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Mar 11

Constraints on Cosmic Rays Acceleration in Bright Gamma-ray Bursts with Observations of Fermi

Gamma-ray bursts (GRBs) are widely suggested as potential sources of ultrahigh-energy cosmic rays (UHECRs). The kinetic energy of the jets dissipates, leading to the production of an enormous amount of gamma-ray photons and possibly also the acceleration of protons. The accelerated protons will interact with the radiation of the GRB via the photomeson and Bethe-Heitler processes, which can initiate electromagnetic cascades. This process can give rise to broadband radiation up to the GeV-TeV gamma-ray regime. The expected gamma-ray flux from cascades depends on properties of the GRB jet, such as the dissipation radius R_{rm diss}, the bulk Lorentz factor Gamma, and the baryon loading factor eta_p. Therefore, observations of Fermi-LAT can impose constraints on these important parameters. In this study, we select 12 GRBs of high keV-MeV fluence and constrain the baryon loading factor, under different combinations of the bulk Lorentz factor and the dissipation radius based on Fermi-LAT's measurements. Our findings indicate a strong constraint of eta_p<10 for most selected GRBs over a large parameter space except for large dissipation radii (gtrsim 10^{15}rm cm) and high bulk Lorentz factors (gtrsim 600). The constraint is comparable to, and in some GRBs even stronger than, that from high-energy neutrinos for stacked GRBs. Our results suggest that for typical bulk Lorentz factor of several hundreds, the dissipation radii of GRBs need be large to avoid overshooting the GeV gamma-ray flux during the prompt emission phase of GRBs, which can be used to constrain GRBs.

Constructing a Singing Style Caption Dataset

Singing voice synthesis and conversion have emerged as significant subdomains of voice generation, leading to much demands on prompt-conditioned generation. Unlike common voice data, generating a singing voice requires an understanding of various associated vocal and musical characteristics, such as the vocal tone of the singer or emotional expressions. However, existing open-source audio-text datasets for voice generation tend to capture only a very limited range of attributes, often missing musical characteristics of the audio. To fill this gap, we introduce S2Cap, an audio-text pair dataset with a diverse set of attributes. S2Cap consists of pairs of textual prompts and music audio samples with a wide range of vocal and musical attributes, including pitch, volume, tempo, mood, singer's gender and age, and musical genre and emotional expression. Utilizing S2Cap, we suggest an effective novel baseline algorithm for singing style captioning. Singing style captioning is a relative task to voice generation that generates text descriptions of vocal characteristics, which we first suggested. First, to mitigate the misalignment between the audio encoder and the text decoder, we present a novel mechanism called CRESCENDO, which utilizes positive-pair similarity learning to synchronize the embedding spaces of a pretrained audio encoder to get similar embeddings with a text encoder. We additionally supervise the model using the singer's voice, which is demixed by the accompaniment. This supervision allows the model to more accurately capture vocal characteristics, leading to improved singing style captions that better reflect the style of the singer. The dataset and the codes are available at https://github.com/HJ-Ok/S2cap.

Constraining atmospheric composition from the outflow: helium observations reveal the fundamental properties of two planets straddling the radius gap

TOI-836 is a ~2-3 Gyr K dwarf with an inner super Earth (R=1.7 R_oplus, P=3.8 d) and an outer mini Neptune (R=2.6 R_oplus, P=8.6 d). JWST/NIRSpec 2.8--5.2 mum transmission spectra are flat for both planets. We present Keck/NIRSPEC observations of escaping helium for super-Earth b, which shows no excess absorption in the 1083 nm triplet to deep limits (<0.2%), and mini-Neptune c, which shows strong (0.7%) excess absorption in both visits. These results demonstrate that planet c retains at least some primordial atmosphere, while planet b is consistent with having lost its entire primordial envelope. Self-consistent 1D radiative-hydrodynamic models of planet c reveal that the helium excess absorption signal is highly sensitive to metallicity: its equivalent width collapses by a factor of 13 as metallicity increases from 10x to 100x solar, and by a further factor of 12 as it increases to 200x solar. The observed equivalent width is 88\% the model prediction for 100x metallicity, suggesting an atmospheric metallicity similar to K2-18b and TOI-270d, the first two mini-Neptunes with detected absorption features in JWST transmission spectra. We highlight the helium triplet as a potentially powerful probe of atmospheric composition, with complementary strengths and weaknesses to atmospheric retrievals. The main strength is its extreme sensitivity to metallicity in the scientifically significant range of 10--200x solar, and the main weakness is the enormous model uncertainties in outflow suppression and confinement mechanisms, such as magnetic fields and stellar winds, which can suppress the signal by at least a factor of ~several.

