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Lei Liu

Publications and source records attributed to Lei Liu.

At least 217 records · Page 12Linked to original sources

Think-in-Memory: Recalling and Post-thinking Enable LLMs with Long-Term Memory

Memory-augmented Large Language Models (LLMs) have demonstrated remarkable performance in long-term human-machine interactions, which basically relies on iterative recalling and reasoning of history to generate high-quality responses. However, such repeated recall-reason steps easily produce biased thoughts, \textit{i.e.}, inconsistent reasoning results when recalling the same history for different questions. On the contrary, humans can keep thoughts in the memory and recall them without repeated reasoning. Motivated by this human capability, we propose a novel memory mechanism called TiM (Think-in-Memory) that enables LLMs to maintain an evolved memory for storing historical thoughts along the conversation stream. The TiM framework consists of two crucial stages: (1) before generating a response, a LLM agent recalls relevant thoughts from memory, and (2) after generating a response, the LLM agent post-thinks and incorporates both historical and new thoughts to update the memory. Thus, TiM can eliminate the issue of repeated reasoning by saving the post-thinking thoughts as the history. Besides, we formulate the basic principles to organize the thoughts in memory based on the well-established operations, (\textit{i.e.}, insert, forget, and merge operations), allowing for dynamic updates and evolution of the thoughts. Furthermore, we introduce Locality-Sensitive Hashing into TiM to achieve efficient retrieval for the long-term conversations. We conduct qualitative and quantitative experiments on real-world and simulated dialogues covering a wide range of topics, demonstrating that equipping existing LLMs with TiM significantly enhances their performance in generating responses for long-term interactions.

cs.CL↗

Algebra of L-banded Matrices

Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an analytically optimized vector damping was proposed for memory message-passing (iterative) algorithms. As a result, it yields a special class of covariance matrices called L-banded matrices. In this paper, we show these matrices have broad algebraic properties arising from their L-banded structure. In particular, compact analytic expressions for the LDL decomposition, the Cholesky decomposition, the determinant after a column substitution, minors, and cofactors are derived. Furthermore, necessary and sufficient conditions for an L-banded matrix to be definite, a recurrence to obtain the characteristic polynomial, and some other properties are given. In addition, we give new derivations of the determinant and the inverse. (It's crucial to emphasize that some works have independently studied matrices with this special structure, named as L-matrices. Specifically, L-banded matrices are regarded as L-matrices with real and finite entries.)

eess.SP↗

On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for constructing orthogonal approximate message passing (OAMP), enabling its applicability to a wide range of prototypes without the constraint of differentiability. We develop two single-input-single-output variational transfer functions for OAMP with Lipschitz continuous local estimators, facilitating an analysis of achievable rates. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP can achieve the constrained capacity predicted by the replica method of LUIS based on matched FEC coding, regardless of the signal distribution. The replica method is rigorously validated for LUIS with Gaussian signaling and certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we present a replica constrained capacity-achieving coding principle for LUIS. This principle serves as the basis for optimizing irregular low-density parity-check (LDPC) codes specifically tailored for binary signaling in our simulation results. The performance of OAMP with these optimized codes exhibits a remarkable improvement over the unoptimized codes and even surpasses the well-known Turbo-LMMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, we observe bit error rates (BER) performance near the replica constrained capacity across diverse channel conditions.

