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Jun 4

CFMDCTCodec: A Low-Bitrate Neural Speech Codec with Noise-Prior-aware Conditional Flow Matching for MDCT-Spectral Enhancement

High-quality speech coding at low bitrates is crucial for bandwidth-constrained applications, yet remains challenging due to the severe loss of quality-critical information in highly compressed representations. To overcome this challenge, we propose CFMDCTCodec, a low-bitrate neural speech codec that operates entirely in the modified discrete cosine transform (MDCT) domain. CFMDCTCodec integrates a lightweight encoder-quantizer-decoder-style MDCT-spectral codec with a noise-prior-aware, conditional-flow-matching (CFM)-based MDCT-spectral enhancer. Within this framework, the codec serves as a base module that compactly discretizes the MDCT spectrum extracted from speech and produces an initial coarse reconstruction, while the enhancer further restores fine-grained spectral details. The enhancer improves the decoded MDCT spectrum by integrating a conditional MDCT velocity-field filter with an ordinary differential equation (ODE) solver, under the guidance of an MDCT-derived magnitude-adaptive noise prior, aiming to emphasize perceptually significant high-energy regions while stabilizing low-energy and silent regions. Finally, the enhanced MDCT spectrum is reconstructed into the decoded speech using the inverse MDCT. When optimizing CFMDCTCodec, we adopt a unified non-adversarial training strategy that jointly combines reconstruction, quantization and CFM objectives. Both objective and subjective evaluations show that CFMDCTCodec outperforms competitive baselines in low-bitrate regimes, e.g., 0.65 kbps, while approaching the perceptual quality of large-scale codecs with significantly fewer parameters and computations.

  • 5 authors
·
May 26

UltraFlux: Data-Model Co-Design for High-quality Native 4K Text-to-Image Generation across Diverse Aspect Ratios

Diffusion transformers have recently delivered strong text-to-image generation around 1K resolution, but we show that extending them to native 4K across diverse aspect ratios exposes a tightly coupled failure mode spanning positional encoding, VAE compression, and optimization. Tackling any of these factors in isolation leaves substantial quality on the table. We therefore take a data-model co-design view and introduce UltraFlux, a Flux-based DiT trained natively at 4K on MultiAspect-4K-1M, a 1M-image 4K corpus with controlled multi-AR coverage, bilingual captions, and rich VLM/IQA metadata for resolution- and AR-aware sampling. On the model side, UltraFlux couples (i) Resonance 2D RoPE with YaRN for training-window-, frequency-, and AR-aware positional encoding at 4K; (ii) a simple, non-adversarial VAE post-training scheme that improves 4K reconstruction fidelity; (iii) an SNR-Aware Huber Wavelet objective that rebalances gradients across timesteps and frequency bands; and (iv) a Stage-wise Aesthetic Curriculum Learning strategy that concentrates high-aesthetic supervision on high-noise steps governed by the model prior. Together, these components yield a stable, detail-preserving 4K DiT that generalizes across wide, square, and tall ARs. On the Aesthetic-Eval at 4096 benchmark and multi-AR 4K settings, UltraFlux consistently outperforms strong open-source baselines across fidelity, aesthetic, and alignment metrics, and-with a LLM prompt refiner-matches or surpasses the proprietary Seedream 4.0.

W2GenAI W2GenAI Lab
·
Nov 22, 2025 2

Efficient Global Optimization of Two-layer ReLU Networks: Quadratic-time Algorithms and Adversarial Training

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, is simpler to implement. It solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

  • 3 authors
·
Jan 6, 2022

Adversarial Training for Defense Against Label Poisoning Attacks

As machine learning models grow in complexity and increasingly rely on publicly sourced data, such as the human-annotated labels used in training large language models, they become more vulnerable to label poisoning attacks. These attacks, in which adversaries subtly alter the labels within a training dataset, can severely degrade model performance, posing significant risks in critical applications. In this paper, we propose FLORAL, a novel adversarial training defense strategy based on support vector machines (SVMs) to counter these threats. Utilizing a bilevel optimization framework, we cast the training process as a non-zero-sum Stackelberg game between an attacker, who strategically poisons critical training labels, and the model, which seeks to recover from such attacks. Our approach accommodates various model architectures and employs a projected gradient descent algorithm with kernel SVMs for adversarial training. We provide a theoretical analysis of our algorithm's convergence properties and empirically evaluate FLORAL's effectiveness across diverse classification tasks. Compared to robust baselines and foundation models such as RoBERTa, FLORAL consistently achieves higher robust accuracy under increasing attacker budgets. These results underscore the potential of FLORAL to enhance the resilience of machine learning models against label poisoning threats, thereby ensuring robust classification in adversarial settings.

  • 3 authors
·
Feb 24, 2025

Improving Generalization of Adversarial Training via Robust Critical Fine-Tuning

Deep neural networks are susceptible to adversarial examples, posing a significant security risk in critical applications. Adversarial Training (AT) is a well-established technique to enhance adversarial robustness, but it often comes at the cost of decreased generalization ability. This paper proposes Robustness Critical Fine-Tuning (RiFT), a novel approach to enhance generalization without compromising adversarial robustness. The core idea of RiFT is to exploit the redundant capacity for robustness by fine-tuning the adversarially trained model on its non-robust-critical module. To do so, we introduce module robust criticality (MRC), a measure that evaluates the significance of a given module to model robustness under worst-case weight perturbations. Using this measure, we identify the module with the lowest MRC value as the non-robust-critical module and fine-tune its weights to obtain fine-tuned weights. Subsequently, we linearly interpolate between the adversarially trained weights and fine-tuned weights to derive the optimal fine-tuned model weights. We demonstrate the efficacy of RiFT on ResNet18, ResNet34, and WideResNet34-10 models trained on CIFAR10, CIFAR100, and Tiny-ImageNet datasets. Our experiments show that \method can significantly improve both generalization and out-of-distribution robustness by around 1.5% while maintaining or even slightly enhancing adversarial robustness. Code is available at https://github.com/microsoft/robustlearn.

