives an equivalence between the category of finitely generated $A$-modules of finite projective dimension and the category of finitely generated $A$-modules of finite injective dimension. For example, Iwanaga-Gorenstein algebras and algebras with finitistic dimension zero on both sides are Cohen-Macaulay, and tensor products of Cohen-Macaulay algebras are again Cohen-Macaulay. They seem to be all of the known examples of Cohen-Macaulay algebras. In this paper, we give the first non-trivial class of Cohen-Macaulay algebras by showing that all contracted preprojective algebras of Dynkin type are Cohen-Macaulay. As a consequence, for each simple singularity $R$ and a maximal Cohen-Macaulay $R$-module $M$, the stable endomorphism algebra $\underline{End}_R(M)$ is Cohen-Macaulay. We also give a negative answer to a question of Auslander-Reiten asking whether the category $CM A$ of Cohen-Macaulay $A$-modules coincides with the category of $d$-th syzygies, where $d\ge1$ is the injective dimension of $W$. In fact, if $A$ is a Cohen-Macaulay algebra that is additionally $d$-Gorenstein in the sense of Auslander, then $CM A$ always coincides with the category of $d$-th syzygies.

math.RT↗

arXiv2024

Large Oscillatory Thermal Hall Effect in Kagome Metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

cond-mat.str-el↗

arXiv2024

Quantum Oscillations Evidence for Topological Bands in Kagome Metal ScV6Sn6

Metals with kagome lattice provide bulk materials to host both the flat-band and Dirac electronic dispersions. A new family of kagome metals is recently discovered in AV6Sn6. The Dirac electronic structures of this material need more experimental evidence to confirm. In the manuscript, we investigate this problem by resolving the quantum oscillations in both electrical transport and magnetization in ScV6Sn6. The revealed orbits are consistent with the electronic band structure models. Furthermore, the Berry phase of a dominating orbit is revealed to be around $π$, providing direct evidence for the topological band structure, which is consistent with calculations. Our results demonstrate a rich physics and shed light on the correlated topological ground state of this kagome metal.

cond-mat.str-el↗

arXiv2024

Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet

The spin-1/2 kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the report of 1/9 magnetization plateau and magnetic oscillations in a kagome antiferromagnet YCu$_3$(OH)$_6$Br$_2$[Br$_x$(OH)$_{1-x}$] (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 Tesla) down to 0.46 Kelvin, and the 1/9 plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of 1/9 plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states (DOS) contributed by other Fermi surfaces. Surprisingly the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near $30$~T above the 1/9 plateau which is another hallmark of fermionic excitations in the specific heat.

cond-mat.str-el↗

arXiv2024

Tailoring Self-Rationalizers with Multi-Reward Distillation

Large language models (LMs) are capable of generating free-text rationales to aid question answering. However, prior work 1) suggests that useful self-rationalization is emergent only at significant scales (e.g., 175B parameter GPT-3); and 2) focuses largely on downstream performance, ignoring the semantics of the rationales themselves, e.g., are they faithful, true, and helpful for humans? In this work, we enable small-scale LMs (approx. 200x smaller than GPT-3) to generate rationales that not only improve downstream task performance, but are also more plausible, consistent, and diverse, assessed both by automatic and human evaluation. Our method, MaRio (Multi-rewArd RatIOnalization), is a multi-reward conditioned self-rationalization algorithm that optimizes multiple distinct properties like plausibility, diversity and consistency. Results on five difficult question-answering datasets StrategyQA, QuaRel, OpenBookQA, NumerSense and QASC show that not only does MaRio improve task accuracy, but it also improves the self-rationalization quality of small LMs across the aforementioned axes better than a supervised fine-tuning (SFT) baseline. Extensive human evaluations confirm that MaRio rationales are preferred vs. SFT rationales, as well as qualitative improvements in plausibility and consistency.

cs.CL↗

arXiv2024

Resprompt: Residual Connection Prompting Advances Multi-Step Reasoning in Large Language Models