cs.IT↗

Vibrational Properties of One-Dimensional Disordered Hyperuniform Atomic Chains

Disorder hyperuniformity (DHU) is a recently discovered exotic state of many-body systems that possess a hidden order in between that of a perfect crystal and a completely disordered system. Recently, this novel DHU state has been observed in a number of quantum materials including amorphous 2D graphene and silica, which are endowed with unexpected electronic transport properties. Here, we numerically investigate 1D atomic chain models, including perfect crystalline, disordered hyperuniform as well as randomly perturbed atom packing configurations to obtain a quantitative understanding of how the unique DHU disorder affects the vibrational properties of these low-dimensional materials. We find that the DHU chains possess lower cohesive energies compared to the randomly perturbed chains, implying their potential reliability in experiments. Our inverse partition ratio (IPR) calculations indicate that the DHU chains can support fully delocalized states just like perfect crystalline chains over a wide range of frequencies, i.e., $ω\in (0, 100)$ cm$^{-1}$, suggesting superior phonon transport behaviors within these frequencies, which was traditionally considered impossible in disordered systems. Interestingly, we observe the emergence of a group of highly localized states associated with $ω\sim 200$ cm$^{-1}$, which is characterized by a significant peak in the IPR and a peak in phonon density of states at the corresponding frequency, and is potentially useful for decoupling electron and phonon degrees of freedom. These unique properties of DHU chains have implications in the design and engineering of novel DHU quantum materials for thermal and phononic applications.

cond-mat.mtrl-sci↗

Memory AMP for Generalized MIMO: Coding Principle and Information-Theoretic Optimality

To support complex communication scenarios in next-generation wireless communications, this paper focuses on a generalized MIMO (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input distributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and correlated channel matrices). The orthogonal/vector approximate message passing (OAMP/VAMP) receiver has been proved to be information-theoretically optimal in GMIMO, but it is limited to high-complexity LMMSE. To solve this problem, a low-complexity memory approximate message passing (MAMP) receiver has recently been shown to be Bayes optimal but limited to uncoded systems. Therefore, how to design a low-complexity and information-theoretically optimal receiver for GMIMO is still an open issue. To address this issue, this paper proposes an information-theoretically optimal MAMP receiver and investigates its achievable rate analysis and optimal coding principle. Specifically, due to the long-memory linear detection, state evolution (SE) for MAMP is intricately multidimensional and cannot be used directly to analyze its achievable rate. To avoid this difficulty, a simplified single-input single-output variational SE (VSE) for MAMP is developed by leveraging the SE fixed-point consistent property of MAMP and OAMP/VAMP. The achievable rate of MAMP is calculated using the VSE, and the optimal coding principle is established to maximize the achievable rate. On this basis, the information-theoretic optimality of MAMP is proved rigorously. Numerical results show that the finite-length performances of MAMP with practical optimized LDPC codes are 0.5-2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performances as OAMP/VAMP with 0.4% of the time consumption for large-scale systems.

cs.IT↗

Low-Complexity and Information-Theoretic Optimal Memory AMP for Coded Generalized MIMO

This paper considers a generalized multiple-input multiple-output (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input distributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and correlated channel matrices). Orthogonal/vector approximate message passing (OAMP/VAMP) has been proved to be information-theoretically optimal in GMIMO, but it is limited to high complexity. Meanwhile, low-complexity memory approximate message passing (MAMP) was shown to be Bayes optimal in GMIMO, but channel coding was ignored. Therefore, how to design a low-complexity and information-theoretic optimal receiver for GMIMO is still an open issue. In this paper, we propose an information-theoretic optimal MAMP receiver for coded GMIMO, whose achievable rate analysis and optimal coding principle are provided to demonstrate its information-theoretic optimality. Specifically, state evolution (SE) for MAMP is intricately multi-dimensional because of the nature of local memory detection. To this end, a fixed-point consistency lemma is proposed to derive the simplified variational SE (VSE) for MAMP, based on which the achievable rate of MAMP is calculated, and the optimal coding principle is derived to maximize the achievable rate. Subsequently, we prove the information-theoretic optimality of MAMP. Numerical results show that the finite-length performances of MAMP with optimized LDPC codes are about 1.0 - 2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performance as OAMP/VAMP with 0.4% of the time consumption for large-scale systems.

cs.IT↗

EVA2.0: Investigating Open-Domain Chinese Dialogue Systems with Large-Scale Pre-Training

