On the biases and asymptotics of partitions with finite choices of parts

Biases in integer partitions have been studied recently. For three disjoint subsets $R,S,I$ of positive integers, let $p_{RSI}(n)$ be the number of partitions of $n$ with parts from $R\cup S\cup I$ and $p_{R>S,I}(n)$ be the number of such partitions with more parts from $R$ than that from $S$. In this paper, in the case that $R,S,I$ are finite we obtain a concrete formula of the asymptotic ratio of $p_{R>S,I}(n)$ to $p_{RSI}(n)$. We also propose a conjecture in the case that $R,S$ are certain infinite arithmetic progressions.Comment: 15 page

SnAG: Scalable and Accurate Video Grounding

Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability -- they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is 43% more accurate and 1.5x faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos.Comment: Accepted to CVPR 2024. Code available at https://github.com/fmu2/snag_releas

MAT: A Multi-strength Adversarial Training Method to Mitigate Adversarial Attacks

Some recent works revealed that deep neural networks (DNNs) are vulnerable to so-called adversarial attacks where input examples are intentionally perturbed to fool DNNs. In this work, we revisit the DNN training process that includes adversarial examples into the training dataset so as to improve DNN's resilience to adversarial attacks, namely, adversarial training. Our experiments show that different adversarial strengths, i.e., perturbation levels of adversarial examples, have different working zones to resist the attack. Based on the observation, we propose a multi-strength adversarial training method (MAT) that combines the adversarial training examples with different adversarial strengths to defend adversarial attacks. Two training structures - mixed MAT and parallel MAT - are developed to facilitate the tradeoffs between training time and memory occupation. Our results show that MAT can substantially minimize the accuracy degradation of deep learning systems to adversarial attacks on MNIST, CIFAR-10, CIFAR-100, and SVHN.Comment: 6 pages, 4 figures, 2 table

NeRFCodec: Neural Feature Compression Meets Neural Radiance Fields for Memory-Efficient Scene Representation

The emergence of Neural Radiance Fields (NeRF) has greatly impacted 3D scene modeling and novel-view synthesis. As a kind of visual media for 3D scene representation, compression with high rate-distortion performance is an eternal target. Motivated by advances in neural compression and neural field representation, we propose NeRFCodec, an end-to-end NeRF compression framework that integrates non-linear transform, quantization, and entropy coding for memory-efficient scene representation. Since training a non-linear transform directly on a large scale of NeRF feature planes is impractical, we discover that pre-trained neural 2D image codec can be utilized for compressing the features when adding content-specific parameters. Specifically, we reuse neural 2D image codec but modify its encoder and decoder heads, while keeping the other parts of the pre-trained decoder frozen. This allows us to train the full pipeline via supervision of rendering loss and entropy loss, yielding the rate-distortion balance by updating the content-specific parameters. At test time, the bitstreams containing latent code, feature decoder head, and other side information are transmitted for communication. Experimental results demonstrate our method outperforms existing NeRF compression methods, enabling high-quality novel view synthesis with a memory budget of 0.5 MB.Comment: Accepted at CVPR2024. The source code will be release

Receptivity of a supersonic jet due to acoustic excitations near the nozzle lip

In this paper, we develop an analytical model to investigate the generation of instability waves triggered by the upstream acoustic forcing near the nozzle lip of a supersonic jet. This represents an important stage, i.e. the jet receptivity, of the screech feedback loop. The upstream acoustic forcing, resulting from the shock-instability interaction, reaches the nozzle lip and excites new shear-layer instability waves. To obtain the newly-excited instability wave, we first determine the scattered sound field due to the upstream forcing using the Wiener-Hopf technique, with the kernel function factored using asymptotic expansions and overlapping approximations. Subsequently, the unsteady Kutta condition is imposed at the nozzle lip, enabling the derivation of the dispersion relation for the newly-excited instability wave. A linear transfer function between the upstream forcing and the newly-excited instability wave is obtained. We calculate the amplitude and phase delay in this receptivity process and examine their variations against the frequency. The phase delay enables us to re-evaluate the phase condition for jet screech and propose a new frequency prediction model. The new model shows improved agreement between the predicted screech frequencies and the experimental data compared to classical models. It is hoped that this model may help in developing a full screech model.Comment: 33 pages, 11 figure

Towards Efficient Hardware Acceleration of Deep Neural Networks on FPGA

Deep neural network (DNN) has achieved remarkable success in many applications because of its powerful capability for data processing. Their performance in computer vision have matched and in some areas even surpassed human capabilities. Deep neural networks can capture complex nonlinear features; however this ability comes at the cost of high computational and memory requirements. State-of-art networks require billions of arithmetic operations and millions of parameters. The brute-force computing model of DNN often requires extremely large hardware resources, introducing severe concerns on its scalability running on traditional von Neumann architecture. The well-known memory wall, and latency brought by the long-range connectivity and communication of DNN severely constrain the computation efficiency of DNN. The acceleration techniques of DNN, either software or hardware, often suffer from poor hardware execution efficiency of the simplified model (software), or inevitable accuracy degradation and limited supportable algorithms (hardware), respectively. In order to preserve the inference accuracy and make the hardware implementation in a more efficient form, a close investigation to the hardware/software co-design methodologies for DNNs is needed. The proposed work first presents an FPGA-based implementation framework for Recurrent Neural Network (RNN) acceleration. At architectural level, we improve the parallelism of RNN training scheme and reduce the computing resource requirement for computation efficiency enhancement. The hardware implementation primarily targets at reducing data communication load. Secondly, we propose a data locality-aware sparse matrix and vector multiplication (SpMV) kernel. At software level, we reorganize a large sparse matrix into many modest-sized blocks by adopting hypergraph-based partitioning and clustering. Available hardware constraints have been taken into consideration for the memory allocation and data access regularization. Thirdly, we present a holistic acceleration to sparse convolutional neural network (CNN). During network training, the data locality is regularized to ease the hardware mapping. The distributed architecture enables high computation parallelism and data reuse. The proposed research results in an hardware/software co-design methodology for fast and accurate DNN acceleration, through the innovations in algorithm optimization, hardware implementation, and the interactive design process across these two domains

A study of energy correction for the electron beam data in the BGO ECAL of the DAMPE

The DArk Matter Particle Explorer (DAMPE) is an orbital experiment aiming at searching for dark matter indirectly by measuring the spectra of photons, electrons and positrons originating from deep space. The BGO electromagnetic calorimeter is one of the key sub-detectors of the DAMPE, which is designed for high energy measurement with a large dynamic range from 5 GeV to 10 TeV. In this paper, some methods for energy correction are discussed and tried, in order to reconstruct the primary energy of the incident electrons. Different methods are chosen for the appropriate energy ranges. The results of Geant4 simulation and beam test data (at CERN) are presented