Chain-of-thought (CoT) prompting, which offers step-by-step problem-solving rationales, has impressively unlocked the reasoning potential of large language models (LLMs). Yet, the standard CoT is less effective in problems demanding multiple reasoning steps. This limitation arises from the complex reasoning process in multi-step problems: later stages often depend on the results of several steps earlier, not just the results of the immediately preceding step. Such complexities suggest the reasoning process is naturally represented as a graph. The almost linear and straightforward structure of CoT prompting, however, struggles to capture this complex reasoning graph. To address this challenge, we propose Residual Connection Prompting (RESPROMPT), a new prompting strategy that advances multi-step reasoning in LLMs. Our key idea is to reconstruct the reasoning graph within prompts. We achieve this by integrating necessary connections-links present in the reasoning graph but missing in the linear CoT flow-into the prompts. Termed "residual connections", these links are pivotal in morphing the linear CoT structure into a graph representation, effectively capturing the complex reasoning graphs inherent in multi-step problems. We evaluate RESPROMPT on six benchmarks across three diverse domains: math, sequential, and commonsense reasoning. For the open-sourced LLaMA family of models, RESPROMPT yields a significant average reasoning accuracy improvement of 12.5% on LLaMA-65B and 6.8% on LLaMA2-70B. Breakdown analysis further highlights RESPROMPT particularly excels in complex multi-step reasoning: for questions demanding at least five reasoning steps, RESPROMPT outperforms the best CoT based benchmarks by a remarkable average improvement of 21.1% on LLaMA-65B and 14.3% on LLaMA2-70B. Through extensive ablation studies and analyses, we pinpoint how to most effectively build residual connections.

cs.CL↗

arXiv2024

Periodic trivial extension algebras and fractionally Calabi-Yau algebras

We study periodicity and twisted periodicity of the trivial extension algebra $T(A)$ of a finite-dimensional algebra $A$. Our main results show that (twisted) periodicity of $T(A)$ is equivalent to $A$ being (twisted) fractionally Calabi-Yau of finite global dimension. We also extend this result to a large class of self-injective orbit algebras. As a significant consequence, these results give a partial answer to the periodicity conjecture of Erdmann-Skowroński, which expects the classes of periodic and twisted periodic algebras to coincide. On the practical side, it allows us to construct a large number of new examples of periodic algebras and fractionally Calabi-Yau algebras. We also establish a connection between periodicity and cluster tilting theory, by showing that twisted periodicity of $T(A)$ is equivalent the $d$-representation-finiteness of the $r$-fold trivial extension algebra $T_r(A)$ for some $r,d\ge 1$. This answers a question by Darpö and Iyama. As applications of our results, we give answers to some other open questions. We construct periodic symmetric algebras of wild representation type with arbitrary large minimal period, answering a question by Skowroński. We also show that the class of twisted fractionally Calabi-Yau algebras is closed under derived equivalence, answering a question by Herschend and Iyama.

math.RT↗

arXiv2024

ReviewFlow: Intelligent Scaffolding to Support Academic Peer Reviewing

Peer review is a cornerstone of science. Research communities conduct peer reviews to assess contributions and to improve the overall quality of science work. Every year, new community members are recruited as peer reviewers for the first time. How could technology help novices adhere to their community's practices and standards for peer reviewing? To better understand peer review practices and challenges, we conducted a formative study with 10 novices and 10 experts. We found that many experts adopt a workflow of annotating, note-taking, and synthesizing notes into well-justified reviews that align with community standards. Novices lack timely guidance on how to read and assess submissions and how to structure paper reviews. To support the peer review process, we developed ReviewFlow -- an AI-driven workflow that scaffolds novices with contextual reflections to critique and annotate submissions, in-situ knowledge support to assess novelty, and notes-to-outline synthesis to help align peer reviews with community expectations. In a within-subjects experiment, 16 inexperienced reviewers wrote reviews in two conditions: using ReviewFlow and using a baseline environment with minimal guidance. With ReviewFlow, participants produced more comprehensive reviews, identifying more pros and cons. While participants appreciated the streamlined process support from ReviewFlow, they also expressed concerns about using AI as part of the scientific review process. We discuss the implications of using AI to scaffold the peer review process on scientific work and beyond.

cs.HC↗

arXiv2024

Copilot Evaluation Harness: Evaluating LLM-Guided Software Programming

The integration of Large Language Models (LLMs) into Development Environments (IDEs) has become a focal point in modern software development. LLMs such as OpenAI GPT-3.5/4 and Code Llama offer the potential to significantly augment developer productivity by serving as intelligent, chat-driven programming assistants. However, utilizing LLMs out of the box is unlikely to be optimal for any given scenario. Rather, each system requires the LLM to be honed to its set of heuristics to ensure the best performance. In this paper, we introduce the Copilot evaluation harness: a set of data and tools for evaluating LLM-guided IDE interactions, covering various programming scenarios and languages. We propose our metrics as a more robust and information-dense evaluation than previous state of the art evaluation systems. We design and compute both static and execution based success metrics for scenarios encompassing a wide range of developer tasks, including code generation from natural language (generate), documentation generation from code (doc), test case generation (test), bug-fixing (fix), and workspace understanding and query resolution (workspace). These success metrics are designed to evaluate the performance of LLMs within a given IDE and its respective parameter space. Our learnings from evaluating three common LLMs using these metrics can inform the development and validation of future scenarios in LLM guided IDEs.