Large-scale pre-training has shown remarkable performance in building open-domain dialogue systems. However, previous works mainly focus on showing and evaluating the conversational performance of the released dialogue model, ignoring the discussion of some key factors towards a powerful human-like chatbot, especially in Chinese scenarios. In this paper, we conduct extensive experiments to investigate these under-explored factors, including data quality control, model architecture designs, training approaches, and decoding strategies. We propose EVA2.0, a large-scale pre-trained open-domain Chinese dialogue model with 2.8 billion parameters, and will make our models and codes publicly available. Automatic and human evaluations show that EVA2.0 significantly outperforms other open-source counterparts. We also discuss the limitations of this work by presenting some failure cases and pose some future research directions on large-scale Chinese open-domain dialogue systems.

cs.CL↗

Orbital configurations of spaceborne interferometers for studying photon rings of supermassive black holes

Recent advances in technology coupled with the progress of observational radio astronomy methods resulted in achieving a major milestone of astrophysics - a direct image of the shadow of a supermassive black hole, taken by the Earth-based Event Horizon Telescope (EHT). The EHT was able to achieve a resolution of $\sim$20 $μ$as, enabling it to resolve the shadows of the black holes in the centres of two celestial objects: the supergiant elliptical galaxy M87 and the Milky Way Galaxy. The EHT results mark the start of a new round of development of next generation Very Long Baseline Interferometers (VLBI) which will be able to operate at millimetre and sub-millimetre wavelengths. The inclusion of baselines exceeding the diameter of the Earth and observation at as short a wavelength as possible is imperative for further development of high resolution astronomical observations. This can be achieved by a spaceborne VLBI system. We consider the preliminary mission design of such a system, specifically focused on the detection and analysis of photon rings, an intrinsic feature of supermassive black holes. Optimised Earth, Sun-Earth L2 and Earth-Moon L2 orbit configurations for the space interferometer system are presented, all of which provide an order of magnitude improvement in resolution compared to the EHT. Such a space-borne interferometer would be able to conduct a comprehensive survey of supermassive black holes in active galactic nuclei and enable uniquely robust and accurate tests of strong gravity, through detection of the photon ring features.

astro-ph.IM↗

Robust Computation Offloading and Trajectory Optimization for Multi-UAV-Assisted MEC: A Multi-Agent DRL Approach

For multiple Unmanned-Aerial-Vehicles (UAVs) assisted Mobile Edge Computing (MEC) networks, we study the problem of combined computation and communication for user equipments deployed with multi-type tasks. Specifically, we consider that the MEC network encompasses both communication and computation uncertainties, where the partial channel state information and the inaccurate estimation of task complexity are only available. We introduce a robust design accounting for these uncertainties and minimize the total weighted energy consumption by jointly optimizing UAV trajectory, task partition, as well as the computation and communication resource allocation in the multi-UAV scenario. The formulated problem is challenging to solve with the coupled optimization variables and the high uncertainties. To overcome this issue, we reformulate a multi-agent Markov decision process and propose a multi-agent proximal policy optimization with Beta distribution framework to achieve a flexible learning policy. Numerical results demonstrate the effectiveness and robustness of the proposed algorithm for the multi-UAV-assisted MEC network, which outperforms the representative benchmarks of the deep reinforcement learning and heuristic algorithms.

eess.SP↗

Time-localized dark modes generated by zero-wavenumber-gain modulational instability

In this work we report on the emergence of a novel type of solitary waves, viz., time-localized solitons in integrable and non-integrable variants of the massive Thirring models and in the three-wave resonant-interaction system, which are models broadly used in plasmas, nonlinear optics and hydrodynamics. An essential finding is that the condition for the existence of time-localized dark solitons, which develop density dips in the course of time evolution, in these models coincides with the condition for the occurrence of the zero-wavenumber-gain (ZWG) modulational instability (MI). Systematic simulations reveal that, whenever the ZWG MI is present, patterns reminiscent of such solitons are generically excited from a chaotic background field as fragments within more complex patterns.