  • 5 authors
·
Aug 1, 2023

Doubly Robust Instance-Reweighted Adversarial Training

Assigning importance weights to adversarial data has achieved great success in training adversarially robust networks under limited model capacity. However, existing instance-reweighted adversarial training (AT) methods heavily depend on heuristics and/or geometric interpretations to determine those importance weights, making these algorithms lack rigorous theoretical justification/guarantee. Moreover, recent research has shown that adversarial training suffers from a severe non-uniform robust performance across the training distribution, e.g., data points belonging to some classes can be much more vulnerable to adversarial attacks than others. To address both issues, in this paper, we propose a novel doubly-robust instance reweighted AT framework, which allows to obtain the importance weights via exploring distributionally robust optimization (DRO) techniques, and at the same time boosts the robustness on the most vulnerable examples. In particular, our importance weights are obtained by optimizing the KL-divergence regularized loss function, which allows us to devise new algorithms with a theoretical convergence guarantee. Experiments on standard classification datasets demonstrate that our proposed approach outperforms related state-of-the-art baseline methods in terms of average robust performance, and at the same time improves the robustness against attacks on the weakest data points. Codes will be available soon.

  • 4 authors
·
Aug 1, 2023

Joint rotational invariance and adversarial training of a dual-stream Transformer yields state of the art Brain-Score for Area V4

Modern high-scoring models of vision in the brain score competition do not stem from Vision Transformers. However, in this paper, we provide evidence against the unexpected trend of Vision Transformers (ViT) being not perceptually aligned with human visual representations by showing how a dual-stream Transformer, a CrossViT~a la Chen et al. (2021), under a joint rotationally-invariant and adversarial optimization procedure yields 2nd place in the aggregate Brain-Score 2022 competition(Schrimpf et al., 2020b) averaged across all visual categories, and at the time of the competition held 1st place for the highest explainable variance of area V4. In addition, our current Transformer-based model also achieves greater explainable variance for areas V4, IT and Behaviour than a biologically-inspired CNN (ResNet50) that integrates a frontal V1-like computation module (Dapello et al.,2020). To assess the contribution of the optimization scheme with respect to the CrossViT architecture, we perform several additional experiments on differently optimized CrossViT's regarding adversarial robustness, common corruption benchmarks, mid-ventral stimuli interpretation and feature inversion. Against our initial expectations, our family of results provides tentative support for an "All roads lead to Rome" argument enforced via a joint optimization rule even for non biologically-motivated models of vision such as Vision Transformers. Code is available at https://github.com/williamberrios/BrainScore-Transformers

  • 2 authors
·
Mar 8, 2022

Improved Training Technique for Shortcut Models

Shortcut models represent a promising, non-adversarial paradigm for generative modeling, uniquely supporting one-step, few-step, and multi-step sampling from a single trained network. However, their widespread adoption has been stymied by critical performance bottlenecks. This paper tackles the five core issues that held shortcut models back: (1) the hidden flaw of compounding guidance, which we are the first to formalize, causing severe image artifacts; (2) inflexible fixed guidance that restricts inference-time control; (3) a pervasive frequency bias driven by a reliance on low-level distances in the direct domain, which biases reconstructions toward low frequencies; (4) divergent self-consistency arising from a conflict with EMA training; and (5) curvy flow trajectories that impede convergence. To address these challenges, we introduce iSM, a unified training framework that systematically resolves each limitation. Our framework is built on four key improvements: Intrinsic Guidance provides explicit, dynamic control over guidance strength, resolving both compounding guidance and inflexibility. A Multi-Level Wavelet Loss mitigates frequency bias to restore high-frequency details. Scaling Optimal Transport (sOT) reduces training variance and learns straighter, more stable generative paths. Finally, a Twin EMA strategy reconciles training stability with self-consistency. Extensive experiments on ImageNet 256 x 256 demonstrate that our approach yields substantial FID improvements over baseline shortcut models across one-step, few-step, and multi-step generation, making shortcut models a viable and competitive class of generative models.

  • 7 authors
·
Oct 24, 2025

XFACTORS: Disentangled Information Bottleneck via Contrastive Supervision

Disentangled representation learning aims to map independent factors of variation to independent representation components. On one hand, purely unsupervised approaches have proven successful on fully disentangled synthetic data, but fail to recover semantic factors from real data without strong inductive biases. On the other hand, supervised approaches are unstable and hard to scale to large attribute sets because they rely on adversarial objectives or auxiliary classifiers. We introduce XFactors, a weakly-supervised VAE framework that disentangles and provides explicit control over a chosen set of factors. Building on the Disentangled Information Bottleneck perspective, we decompose the representation into a residual subspace S and factor-specific subspaces T_1,ldots,T_K and a residual subspace S. Each target factor is encoded in its assigned T_i through contrastive supervision: an InfoNCE loss pulls together latents sharing the same factor value and pushes apart mismatched pairs. In parallel, KL regularization imposes a Gaussian structure on both S and the aggregated factor subspaces, organizing the geometry without additional supervision for non-targeted factors and avoiding adversarial training and classifiers. Across multiple datasets, with constant hyperparameters, XFactors achieves state-of-the-art disentanglement scores and yields consistent qualitative factor alignment in the corresponding subspaces, enabling controlled factor swapping via latent replacement. We further demonstrate that our method scales correctly with increasing latent capacity and evaluate it on the real-world dataset CelebA. Our code is available at https://github.com/ICML26-anon/XFactors{github.com/ICML26-anon/XFactors}.