Constraints on the variation of the fine-structure constant at 3<z<10 with JWST emission-line galaxies

We present constraints on the spacetime variation of the fine-structure constant alpha at redshifts 2.5le z<9.5 using JWST emission-line galaxies. The galaxy sample consists of 621 high-quality spectra with strong and narrow [O III] lambdalambda4959,5007 doublet emission lines from 578 galaxies, including 232 spectra at z>5. The [O III] doublet lines are arguably the best emission lines to probe the variation in alpha. We divide our sample into six subsamples based on redshift and calculate the relative variation Deltaalpha/alpha for the individual subsamples. The calculated Deltaalpha/alpha values are consistent with zero within 1sigma at all redshifts, suggesting no time variation in alpha above a level of (1-2) times10^{-4} (1sigma) in the past 13.2 billion years. When the whole sample is combined, the constraint is improved to be Deltaalpha/alpha = (0.2pm0.7) times10^{-4}. We further test the spatial variation in alpha using four subsamples of galaxies in four different directions on the sky. The measured Deltaalpha/alpha values are consistent with zero at a 1sigma level of sim 2times10^{-4}. While the constraints in this work are not as stringent as those from lower-redshift quasar absorption lines in previous studies, this work uses an independent tracer and provides the first constraints on Deltaalpha/alpha at the highest redshifts. With the growing number of emission-line galaxies from JWST, we expect to achieve stronger constraints in the future.

Constellation Dataset: Benchmarking High-Altitude Object Detection for an Urban Intersection

We introduce Constellation, a dataset of 13K images suitable for research on detection of objects in dense urban streetscapes observed from high-elevation cameras, collected for a variety of temporal conditions. The dataset addresses the need for curated data to explore problems in small object detection exemplified by the limited pixel footprint of pedestrians observed tens of meters from above. It enables the testing of object detection models for variations in lighting, building shadows, weather, and scene dynamics. We evaluate contemporary object detection architectures on the dataset, observing that state-of-the-art methods have lower performance in detecting small pedestrians compared to vehicles, corresponding to a 10% difference in average precision (AP). Using structurally similar datasets for pretraining the models results in an increase of 1.8% mean AP (mAP). We further find that incorporating domain-specific data augmentations helps improve model performance. Using pseudo-labeled data, obtained from inference outcomes of the best-performing models, improves the performance of the models. Finally, comparing the models trained using the data collected in two different time intervals, we find a performance drift in models due to the changes in intersection conditions over time. The best-performing model achieves a pedestrian AP of 92.0% with 11.5 ms inference time on NVIDIA A100 GPUs, and an mAP of 95.4%.