nlin.PS↗

Cuing Without Sharing: A Federated Cued Speech Recognition Framework via Mutual Knowledge Distillation

Cued Speech (CS) is a visual coding tool to encode spoken languages at the phonetic level, which combines lip-reading and hand gestures to effectively assist communication among people with hearing impairments. The Automatic CS Recognition (ACSR) task aims to recognize CS videos into linguistic texts, which involves both lips and hands as two distinct modalities conveying complementary information. However, the traditional centralized training approach poses potential privacy risks due to the use of facial and gesture videos in CS data. To address this issue, we propose a new Federated Cued Speech Recognition (FedCSR) framework to train an ACSR model over the decentralized CS data without sharing private information. In particular, a mutual knowledge distillation method is proposed to maintain cross-modal semantic consistency of the Non-IID CS data, which ensures learning a unified feature space for both linguistic and visual information. On the server side, a globally shared linguistic model is trained to capture the long-term dependencies in the text sentences, which is aligned with the visual information from the local clients via visual-to-linguistic distillation. On the client side, the visual model of each client is trained with its own local data, assisted by linguistic-to-visual distillation treating the linguistic model as the teacher. To the best of our knowledge, this is the first approach to consider the federated ACSR task for privacy protection. Experimental results on the Chinese CS dataset with multiple cuers demonstrate that our approach outperforms both mainstream federated learning baselines and existing centralized state-of-the-art ACSR methods, achieving 9.7% performance improvement for character error rate (CER) and 15.0% for word error rate (WER).

cs.MM↗

Global Surfaces of Section and Periodic Orbits in The Spatial Isosceles Three Body Problem

We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, we find some disk-like global surfaces of section with the Euler orbit as their common boundary, and a brake orbit passing through them. By considering the Poincaré maps of these global surfaces of section, we prove the existence of all kinds of different periodic orbits under certain assumption. Moreover, we are able to prove, for generic choices of masses, the system always has infinitely many periodic orbits. One of the key is to estimate the rotation numbers of the Euler orbit and the brake orbit with respect to the Poincaré map. For this, we establish formulas connected these numbers with the mean indices of the corresponding orbits using the Maslov-type index.

math.DS↗

A symplectic dynamics approach to the spatial isosceles three-body problem

We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the energy surface is equivalent to a Reeb flow on the tight three-sphere. We find a Hopf link formed by the Euler orbit and a symmetric brake orbit, which spans an open book decomposition whose pages are annulus-like global surfaces of section. In the case of large mass ratios, the Hopf link is non-resonant, forcing the existence of infinitely many periodic orbits. The rotation number of the Euler orbit plays a fundamental role in the existence of periodic orbits and their symmetries. We explore such symmetries in the Hill region and show that the Euler orbit is negative hyperbolic for an open set of parameters while it can never be positive hyperbolic. Finally, we address convexity and determine for each parameter whether the energy surface is strictly convex, convex, or non-convex. Dynamical consequences of this fact are then discussed.

math.DS↗

Graph Contrastive Topic Model

Existing NTMs with contrastive learning suffer from the sample bias problem owing to the word frequency-based sampling strategy, which may result in false negative samples with similar semantics to the prototypes. In this paper, we aim to explore the efficient sampling strategy and contrastive learning in NTMs to address the aforementioned issue. We propose a new sampling assumption that negative samples should contain words that are semantically irrelevant to the prototype. Based on it, we propose the graph contrastive topic model (GCTM), which conducts graph contrastive learning (GCL) using informative positive and negative samples that are generated by the graph-based sampling strategy leveraging in-depth correlation and irrelevance among documents and words. In GCTM, we first model the input document as the document word bipartite graph (DWBG), and construct positive and negative word co-occurrence graphs (WCGs), encoded by graph neural networks, to express in-depth semantic correlation and irrelevance among words. Based on the DWBG and WCGs, we design the document-word information propagation (DWIP) process to perform the edge perturbation of DWBG, based on multi-hop correlations/irrelevance among documents and words. This yields the desired negative and positive samples, which will be utilized for GCL together with the prototypes to improve learning document topic representations and latent topics. We further show that GCL can be interpreted as the structured variational graph auto-encoder which maximizes the mutual information of latent topic representations of different perspectives on DWBG. Experiments on several benchmark datasets demonstrate the effectiveness of our method for topic coherence and document representation learning compared with existing SOTA methods.