  • 6 authors
·
Jan 29

Reinforced Disentanglement for Face Swapping without Skip Connection

The SOTA face swap models still suffer the problem of either target identity (i.e., shape) being leaked or the target non-identity attributes (i.e., background, hair) failing to be fully preserved in the final results. We show that this insufficient disentanglement is caused by two flawed designs that were commonly adopted in prior models: (1) counting on only one compressed encoder to represent both the semantic-level non-identity facial attributes(i.e., pose) and the pixel-level non-facial region details, which is contradictory to satisfy at the same time; (2) highly relying on long skip-connections between the encoder and the final generator, leaking a certain amount of target face identity into the result. To fix them, we introduce a new face swap framework called 'WSC-swap' that gets rid of skip connections and uses two target encoders to respectively capture the pixel-level non-facial region attributes and the semantic non-identity attributes in the face region. To further reinforce the disentanglement learning for the target encoder, we employ both identity removal loss via adversarial training (i.e., GAN) and the non-identity preservation loss via prior 3DMM models like [11]. Extensive experiments on both FaceForensics++ and CelebA-HQ show that our results significantly outperform previous works on a rich set of metrics, including one novel metric for measuring identity consistency that was completely neglected before.

  • 5 authors
·
Jul 15, 2023

DiffRenderGAN: Addressing Training Data Scarcity in Deep Segmentation Networks for Quantitative Nanomaterial Analysis through Differentiable Rendering and Generative Modelling

Nanomaterials exhibit distinctive properties governed by parameters such as size, shape, and surface characteristics, which critically influence their applications and interactions across technological, biological, and environmental contexts. Accurate quantification and understanding of these materials are essential for advancing research and innovation. In this regard, deep learning segmentation networks have emerged as powerful tools that enable automated insights and replace subjective methods with precise quantitative analysis. However, their efficacy depends on representative annotated datasets, which are challenging to obtain due to the costly imaging of nanoparticles and the labor-intensive nature of manual annotations. To overcome these limitations, we introduce DiffRenderGAN, a novel generative model designed to produce annotated synthetic data. By integrating a differentiable renderer into a Generative Adversarial Network (GAN) framework, DiffRenderGAN optimizes textural rendering parameters to generate realistic, annotated nanoparticle images from non-annotated real microscopy images. This approach reduces the need for manual intervention and enhances segmentation performance compared to existing synthetic data methods by generating diverse and realistic data. Tested on multiple ion and electron microscopy cases, including titanium dioxide (TiO_2), silicon dioxide (SiO_2)), and silver nanowires (AgNW), DiffRenderGAN bridges the gap between synthetic and real data, advancing the quantification and understanding of complex nanomaterial systems.

  • 14 authors
·
Feb 13, 2025

Contrastive Learning with Adversarial Perturbations for Conditional Text Generation

Recently, sequence-to-sequence (seq2seq) models with the Transformer architecture have achieved remarkable performance on various conditional text generation tasks, such as machine translation. However, most of them are trained with teacher forcing with the ground truth label given at each time step, without being exposed to incorrectly generated tokens during training, which hurts its generalization to unseen inputs, that is known as the "exposure bias" problem. In this work, we propose to mitigate the conditional text generation problem by contrasting positive pairs with negative pairs, such that the model is exposed to various valid or incorrect perturbations of the inputs, for improved generalization. However, training the model with naive contrastive learning framework using random non-target sequences as negative examples is suboptimal, since they are easily distinguishable from the correct output, especially so with models pretrained with large text corpora. Also, generating positive examples requires domain-specific augmentation heuristics which may not generalize over diverse domains. To tackle this problem, we propose a principled method to generate positive and negative samples for contrastive learning of seq2seq models. Specifically, we generate negative examples by adding small perturbations to the input sequence to minimize its conditional likelihood, and positive examples by adding large perturbations while enforcing it to have a high conditional likelihood. Such "hard" positive and negative pairs generated using our method guides the model to better distinguish correct outputs from incorrect ones. We empirically show that our proposed method significantly improves the generalization of the seq2seq on three text generation tasks - machine translation, text summarization, and question generation.

  • 3 authors
·
Dec 14, 2020

Beyond Worst-case Attacks: Robust RL with Adaptive Defense via Non-dominated Policies

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches largely revolve around solving a minimax problem to prepare for potential worst-case scenarios. While effective against strong attacks, these methods often compromise performance in the absence of attacks or the presence of only weak attacks. To address this, we study policy robustness under the well-accepted state-adversarial attack model, extending our focus beyond only worst-case attacks. We first formalize this task at test time as a regret minimization problem and establish its intrinsic hardness in achieving sublinear regret when the baseline policy is from a general continuous policy class, Pi. This finding prompts us to refine the baseline policy class Pi prior to test time, aiming for efficient adaptation within a finite policy class Pi, which can resort to an adversarial bandit subroutine. In light of the importance of a small, finite Pi, we propose a novel training-time algorithm to iteratively discover non-dominated policies, forming a near-optimal and minimal Pi, thereby ensuring both robustness and test-time efficiency. Empirical validation on the Mujoco corroborates the superiority of our approach in terms of natural and robust performance, as well as adaptability to various attack scenarios.

  • 5 authors
·
Feb 19, 2024

Adversarially Regularising Neural NLI Models to Integrate Logical Background Knowledge

Adversarial examples are inputs to machine learning models designed to cause the model to make a mistake. They are useful for understanding the shortcomings of machine learning models, interpreting their results, and for regularisation. In NLP, however, most example generation strategies produce input text by using known, pre-specified semantic transformations, requiring significant manual effort and in-depth understanding of the problem and domain. In this paper, we investigate the problem of automatically generating adversarial examples that violate a set of given First-Order Logic constraints in Natural Language Inference (NLI). We reduce the problem of identifying such adversarial examples to a combinatorial optimisation problem, by maximising a quantity measuring the degree of violation of such constraints and by using a language model for generating linguistically-plausible examples. Furthermore, we propose a method for adversarially regularising neural NLI models for incorporating background knowledge. Our results show that, while the proposed method does not always improve results on the SNLI and MultiNLI datasets, it significantly and consistently increases the predictive accuracy on adversarially-crafted datasets -- up to a 79.6% relative improvement -- while drastically reducing the number of background knowledge violations. Furthermore, we show that adversarial examples transfer among model architectures, and that the proposed adversarial training procedure improves the robustness of NLI models to adversarial examples.