cs.SE↗

arXiv2024

Dominant Auslander-Gorenstein algebras and mixed cluster tilting

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also introduce mixed (pre)cluster tilting modules as a generalisation of (pre)cluster tilting modules, and establish an Auslander type correspondence by showing that dominant Auslander-Gorenstein (respectively, Auslander-regular) algebras correspond bijectively with mixed precluster (respectively, cluster) tilting modules. We show that every trivial extension algebra $T(A)$ of a $d$-representation-finite algebra A admits a mixed cluster tilting module and show that this can be seen as a generalisation of the well known result that $d$-representation-finite algebras are fractionally Calabi-Yau. We show that iterated SGC-extensions of a gendo-symmetric dominant Auslander-Gorenstein algebra admit mixed precluster tilting modules.

math.RT↗

arXiv2023

Marked non-orientable surfaces and cluster categories via symmetric representations

We initiate the investigation of representation theory of non-orientable surfaces. As a first step towards finding an additive categorification of Dupont and Palesi's quasi-cluster algebras associated marked non-orientable surfaces, we study a certain modification on the objects of the cluster category associated to the orientable double covers in the unpunctured case. More precisely, we consider symmetric representation theory studied by Derksen-Weyman and Boos-Cerulli Irelli, and lift it to the cluster category. This gives a way to consider `indecomposable orbits of objects' under a contravariant duality functor. Hence, we can assign curves on a non-orientable surface $(\mathbb{S}, \mathbb{M})$ to indecomposable symmetric objects. Moreover, we define a new notion of symmetric extension, and show that the arcs and quasi-arcs on $(\mathbb{S}, \mathbb{M})$ correspond to the indecomposable symmetric objects without symmetric self-extension. Consequently, we show that quasi-triangulations of $(\mathbb{S}, \mathbb{M})$ correspond to a symmetric analogue of cluster tilting objects.

math.RT↗

arXiv2023

Universal sublinear resistivity in vanadium kagome materials hosting charge density waves

The recent discovery of a charge density (CDW) state in ScV$_6$Sn$_6$ at $T_{\textrm{CDW}}$ = 91 K offers new opportunities to understand the origins of electronic instabilities in topological kagome systems. By comparing to the isostructural non-CDW compound LuV$_6$Sn$_6$, we unravel interesting electrical transport properties in ScV$_6$Sn$_6$, above and below the charge ordering temperature. We observed that by applying a magnetic field along the $a$ axis, the temperature behavior of the longitudinal resistivity in ScV$_6$Sn$_6$ changes from metal-like to insulator-like above the CDW transition. We show that in the charge ordered state ScV$_6$Sn$_6$ follows the Fermi liquid behavior while above that, it transforms into a non-Fermi liquid phase in which the resistivity varies sublinearly over a broad temperature range. The sublinear resistivity, which scales by $T^{3/5}$ is a common feature among other vanadium-containing kagome compounds exhibiting CDW states such as KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$. By contrast, the non-Fermi liquid behavior does not occur in LuV$_6$Sn$_6$. We explain the $T^{3/5}$ universal scaling behavior from the Coulomb scattering between Dirac electrons and Van Hove singularities; common features in the electronic structure of kagome materials. Finally, we show anomalous Hall-like behavior in ScV$_6$Sn$_6$ below $T_{\textrm{CDW}}$, which is absent in the Lu compound. Comparing the transport properties of ScV$_6$Sn$_6$ and LuV$_6$Sn$_6$ is valuable to highlight the impacts of the unusual CDW in the Sc compound.

cond-mat.str-el↗

arXiv2023

Transformer-based Vulnerability Detection in Code at EditTime: Zero-shot, Few-shot, or Fine-tuning?