cs.CL↗

Sufficient-Statistic Memory AMP

Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. While state evolution is a useful analytic tool, its convergence is not guaranteed. To solve the convergence problem of the state evolution of AMP-type algorithms in principle, this paper proposes a sufficient-statistic memory AMP (SS-MAMP) algorithm framework under the conditions of right-unitarily invariant sensing matrices, Lipschitz-continuous local processors and the sufficient-statistic constraint (i.e., the current message of each local processor is a sufficient statistic of the signal vector given the current and all preceding messages). We show that the covariance matrices of SS-MAMP are L-banded and convergent, which is an optimal framework (from the local MMSE/LMMSE perspective) for AMP-type algorithms given the Lipschitz-continuous local processors. Given an arbitrary MAMP, we can construct an SS-MAMP by damping, which not only ensures the convergence of the state evolution, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution. As a byproduct, we prove that the Bayes-optimal orthogonal/vector AMP (BO-OAMP/VAMP) is an SS-MAMP. As an example, we construct a sufficient-statistic Bayes-optimal MAMP (SS-BO-MAMP) whose state evolution converges to the minimum (i.e., Bayes-optimal) mean square error (MSE) predicted by replica methods when it has a unique fixed point. In addition, the MSE of SS-BO-MAMP is not worse than the original BO-MAMP. Finally, simulations are provided to support the theoretical results.

cs.IT↗

Formation of rogue waves and modulational instability with zero-wavenumber gain in multi-component systems with coherent coupling

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multi-component systems-in particular, in the massive Thirring model.

nlin.PS↗

The qualitative behavior at a vortex point for the Chern-Simon-Higgs equation

In this paper, we study the qualitative behavior at a vortex blow-up point for Chern-Simon-Higgs equation. Roughly speaking, we will establish an energy identity at a each such point, i.e. the local mass is the sum of the bubbles. Moreover, we prove that either there is only one bubble which is a singular bubble or there are more than two bubbles which contains no singular bubble. Meanwhile, we prove that the energies of these bubbles must satisfy a quadratic polynomial which can be used to prove the simple blow-up property when the multiplicity is small. As is well known, for many Liouville type system, Pohozaev type identity is a quadratic polynomial corresponding to energies which can be used directly to compute the local mass at a blow-up point. The difficulty here is that, besides the energy's integration, there is a additional term in the Pohozaev type identity of Chern-Simon-Higgs equation. We need some more detailed and delicated analysis to deal with it.

math.AP↗

Prompt Learning to Mitigate Catastrophic Forgetting in Cross-lingual Transfer for Open-domain Dialogue Generation

Dialogue systems for non-English languages have long been under-explored. In this paper, we take the first step to investigate few-shot cross-lingual transfer learning (FS-XLT) and multitask learning (MTL) in the context of open-domain dialogue generation for non-English languages with limited data. We observed catastrophic forgetting in both FS-XLT and MTL for all 6 languages in our preliminary experiments. To mitigate the issue, we propose a simple yet effective prompt learning approach that can preserve the multilinguality of multilingual pre-trained language model (mPLM) in FS-XLT and MTL by bridging the gap between pre-training and fine-tuning with Fixed-prompt LM Tuning and our hand-crafted prompts. Experimental results on all 6 languages in terms of both automatic and human evaluations demonstrate the effectiveness of our approach. Our code is available at https://github.com/JeremyLeiLiu/XLinguDial.

cs.CL↗