  • 2 authors
·
Aug 25, 2018

NoProp: Training Neural Networks without Back-propagation or Forward-propagation

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

  • 3 authors
·
Mar 31, 2025

Robust Training Using Natural Transformation

Previous robustness approaches for deep learning models such as data augmentation techniques via data transformation or adversarial training cannot capture real-world variations that preserve the semantics of the input, such as a change in lighting conditions. To bridge this gap, we present NaTra, an adversarial training scheme that is designed to improve the robustness of image classification algorithms. We target attributes of the input images that are independent of the class identification, and manipulate those attributes to mimic real-world natural transformations (NaTra) of the inputs, which are then used to augment the training dataset of the image classifier. Specifically, we apply Batch Inverse Encoding and Shifting to map a batch of given images to corresponding disentangled latent codes of well-trained generative models. Latent Codes Expansion is used to boost image reconstruction quality through the incorporation of extended feature maps. Unsupervised Attribute Directing and Manipulation enables identification of the latent directions that correspond to specific attribute changes, and then produce interpretable manipulations of those attributes, thereby generating natural transformations to the input data. We demonstrate the efficacy of our scheme by utilizing the disentangled latent representations derived from well-trained GANs to mimic transformations of an image that are similar to real-world natural variations (such as lighting conditions or hairstyle), and train models to be invariant to these natural transformations. Extensive experiments show that our method improves generalization of classification models and increases its robustness to various real-world distortions

  • 6 authors
·
May 9, 2021

Mitigating the Accuracy-Robustness Trade-off via Multi-Teacher Adversarial Distillation

Adversarial training is a practical approach for improving the robustness of deep neural networks against adversarial attacks. Although bringing reliable robustness, the performance toward clean examples is negatively affected after adversarial training, which means a trade-off exists between accuracy and robustness. Recently, some studies have tried to use knowledge distillation methods in adversarial training, achieving competitive performance in improving the robustness but the accuracy for clean samples is still limited. In this paper, to mitigate the accuracy-robustness trade-off, we introduce the Multi-Teacher Adversarial Robustness Distillation (MTARD) to guide the model's adversarial training process by applying a strong clean teacher and a strong robust teacher to handle the clean examples and adversarial examples, respectively. During the optimization process, to ensure that different teachers show similar knowledge scales, we design the Entropy-Based Balance algorithm to adjust the teacher's temperature and keep the teachers' information entropy consistent. Besides, to ensure that the student has a relatively consistent learning speed from multiple teachers, we propose the Normalization Loss Balance algorithm to adjust the learning weights of different types of knowledge. A series of experiments conducted on public datasets demonstrate that MTARD outperforms the state-of-the-art adversarial training and distillation methods against various adversarial attacks.

  • 3 authors
·
Jun 28, 2023

Adversarial Training for High-Stakes Reliability

In the future, powerful AI systems may be deployed in high-stakes settings, where a single failure could be catastrophic. One technique for improving AI safety in high-stakes settings is adversarial training, which uses an adversary to generate examples to train on in order to achieve better worst-case performance. In this work, we used a safe language generation task (``avoid injuries'') as a testbed for achieving high reliability through adversarial training. We created a series of adversarial training techniques -- including a tool that assists human adversaries -- to find and eliminate failures in a classifier that filters text completions suggested by a generator. In our task, we determined that we can set very conservative classifier thresholds without significantly impacting the quality of the filtered outputs. We found that adversarial training increased robustness to the adversarial attacks that we trained on -- doubling the time for our contractors to find adversarial examples both with our tool (from 13 to 26 minutes) and without (from 20 to 44 minutes) -- without affecting in-distribution performance. We hope to see further work in the high-stakes reliability setting, including more powerful tools for enhancing human adversaries and better ways to measure high levels of reliability, until we can confidently rule out the possibility of catastrophic deployment-time failures of powerful models.

  • 12 authors
·
May 3, 2022

Efficient Adversarial Training in LLMs with Continuous Attacks

Large language models (LLMs) are vulnerable to adversarial attacks that can bypass their safety guardrails. In many domains, adversarial training has proven to be one of the most promising methods to reliably improve robustness against such attacks. Yet, in the context of LLMs, current methods for adversarial training are hindered by the high computational costs required to perform discrete adversarial attacks at each training iteration. We address this problem by instead calculating adversarial attacks in the continuous embedding space of the LLM, which is orders of magnitudes more efficient. We propose a fast adversarial training algorithm (C-AdvUL) composed of two losses: the first makes the model robust on continuous embedding attacks computed on an adversarial behaviour dataset; the second ensures the usefulness of the final model by fine-tuning on utility data. Moreover, we introduce C-AdvIPO, an adversarial variant of IPO that does not require utility data for adversarially robust alignment. Our empirical evaluation on four models from different families (Gemma, Phi3, Mistral, Zephyr) and at different scales (2B, 3.8B, 7B) shows that both algorithms substantially enhance LLM robustness against discrete attacks (GCG, AutoDAN, PAIR), while maintaining utility. Our results demonstrate that robustness to continuous perturbations can extrapolate to discrete threat models. Thereby, we present a path toward scalable adversarial training algorithms for robustly aligning LLMs.

  • 5 authors
·
May 24, 2024

Imbalanced Adversarial Training with Reweighting

Adversarial training has been empirically proven to be one of the most effective and reliable defense methods against adversarial attacks. However, almost all existing studies about adversarial training are focused on balanced datasets, where each class has an equal amount of training examples. Research on adversarial training with imbalanced training datasets is rather limited. As the initial effort to investigate this problem, we reveal the facts that adversarially trained models present two distinguished behaviors from naturally trained models in imbalanced datasets: (1) Compared to natural training, adversarially trained models can suffer much worse performance on under-represented classes, when the training dataset is extremely imbalanced. (2) Traditional reweighting strategies may lose efficacy to deal with the imbalance issue for adversarial training. For example, upweighting the under-represented classes will drastically hurt the model's performance on well-represented classes, and as a result, finding an optimal reweighting value can be tremendously challenging. In this paper, to further understand our observations, we theoretically show that the poor data separability is one key reason causing this strong tension between under-represented and well-represented classes. Motivated by this finding, we propose Separable Reweighted Adversarial Training (SRAT) to facilitate adversarial training under imbalanced scenarios, by learning more separable features for different classes. Extensive experiments on various datasets verify the effectiveness of the proposed framework.