Software vulnerabilities bear enterprises significant costs. Despite extensive efforts in research and development of software vulnerability detection methods, uncaught vulnerabilities continue to put software owners and users at risk. Many current vulnerability detection methods require that code snippets can compile and build before attempting detection. This, unfortunately, introduces a long latency between the time a vulnerability is injected to the time it is removed, which can substantially increases the cost of fixing a vulnerability. We recognize that the current advances in machine learning can be used to detect vulnerable code patterns on syntactically incomplete code snippets as the developer is writing the code at EditTime. In this paper we present a practical system that leverages deep learning on a large-scale data set of vulnerable code patterns to learn complex manifestations of more than 250 vulnerability types and detect vulnerable code patterns at EditTime. We discuss zero-shot, few-shot, and fine-tuning approaches on state of the art pre-trained Large Language Models (LLMs). We show that in comparison with state of the art vulnerability detection models our approach improves the state of the art by 10%. We also evaluate our approach to detect vulnerability in auto-generated code by code LLMs. Evaluation on a benchmark of high-risk code scenarios shows a reduction of up to 90% vulnerability reduction.

cs.CR↗

arXiv2023

KNIFE: Distilling Reasoning Knowledge From Free-Text Rationales

Language models (LMs) have yielded impressive results on many language reasoning tasks, but their unexpected errors raise doubts about their reasoning abilities. In light of this, there is growing interest in finetuning/prompting LMs with both task instances and their associated free-text rationales (FTRs), which explain the correct reasoning process for predicting the correct task output (i.e., how to be "right for the right reasons"). However, existing finetuning methods fail to improve LM performance, while prompting needs prohibitively large (i.e., >50B) LMs to work well. We propose KNIFE, which shows that reasoning knowledge can be effectively distilled from FTRs into a small (i.e., <1B) LM and improve the LM's performance. First, KNIFE finetunes a teacher LM (given task input and FTR) to predict the task output, transferring reasoning knowledge from the FTRs to the teacher's hidden states. Second, KNIFE finetunes a student LM (given task input only) such that its hidden states are aligned with the teacher's. Thus, the student is endowed with reasoning knowledge but can be used for inference without direct FTR input. On two question-answering datasets, KNIFE outperforms various finetuning and prompting baselines in fully-supervised and low-resource settings. Also, we observe that FTR quality is crucial to KNIFE's performance.

cs.CL↗

arXiv2023

Are Machine Rationales (Not) Useful to Humans? Measuring and Improving Human Utility of Free-Text Rationales

Among the remarkable emergent capabilities of large language models (LMs) is free-text rationalization; beyond a certain scale, large LMs are capable of generating seemingly useful rationalizations, which in turn, can dramatically enhance their performances on leaderboards. This phenomenon raises a question: can machine generated rationales also be useful for humans, especially when lay humans try to answer questions based on those machine rationales? We observe that human utility of existing rationales is far from satisfactory, and expensive to estimate with human studies. Existing metrics like task performance of the LM generating the rationales, or similarity between generated and gold rationales are not good indicators of their human utility. While we observe that certain properties of rationales like conciseness and novelty are correlated with their human utility, estimating them without human involvement is challenging. We show that, by estimating a rationale's helpfulness in answering similar unseen instances, we can measure its human utility to a better extent. We also translate this finding into an automated score, GEN-U, that we propose, which can help improve LMs' ability to generate rationales with better human utility, while maintaining most of its task performance. Lastly, we release all code and collected data with this project.

cs.CL↗

arXiv2023

PINTO: Faithful Language Reasoning Using Prompt-Generated Rationales

Neural language models (LMs) have achieved impressive results on various language-based reasoning tasks by utilizing latent knowledge encoded in their own pretrained parameters. To make this reasoning process more explicit, recent works retrieve a rationalizing LM's internal knowledge by training or prompting it to generate free-text rationales, which can be used to guide task predictions made by either the same LM or a separate reasoning LM. However, rationalizing LMs require expensive rationale annotation and/or computation, without any assurance that their generated rationales improve LM task performance or faithfully reflect LM decision-making. In this paper, we propose PINTO, an LM pipeline that rationalizes via prompt-based learning, and learns to faithfully reason over rationales via counterfactual regularization. First, PINTO maps out a suitable reasoning process for the task input by prompting a frozen rationalizing LM to generate a free-text rationale. Second, PINTO's reasoning LM is fine-tuned to solve the task using the generated rationale as context, while regularized to output less confident predictions when the rationale is perturbed. Across four datasets, we show that PINTO significantly improves the generalization ability of the reasoning LM, yielding higher performance on both in-distribution and out-of-distribution test sets. Also, we find that PINTO's rationales are more faithful to its task predictions than those generated by competitive baselines.

cs.CL↗