Constrained Decoding for Cross-lingual Label Projection

Zero-shot cross-lingual transfer utilizing multilingual LLMs has become a popular learning paradigm for low-resource languages with no labeled training data. However, for NLP tasks that involve fine-grained predictions on words and phrases, the performance of zero-shot cross-lingual transfer learning lags far behind supervised fine-tuning methods. Therefore, it is common to exploit translation and label projection to further improve the performance by (1) translating training data that is available in a high-resource language (e.g., English) together with the gold labels into low-resource languages, and/or (2) translating test data in low-resource languages to a high-source language to run inference on, then projecting the predicted span-level labels back onto the original test data. However, state-of-the-art marker-based label projection methods suffer from translation quality degradation due to the extra label markers injected in the input to the translation model. In this work, we explore a new direction that leverages constrained decoding for label projection to overcome the aforementioned issues. Our new method not only can preserve the quality of translated texts but also has the versatility of being applicable to both translating training and translating test data strategies. This versatility is crucial as our experiments reveal that translating test data can lead to a considerable boost in performance compared to translating only training data. We evaluate on two cross-lingual transfer tasks, namely Named Entity Recognition and Event Argument Extraction, spanning 20 languages. The results demonstrate that our approach outperforms the state-of-the-art marker-based method by a large margin and also shows better performance than other label projection methods that rely on external word alignment.

Constrained Bi-Level Optimization: Proximal Lagrangian Value function Approach and Hessian-free Algorithm

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such problems have recently gained significant attention due to their broad applicability in machine learning. However, conventional gradient-based methods unavoidably rely on computationally intensive calculations related to the Hessian matrix. To address this challenge, we begin by devising a smooth proximal Lagrangian value function to handle the constrained lower-level problem. Utilizing this construct, we introduce a single-level reformulation for constrained BLOs that transforms the original BLO problem into an equivalent optimization problem with smooth constraints. Enabled by this reformulation, we develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA)-that is straightforward to implement in a single loop manner. Consequently, LV-HBA is especially well-suited for machine learning applications. Furthermore, we offer non-asymptotic convergence analysis for LV-HBA, eliminating the need for traditional strong convexity assumptions for the lower-level problem while also being capable of accommodating non-singleton scenarios. Empirical results substantiate the algorithm's superior practical performance.

An End-to-End Reinforcement Learning Approach for Job-Shop Scheduling Problems Based on Constraint Programming

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

Constructing interval variables via faceted Rasch measurement and multitask deep learning: a hate speech application

We propose a general method for measuring complex variables on a continuous, interval spectrum by combining supervised deep learning with the Constructing Measures approach to faceted Rasch item response theory (IRT). We decompose the target construct, hate speech in our case, into multiple constituent components that are labeled as ordinal survey items. Those survey responses are transformed via IRT into a debiased, continuous outcome measure. Our method estimates the survey interpretation bias of the human labelers and eliminates that influence on the generated continuous measure. We further estimate the response quality of each labeler using faceted IRT, allowing responses from low-quality labelers to be removed. Our faceted Rasch scaling procedure integrates naturally with a multitask deep learning architecture for automated prediction on new data. The ratings on the theorized components of the target outcome are used as supervised, ordinal variables for the neural networks' internal concept learning. We test the use of an activation function (ordinal softmax) and loss function (ordinal cross-entropy) designed to exploit the structure of ordinal outcome variables. Our multitask architecture leads to a new form of model interpretation because each continuous prediction can be directly explained by the constituent components in the penultimate layer. We demonstrate this new method on a dataset of 50,000 social media comments sourced from YouTube, Twitter, and Reddit and labeled by 11,000 U.S.-based Amazon Mechanical Turk workers to measure a continuous spectrum from hate speech to counterspeech. We evaluate Universal Sentence Encoders, BERT, and RoBERTa as language representation models for the comment text, and compare our predictive accuracy to Google Jigsaw's Perspective API models, showing significant improvement over this standard benchmark.

PosterLLaVa: Constructing a Unified Multi-modal Layout Generator with LLM

Layout generation is the keystone in achieving automated graphic design, requiring arranging the position and size of various multi-modal design elements in a visually pleasing and constraint-following manner. Previous approaches are either inefficient for large-scale applications or lack flexibility for varying design requirements. Our research introduces a unified framework for automated graphic layout generation, leveraging the multi-modal large language model (MLLM) to accommodate diverse design tasks. In contrast, our data-driven method employs structured text (JSON format) and visual instruction tuning to generate layouts under specific visual and textual constraints, including user-defined natural language specifications. We conducted extensive experiments and achieved state-of-the-art (SOTA) performance on public multi-modal layout generation benchmarks, demonstrating the effectiveness of our method. Moreover, recognizing existing datasets' limitations in capturing the complexity of real-world graphic designs, we propose two new datasets for much more challenging tasks (user-constrained generation and complicated poster), further validating our model's utility in real-life settings. Marking by its superior accessibility and adaptability, this approach further automates large-scale graphic design tasks. The code and datasets will be publicly available on https://github.com/posterllava/PosterLLaVA.