  • 6 authors
·
Jul 28, 2021

All You Need is RAW: Defending Against Adversarial Attacks with Camera Image Pipelines

Existing neural networks for computer vision tasks are vulnerable to adversarial attacks: adding imperceptible perturbations to the input images can fool these methods to make a false prediction on an image that was correctly predicted without the perturbation. Various defense methods have proposed image-to-image mapping methods, either including these perturbations in the training process or removing them in a preprocessing denoising step. In doing so, existing methods often ignore that the natural RGB images in today's datasets are not captured but, in fact, recovered from RAW color filter array captures that are subject to various degradations in the capture. In this work, we exploit this RAW data distribution as an empirical prior for adversarial defense. Specifically, we proposed a model-agnostic adversarial defensive method, which maps the input RGB images to Bayer RAW space and back to output RGB using a learned camera image signal processing (ISP) pipeline to eliminate potential adversarial patterns. The proposed method acts as an off-the-shelf preprocessing module and, unlike model-specific adversarial training methods, does not require adversarial images to train. As a result, the method generalizes to unseen tasks without additional retraining. Experiments on large-scale datasets (e.g., ImageNet, COCO) for different vision tasks (e.g., classification, semantic segmentation, object detection) validate that the method significantly outperforms existing methods across task domains.

  • 3 authors
·
Dec 16, 2021

RAMP: Boosting Adversarial Robustness Against Multiple l_p Perturbations for Universal Robustness

Most existing works focus on improving robustness against adversarial attacks bounded by a single l_p norm using adversarial training (AT). However, these AT models' multiple-norm robustness (union accuracy) is still low, which is crucial since in the real-world an adversary is not necessarily bounded by a single norm. The tradeoffs among robustness against multiple l_p perturbations and accuracy/robustness make obtaining good union and clean accuracy challenging. We design a logit pairing loss to improve the union accuracy by analyzing the tradeoffs from the lens of distribution shifts. We connect natural training (NT) with AT via gradient projection, to incorporate useful information from NT into AT, where we empirically and theoretically show it moderates the accuracy/robustness tradeoff. We propose a novel training framework RAMP, to boost the robustness against multiple l_p perturbations. RAMP can be easily adapted for robust fine-tuning and full AT. For robust fine-tuning, RAMP obtains a union accuracy up to 53.3% on CIFAR-10, and 29.1% on ImageNet. For training from scratch, RAMP achieves a union accuracy of 44.6% and good clean accuracy of 81.2% on ResNet-18 against AutoAttack on CIFAR-10. Beyond multi-norm robustness RAMP-trained models achieve superior universal robustness, effectively generalizing against a range of unseen adversaries and natural corruptions.

Hard No-Box Adversarial Attack on Skeleton-Based Human Action Recognition with Skeleton-Motion-Informed Gradient

Recently, methods for skeleton-based human activity recognition have been shown to be vulnerable to adversarial attacks. However, these attack methods require either the full knowledge of the victim (i.e. white-box attacks), access to training data (i.e. transfer-based attacks) or frequent model queries (i.e. black-box attacks). All their requirements are highly restrictive, raising the question of how detrimental the vulnerability is. In this paper, we show that the vulnerability indeed exists. To this end, we consider a new attack task: the attacker has no access to the victim model or the training data or labels, where we coin the term hard no-box attack. Specifically, we first learn a motion manifold where we define an adversarial loss to compute a new gradient for the attack, named skeleton-motion-informed (SMI) gradient. Our gradient contains information of the motion dynamics, which is different from existing gradient-based attack methods that compute the loss gradient assuming each dimension in the data is independent. The SMI gradient can augment many gradient-based attack methods, leading to a new family of no-box attack methods. Extensive evaluation and comparison show that our method imposes a real threat to existing classifiers. They also show that the SMI gradient improves the transferability and imperceptibility of adversarial samples in both no-box and transfer-based black-box settings.

  • 5 authors
·
Aug 10, 2023

Towards Robust Knowledge Unlearning: An Adversarial Framework for Assessing and Improving Unlearning Robustness in Large Language Models

LLM have achieved success in many fields but still troubled by problematic content in the training corpora. LLM unlearning aims at reducing their influence and avoid undesirable behaviours. However, existing unlearning methods remain vulnerable to adversarial queries and the unlearned knowledge resurfaces after the manually designed attack queries. As part of a red-team effort to proactively assess the vulnerabilities of unlearned models, we design Dynamic Unlearning Attack (DUA), a dynamic and automated framework to attack these models and evaluate their robustness. It optimizes adversarial suffixes to reintroduce the unlearned knowledge in various scenarios. We find that unlearned knowledge can be recovered in 55.2% of the questions, even without revealing the unlearned model's parameters. In response to this vulnerability, we propose Latent Adversarial Unlearning (LAU), a universal framework that effectively enhances the robustness of the unlearned process. It formulates the unlearning process as a min-max optimization problem and resolves it through two stages: an attack stage, where perturbation vectors are trained and added to the latent space of LLMs to recover the unlearned knowledge, and a defense stage, where previously trained perturbation vectors are used to enhance unlearned model's robustness. With our LAU framework, we obtain two robust unlearning methods, AdvGA and AdvNPO. We conduct extensive experiments across multiple unlearning benchmarks and various models, and demonstrate that they improve the unlearning effectiveness by over 53.5%, cause only less than a 11.6% reduction in neighboring knowledge, and have almost no impact on the model's general capabilities.