Toffee: Efficient Million-Scale Dataset Construction for Subject-Driven Text-to-Image Generation

In subject-driven text-to-image generation, recent works have achieved superior performance by training the model on synthetic datasets containing numerous image pairs. Trained on these datasets, generative models can produce text-aligned images for specific subject from arbitrary testing image in a zero-shot manner. They even outperform methods which require additional fine-tuning on testing images. However, the cost of creating such datasets is prohibitive for most researchers. To generate a single training pair, current methods fine-tune a pre-trained text-to-image model on the subject image to capture fine-grained details, then use the fine-tuned model to create images for the same subject based on creative text prompts. Consequently, constructing a large-scale dataset with millions of subjects can require hundreds of thousands of GPU hours. To tackle this problem, we propose Toffee, an efficient method to construct datasets for subject-driven editing and generation. Specifically, our dataset construction does not need any subject-level fine-tuning. After pre-training two generative models, we are able to generate infinite number of high-quality samples. We construct the first large-scale dataset for subject-driven image editing and generation, which contains 5 million image pairs, text prompts, and masks. Our dataset is 5 times the size of previous largest dataset, yet our cost is tens of thousands of GPU hours lower. To test the proposed dataset, we also propose a model which is capable of both subject-driven image editing and generation. By simply training the model on our proposed dataset, it obtains competitive results, illustrating the effectiveness of the proposed dataset construction framework.

Sparsity-Constrained Optimal Transport

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning that all sources are (fractionally) matched with all targets. To address this issue, several works have investigated quadratic regularization instead. This regularization preserves sparsity and leads to unconstrained and smooth (semi) dual objectives, that can be solved with off-the-shelf gradient methods. Unfortunately, quadratic regularization does not give direct control over the cardinality (number of nonzeros) of the transportation plan. We propose in this paper a new approach for OT with explicit cardinality constraints on the transportation plan. Our work is motivated by an application to sparse mixture of experts, where OT can be used to match input tokens such as image patches with expert models such as neural networks. Cardinality constraints ensure that at most k tokens are matched with an expert, which is crucial for computational performance reasons. Despite the nonconvexity of cardinality constraints, we show that the corresponding (semi) dual problems are tractable and can be solved with first-order gradient methods. Our method can be thought as a middle ground between unregularized OT (recovered in the limit case k=1) and quadratically-regularized OT (recovered when k is large enough). The smoothness of the objectives increases as k increases, giving rise to a trade-off between convergence speed and sparsity of the optimal plan.

The Construction of Instruction-tuned LLMs for Finance without Instruction Data Using Continual Pretraining and Model Merging

This paper proposes a novel method for constructing instruction-tuned large language models (LLMs) for finance without instruction data. Traditionally, developing such domain-specific LLMs has been resource-intensive, requiring a large dataset and significant computational power for continual pretraining and instruction tuning. Our study proposes a simpler approach that combines domain-specific continual pretraining with model merging. Given that general-purpose pretrained LLMs and their instruction-tuned LLMs are often publicly available, they can be leveraged to obtain the necessary instruction task vector. By merging this with a domain-specific pretrained vector, we can effectively create instruction-tuned LLMs for finance without additional instruction data. Our process involves two steps: first, we perform continual pretraining on financial data; second, we merge the instruction-tuned vector with the domain-specific pretrained vector. Our experiments demonstrate the successful construction of instruction-tuned LLMs for finance. One major advantage of our method is that the instruction-tuned and domain-specific pretrained vectors are nearly independent. This independence makes our approach highly effective. The Japanese financial instruction-tuned LLMs we developed in this study are available at https://huggingface.co/pfnet/nekomata-14b-pfn-qfin-inst-merge.