  • 6 authors
·
Aug 19, 2024

Joint Discriminative-Generative Modeling via Dual Adversarial Training

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but are often limited by the instability and poor sample quality inherent in SGLD-based training. We address these limitations by proposing a novel training framework that integrates adversarial training (AT) principles for both discriminative robustness and stable generative learning. The proposed method introduces three key innovations: (1) the replacement of SGLD-based JEM learning with a stable, AT-based approach that optimizes the energy function by discriminating between real data and PGD-generated contrastive samples using the BCE loss; (2) synergistic adversarial training for the discriminative component that enhances classification robustness while eliminating the need for explicit gradient penalties; and (3) a two-stage training procedure to resolve the incompatibility between batch normalization and EBM training. Experiments on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method substantially improves adversarial robustness over existing hybrid models while maintaining competitive generative performance. On ImageNet, when optimized for generative modeling, our model's generative fidelity surpasses that of BigGAN and approaches diffusion models, representing the first MCMC-based EBM approach to achieve high-quality generation on complex, high-resolution datasets. Our approach addresses key stability issues that have limited JEM scaling and demonstrates that adversarial training can serve as an effective foundation for unified frameworks capable of generating and robustly classifying visual data.

  • 5 authors
·
Oct 13, 2025

Negative Token Merging: Image-based Adversarial Feature Guidance

Text-based adversarial guidance using a negative prompt has emerged as a widely adopted approach to push the output features away from undesired concepts. While useful, performing adversarial guidance using text alone can be insufficient to capture complex visual concepts and avoid undesired visual elements like copyrighted characters. In this paper, for the first time we explore an alternate modality in this direction by performing adversarial guidance directly using visual features from a reference image or other images in a batch. In particular, we introduce negative token merging (NegToMe), a simple but effective training-free approach which performs adversarial guidance by selectively pushing apart matching semantic features (between reference and output generation) during the reverse diffusion process. When used w.r.t. other images in the same batch, we observe that NegToMe significantly increases output diversity (racial, gender, visual) without sacrificing output image quality. Similarly, when used w.r.t. a reference copyrighted asset, NegToMe helps reduce visual similarity with copyrighted content by 34.57%. NegToMe is simple to implement using just few-lines of code, uses only marginally higher (<4%) inference times and generalizes to different diffusion architectures like Flux, which do not natively support the use of a separate negative prompt. Code is available at https://negtome.github.io

  • 10 authors
·
Dec 2, 2024 6

Reliable Unlearning Harmful Information in LLMs with Metamorphosis Representation Projection

While Large Language Models (LLMs) have demonstrated impressive performance in various domains and tasks, concerns about their safety are becoming increasingly severe. In particular, since models may store unsafe knowledge internally, machine unlearning has emerged as a representative paradigm to ensure model safety. Existing approaches employ various training techniques, such as gradient ascent and negative preference optimization, in attempts to eliminate the influence of undesired data on target models. However, these methods merely suppress the activation of undesired data through parametric training without completely eradicating its informational traces within the model. This fundamental limitation makes it difficult to achieve effective continuous unlearning, rendering these methods vulnerable to relearning attacks. To overcome these challenges, we propose a Metamorphosis Representation Projection (MRP) approach that pioneers the application of irreversible projection properties to machine unlearning. By implementing projective transformations in the hidden state space of specific network layers, our method effectively eliminates harmful information while preserving useful knowledge. Experimental results demonstrate that our approach enables effective continuous unlearning and successfully defends against relearning attacks, achieving state-of-the-art performance in unlearning effectiveness while preserving natural performance. Our code is available in https://github.com/ChengcanWu/MRP.

  • 5 authors
·
Aug 21, 2025

Shedding More Light on Robust Classifiers under the lens of Energy-based Models

By reinterpreting a robust discriminative classifier as Energy-based Model (EBM), we offer a new take on the dynamics of adversarial training (AT). Our analysis of the energy landscape during AT reveals that untargeted attacks generate adversarial images much more in-distribution (lower energy) than the original data from the point of view of the model. Conversely, we observe the opposite for targeted attacks. On the ground of our thorough analysis, we present new theoretical and practical results that show how interpreting AT energy dynamics unlocks a better understanding: (1) AT dynamic is governed by three phases and robust overfitting occurs in the third phase with a drastic divergence between natural and adversarial energies (2) by rewriting the loss of TRadeoff-inspired Adversarial DEfense via Surrogate-loss minimization (TRADES) in terms of energies, we show that TRADES implicitly alleviates overfitting by means of aligning the natural energy with the adversarial one (3) we empirically show that all recent state-of-the-art robust classifiers are smoothing the energy landscape and we reconcile a variety of studies about understanding AT and weighting the loss function under the umbrella of EBMs. Motivated by rigorous evidence, we propose Weighted Energy Adversarial Training (WEAT), a novel sample weighting scheme that yields robust accuracy matching the state-of-the-art on multiple benchmarks such as CIFAR-10 and SVHN and going beyond in CIFAR-100 and Tiny-ImageNet. We further show that robust classifiers vary in the intensity and quality of their generative capabilities, and offer a simple method to push this capability, reaching a remarkable Inception Score (IS) and FID using a robust classifier without training for generative modeling. The code to reproduce our results is available at http://github.com/OmnAI-Lab/Robust-Classifiers-under-the-lens-of-EBM/ .

  • 4 authors
·
Jul 8, 2024

Bidirectional Learning for Robust Neural Networks

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. The learning process of BL tries to reproduce the neuroplasticity stated in Hebbian theory using only backward propagation of errors. In this paper, two novel learning techniques are introduced which use BL for improving robustness to white noise static and adversarial examples. The first method is bidirectional propagation of errors, which the error propagation occurs in backward and forward directions. Motivated by the fact that its generative model receives as input a constant vector per class, we introduce as a second method the hybrid adversarial networks (HAN). Its generative model receives a random vector as input and its training is based on generative adversarial networks (GAN). To assess the performance of BL, we perform experiments using several architectures with fully and convolutional layers, with and without bias. Experimental results show that both methods improve robustness to white noise static and adversarial examples, and even increase accuracy, but have different behavior depending on the architecture and task, being more beneficial to use the one or the other. Nevertheless, HAN using a convolutional architecture with batch normalization presents outstanding robustness, reaching state-of-the-art accuracy on adversarial examples of hand-written digits.

  • 2 authors
·
May 21, 2018

AccelAT: A Framework for Accelerating the Adversarial Training of Deep Neural Networks through Accuracy Gradient

Adversarial training is exploited to develop a robust Deep Neural Network (DNN) model against the malicious altered data. These attacks may have catastrophic effects on DNN models but are indistinguishable for a human being. For example, an external attack can modify an image adding noises invisible for a human eye, but a DNN model misclassified the image. A key objective for developing robust DNN models is to use a learning algorithm that is fast but can also give model that is robust against different types of adversarial attacks. Especially for adversarial training, enormously long training times are needed for obtaining high accuracy under many different types of adversarial samples generated using different adversarial attack techniques. This paper aims at accelerating the adversarial training to enable fast development of robust DNN models against adversarial attacks. The general method for improving the training performance is the hyperparameters fine-tuning, where the learning rate is one of the most crucial hyperparameters. By modifying its shape (the value over time) and value during the training, we can obtain a model robust to adversarial attacks faster than standard training. First, we conduct experiments on two different datasets (CIFAR10, CIFAR100), exploring various techniques. Then, this analysis is leveraged to develop a novel fast training methodology, AccelAT, which automatically adjusts the learning rate for different epochs based on the accuracy gradient. The experiments show comparable results with the related works, and in several experiments, the adversarial training of DNNs using our AccelAT framework is conducted up to 2 times faster than the existing techniques. Thus, our findings boost the speed of adversarial training in an era in which security and performance are fundamental optimization objectives in DNN-based applications.

  • 4 authors
·
Oct 13, 2022

I See Dead People: Gray-Box Adversarial Attack on Image-To-Text Models

Modern image-to-text systems typically adopt the encoder-decoder framework, which comprises two main components: an image encoder, responsible for extracting image features, and a transformer-based decoder, used for generating captions. Taking inspiration from the analysis of neural networks' robustness against adversarial perturbations, we propose a novel gray-box algorithm for creating adversarial examples in image-to-text models. Unlike image classification tasks that have a finite set of class labels, finding visually similar adversarial examples in an image-to-text task poses greater challenges because the captioning system allows for a virtually infinite space of possible captions. In this paper, we present a gray-box adversarial attack on image-to-text, both untargeted and targeted. We formulate the process of discovering adversarial perturbations as an optimization problem that uses only the image-encoder component, meaning the proposed attack is language-model agnostic. Through experiments conducted on the ViT-GPT2 model, which is the most-used image-to-text model in Hugging Face, and the Flickr30k dataset, we demonstrate that our proposed attack successfully generates visually similar adversarial examples, both with untargeted and targeted captions. Notably, our attack operates in a gray-box manner, requiring no knowledge about the decoder module. We also show that our attacks fool the popular open-source platform Hugging Face.

  • 2 authors
·
Jun 13, 2023

Model-tuning Via Prompts Makes NLP Models Adversarially Robust

In recent years, NLP practitioners have converged on the following practice: (i) import an off-the-shelf pretrained (masked) language model; (ii) append a multilayer perceptron atop the CLS token's hidden representation (with randomly initialized weights); and (iii) fine-tune the entire model on a downstream task (MLP-FT). This procedure has produced massive gains on standard NLP benchmarks, but these models remain brittle, even to mild adversarial perturbations. In this work, we demonstrate surprising gains in adversarial robustness enjoyed by Model-tuning Via Prompts (MVP), an alternative method of adapting to downstream tasks. Rather than appending an MLP head to make output prediction, MVP appends a prompt template to the input, and makes prediction via text infilling/completion. Across 5 NLP datasets, 4 adversarial attacks, and 3 different models, MVP improves performance against adversarial substitutions by an average of 8% over standard methods and even outperforms adversarial training-based state-of-art defenses by 3.5%. By combining MVP with adversarial training, we achieve further improvements in adversarial robustness while maintaining performance on unperturbed examples. Finally, we conduct ablations to investigate the mechanism underlying these gains. Notably, we find that the main causes of vulnerability of MLP-FT can be attributed to the misalignment between pre-training and fine-tuning tasks, and the randomly initialized MLP parameters.

  • 5 authors
·
Mar 13, 2023

RIGID: A Training-free and Model-Agnostic Framework for Robust AI-Generated Image Detection

The rapid advances in generative AI models have empowered the creation of highly realistic images with arbitrary content, raising concerns about potential misuse and harm, such as Deepfakes. Current research focuses on training detectors using large datasets of generated images. However, these training-based solutions are often computationally expensive and show limited generalization to unseen generated images. In this paper, we propose a training-free method to distinguish between real and AI-generated images. We first observe that real images are more robust to tiny noise perturbations than AI-generated images in the representation space of vision foundation models. Based on this observation, we propose RIGID, a training-free and model-agnostic method for robust AI-generated image detection. RIGID is a simple yet effective approach that identifies whether an image is AI-generated by comparing the representation similarity between the original and the noise-perturbed counterpart. Our evaluation on a diverse set of AI-generated images and benchmarks shows that RIGID significantly outperforms existing trainingbased and training-free detectors. In particular, the average performance of RIGID exceeds the current best training-free method by more than 25%. Importantly, RIGID exhibits strong generalization across different image generation methods and robustness to image corruptions.