SeisFusion: Constrained Diffusion Model with Input Guidance for 3D Seismic Data Interpolation and Reconstruction

Geographical, physical, or economic constraints often result in missing traces within seismic data, making the reconstruction of complete seismic data a crucial step in seismic data processing. Traditional methods for seismic data reconstruction require the selection of multiple empirical parameters and struggle to handle large-scale continuous missing data. With the development of deep learning, various neural networks have demonstrated powerful reconstruction capabilities. However, these convolutional neural networks represent a point-to-point reconstruction approach that may not cover the entire distribution of the dataset. Consequently, when dealing with seismic data featuring complex missing patterns, such networks may experience varying degrees of performance degradation. In response to this challenge, we propose a novel diffusion model reconstruction framework tailored for 3D seismic data. To constrain the results generated by the diffusion model, we introduce conditional supervision constraints into the diffusion model, constraining the generated data of the diffusion model based on the input data to be reconstructed. We introduce a 3D neural network architecture into the diffusion model, successfully extending the 2D diffusion model to 3D space. Additionally, we refine the model's generation process by incorporating missing data into the generation process, resulting in reconstructions with higher consistency. Through ablation studies determining optimal parameter values, our method exhibits superior reconstruction accuracy when applied to both field datasets and synthetic datasets, effectively addressing a wide range of complex missing patterns. Our implementation is available at https://github.com/WAL-l/SeisFusion.

STAR: Constraint LoRA with Dynamic Active Learning for Data-Efficient Fine-Tuning of Large Language Models

Though Large Language Models (LLMs) have demonstrated the powerful capabilities of few-shot learning through prompting methods, supervised training is still necessary for complex reasoning tasks. Because of their extensive parameters and memory consumption, both Parameter-Efficient Fine-Tuning (PEFT) methods and Memory-Efficient Fine-Tuning methods have been proposed for LLMs. Nevertheless, the issue of large annotated data consumption, the aim of Data-Efficient Fine-Tuning, remains unexplored. One obvious way is to combine the PEFT method with active learning. However, the experimental results show that such a combination is not trivial and yields inferior results. Through probe experiments, such observation might be explained by two main reasons: uncertainty gap and poor model calibration. Therefore, in this paper, we propose a novel approach to effectively integrate uncertainty-based active learning and LoRA. Specifically, for the uncertainty gap, we introduce a dynamic uncertainty measurement that combines the uncertainty of the base model and the uncertainty of the full model during the iteration of active learning. For poor model calibration, we incorporate the regularization method during LoRA training to keep the model from being over-confident, and the Monte-Carlo dropout mechanism is employed to enhance the uncertainty estimation. Experimental results show that the proposed approach outperforms existing baseline models on three complex reasoning tasks.

Domain constraints improve risk prediction when outcome data is missing

Machine learning models are often trained to predict the outcome resulting from a human decision. For example, if a doctor decides to test a patient for disease, will the patient test positive? A challenge is that historical decision-making determines whether the outcome is observed: we only observe test outcomes for patients doctors historically tested. Untested patients, for whom outcomes are unobserved, may differ from tested patients along observed and unobserved dimensions. We propose a Bayesian model class which captures this setting. The purpose of the model is to accurately estimate risk for both tested and untested patients. Estimating this model is challenging due to the wide range of possibilities for untested patients. To address this, we propose two domain constraints which are plausible in health settings: a prevalence constraint, where the overall disease prevalence is known, and an expertise constraint, where the human decision-maker deviates from purely risk-based decision-making only along a constrained feature set. We show theoretically and on synthetic data that domain constraints improve parameter inference. We apply our model to a case study of cancer risk prediction, showing that the model's inferred risk predicts cancer diagnoses, its inferred testing policy captures known public health policies, and it can identify suboptimalities in test allocation. Though our case study is in healthcare, our analysis reveals a general class of domain constraints which can improve model estimation in many settings.