  • 3 authors
·
May 30, 2024

CLIP is Strong Enough to Fight Back: Test-time Counterattacks towards Zero-shot Adversarial Robustness of CLIP

Despite its prevalent use in image-text matching tasks in a zero-shot manner, CLIP has been shown to be highly vulnerable to adversarial perturbations added onto images. Recent studies propose to finetune the vision encoder of CLIP with adversarial samples generated on the fly, and show improved robustness against adversarial attacks on a spectrum of downstream datasets, a property termed as zero-shot robustness. In this paper, we show that malicious perturbations that seek to maximise the classification loss lead to `falsely stable' images, and propose to leverage the pre-trained vision encoder of CLIP to counterattack such adversarial images during inference to achieve robustness. Our paradigm is simple and training-free, providing the first method to defend CLIP from adversarial attacks at test time, which is orthogonal to existing methods aiming to boost zero-shot adversarial robustness of CLIP. We conduct experiments across 16 classification datasets, and demonstrate stable and consistent gains compared to test-time defence methods adapted from existing adversarial robustness studies that do not rely on external networks, without noticeably impairing performance on clean images. We also show that our paradigm can be employed on CLIP models that have been adversarially finetuned to further enhance their robustness at test time. Our code is available https://github.com/Sxing2/CLIP-Test-time-Counterattacks{here}.

  • 3 authors
·
Mar 4, 2025

DVERGE: Diversifying Vulnerabilities for Enhanced Robust Generation of Ensembles

Recent research finds CNN models for image classification demonstrate overlapped adversarial vulnerabilities: adversarial attacks can mislead CNN models with small perturbations, which can effectively transfer between different models trained on the same dataset. Adversarial training, as a general robustness improvement technique, eliminates the vulnerability in a single model by forcing it to learn robust features. The process is hard, often requires models with large capacity, and suffers from significant loss on clean data accuracy. Alternatively, ensemble methods are proposed to induce sub-models with diverse outputs against a transfer adversarial example, making the ensemble robust against transfer attacks even if each sub-model is individually non-robust. Only small clean accuracy drop is observed in the process. However, previous ensemble training methods are not efficacious in inducing such diversity and thus ineffective on reaching robust ensemble. We propose DVERGE, which isolates the adversarial vulnerability in each sub-model by distilling non-robust features, and diversifies the adversarial vulnerability to induce diverse outputs against a transfer attack. The novel diversity metric and training procedure enables DVERGE to achieve higher robustness against transfer attacks comparing to previous ensemble methods, and enables the improved robustness when more sub-models are added to the ensemble. The code of this work is available at https://github.com/zjysteven/DVERGE

  • 9 authors
·
Sep 30, 2020

Downstream-agnostic Adversarial Examples

Self-supervised learning usually uses a large amount of unlabeled data to pre-train an encoder which can be used as a general-purpose feature extractor, such that downstream users only need to perform fine-tuning operations to enjoy the benefit of "large model". Despite this promising prospect, the security of pre-trained encoder has not been thoroughly investigated yet, especially when the pre-trained encoder is publicly available for commercial use. In this paper, we propose AdvEncoder, the first framework for generating downstream-agnostic universal adversarial examples based on the pre-trained encoder. AdvEncoder aims to construct a universal adversarial perturbation or patch for a set of natural images that can fool all the downstream tasks inheriting the victim pre-trained encoder. Unlike traditional adversarial example works, the pre-trained encoder only outputs feature vectors rather than classification labels. Therefore, we first exploit the high frequency component information of the image to guide the generation of adversarial examples. Then we design a generative attack framework to construct adversarial perturbations/patches by learning the distribution of the attack surrogate dataset to improve their attack success rates and transferability. Our results show that an attacker can successfully attack downstream tasks without knowing either the pre-training dataset or the downstream dataset. We also tailor four defenses for pre-trained encoders, the results of which further prove the attack ability of AdvEncoder.

  • 7 authors
·
Jul 23, 2023

Making Attention Mechanisms More Robust and Interpretable with Virtual Adversarial Training

Although attention mechanisms have become fundamental components of deep learning models, they are vulnerable to perturbations, which may degrade the prediction performance and model interpretability. Adversarial training (AT) for attention mechanisms has successfully reduced such drawbacks by considering adversarial perturbations. However, this technique requires label information, and thus, its use is limited to supervised settings. In this study, we explore the concept of incorporating virtual AT (VAT) into the attention mechanisms, by which adversarial perturbations can be computed even from unlabeled data. To realize this approach, we propose two general training techniques, namely VAT for attention mechanisms (Attention VAT) and "interpretable" VAT for attention mechanisms (Attention iVAT), which extend AT for attention mechanisms to a semi-supervised setting. In particular, Attention iVAT focuses on the differences in attention; thus, it can efficiently learn clearer attention and improve model interpretability, even with unlabeled data. Empirical experiments based on six public datasets revealed that our techniques provide better prediction performance than conventional AT-based as well as VAT-based techniques, and stronger agreement with evidence that is provided by humans in detecting important words in sentences. Moreover, our proposal offers these advantages without needing to add the careful selection of unlabeled data. That is, even if the model using our VAT-based technique is trained on unlabeled data from a source other than the target task, both the prediction performance and model interpretability can be improved.

  • 2 authors
·
Apr 18, 2021

Backpropagation-free Training of Deep Physical Neural Networks

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase unceasingly. This growth of the deep learning models is accompanied by issues related to their considerable energy consumption, both during the training and inference phases, as well as their scalability. Although a number of work based on unconventional physical systems have been proposed which addresses the issue of energy efficiency in the inference phase, efficient training of deep learning models has remained unaddressed. So far, training of digital deep learning models mainly relies on backpropagation, which is not suitable for physical implementation as it requires perfect knowledge of the computation performed in the so-called forward pass of the neural network. Here, we tackle this issue by proposing a simple deep neural network architecture augmented by a biologically plausible learning algorithm, referred to as "model-free forward-forward training". The proposed architecture enables training deep physical neural networks consisting of layers of physical nonlinear systems, without requiring detailed knowledge of the nonlinear physical layers' properties. We show that our method outperforms state-of-the-art hardware-aware training methods by improving training speed, decreasing digital computations, and reducing power consumption in physical systems. We demonstrate the adaptability of the proposed method, even in systems exposed to dynamic or unpredictable external perturbations. To showcase the universality of our approach, we train diverse wave-based physical neural networks that vary in the underlying wave phenomenon and the type of non-linearity they use, to perform vowel and image classification tasks experimentally.

  • 5 authors
·
Apr 20, 2023