Exploring Cross-Cultural Differences in English Hate Speech Annotations: From Dataset Construction to Analysis

Warning: this paper contains content that may be offensive or upsetting. Most hate speech datasets neglect the cultural diversity within a single language, resulting in a critical shortcoming in hate speech detection. To address this, we introduce CREHate, a CRoss-cultural English Hate speech dataset. To construct CREHate, we follow a two-step procedure: 1) cultural post collection and 2) cross-cultural annotation. We sample posts from the SBIC dataset, which predominantly represents North America, and collect posts from four geographically diverse English-speaking countries (Australia, United Kingdom, Singapore, and South Africa) using culturally hateful keywords we retrieve from our survey. Annotations are collected from the four countries plus the United States to establish representative labels for each country. Our analysis highlights statistically significant disparities across countries in hate speech annotations. Only 56.2% of the posts in CREHate achieve consensus among all countries, with the highest pairwise label difference rate of 26%. Qualitative analysis shows that label disagreement occurs mostly due to different interpretations of sarcasm and the personal bias of annotators on divisive topics. Lastly, we evaluate large language models (LLMs) under a zero-shot setting and show that current LLMs tend to show higher accuracies on Anglosphere country labels in CREHate. Our dataset and codes are available at: https://github.com/nlee0212/CREHate

Dynamic Constrained Submodular Optimization with Polylogarithmic Update Time

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagation

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to small networks. In this paper, we develop an efficient framework for computing the ell_infty local Lipschitz constant of a neural network by tightly upper bounding the norm of Clarke Jacobian via linear bound propagation. We formulate the computation of local Lipschitz constants with a linear bound propagation process on a high-order backward graph induced by the chain rule of Clarke Jacobian. To enable linear bound propagation, we derive tight linear relaxations for specific nonlinearities in Clarke Jacobian. This formulate unifies existing ad-hoc approaches such as RecurJac, which can be seen as a special case of ours with weaker relaxations. The bound propagation framework also allows us to easily borrow the popular Branch-and-Bound (BaB) approach from neural network verification to further tighten Lipschitz constants. Experiments show that on tiny models, our method produces comparable bounds compared to exact methods that cannot scale to slightly larger models; on larger models, our method efficiently produces tighter results than existing relaxed or naive methods, and our method scales to much larger practical models that previous works could not handle. We also demonstrate an application on provable monotonicity analysis. Code is available at https://github.com/shizhouxing/Local-Lipschitz-Constants.

Learning Discrete Representations via Constrained Clustering for Effective and Efficient Dense Retrieval

Dense Retrieval (DR) has achieved state-of-the-art first-stage ranking effectiveness. However, the efficiency of most existing DR models is limited by the large memory cost of storing dense vectors and the time-consuming nearest neighbor search (NNS) in vector space. Therefore, we present RepCONC, a novel retrieval model that learns discrete Representations via CONstrained Clustering. RepCONC jointly trains dual-encoders and the Product Quantization (PQ) method to learn discrete document representations and enables fast approximate NNS with compact indexes. It models quantization as a constrained clustering process, which requires the document embeddings to be uniformly clustered around the quantization centroids and supports end-to-end optimization of the quantization method and dual-encoders. We theoretically demonstrate the importance of the uniform clustering constraint in RepCONC and derive an efficient approximate solution for constrained clustering by reducing it to an instance of the optimal transport problem. Besides constrained clustering, RepCONC further adopts a vector-based inverted file system (IVF) to support highly efficient vector search on CPUs. Extensive experiments on two popular ad-hoc retrieval benchmarks show that RepCONC achieves better ranking effectiveness than competitive vector quantization baselines under different compression ratio settings. It also substantially outperforms a wide range of existing retrieval models in terms of retrieval effectiveness, memory efficiency, and time efficiency.