CVNov 16, 2022Code
MAGE: MAsked Generative Encoder to Unify Representation Learning and Image SynthesisTianhong Li, Huiwen Chang, Shlok Kumar Mishra et al.
Generative modeling and representation learning are two key tasks in computer vision. However, these models are typically trained independently, which ignores the potential for each task to help the other, and leads to training and model maintenance overheads. In this work, we propose MAsked Generative Encoder (MAGE), the first framework to unify SOTA image generation and self-supervised representation learning. Our key insight is that using variable masking ratios in masked image modeling pre-training can allow generative training (very high masking ratio) and representation learning (lower masking ratio) under the same training framework. Inspired by previous generative models, MAGE uses semantic tokens learned by a vector-quantized GAN at inputs and outputs, combining this with masking. We can further improve the representation by adding a contrastive loss to the encoder output. We extensively evaluate the generation and representation learning capabilities of MAGE. On ImageNet-1K, a single MAGE ViT-L model obtains 9.10 FID in the task of class-unconditional image generation and 78.9% top-1 accuracy for linear probing, achieving state-of-the-art performance in both image generation and representation learning. Code is available at https://github.com/LTH14/mage.
CVJul 6, 2022
Unsupervised Learning for Human Sensing Using Radio SignalsTianhong Li, Lijie Fan, Yuan Yuan et al.
There is a growing literature demonstrating the feasibility of using Radio Frequency (RF) signals to enable key computer vision tasks in the presence of occlusions and poor lighting. It leverages that RF signals traverse walls and occlusions to deliver through-wall pose estimation, action recognition, scene captioning, and human re-identification. However, unlike RGB datasets which can be labeled by human workers, labeling RF signals is a daunting task because such signals are not human interpretable. Yet, it is fairly easy to collect unlabelled RF signals. It would be highly beneficial to use such unlabeled RF data to learn useful representations in an unsupervised manner. Thus, in this paper, we explore the feasibility of adapting RGB-based unsupervised representation learning to RF signals. We show that while contrastive learning has emerged as the main technique for unsupervised representation learning from images and videos, such methods produce poor performance when applied to sensing humans using RF signals. In contrast, predictive unsupervised learning methods learn high-quality representations that can be used for multiple downstream RF-based sensing tasks. Our empirical results show that this approach outperforms state-of-the-art RF-based human sensing on various tasks, opening the possibility of unsupervised representation learning from this novel modality.
CVOct 5, 2023
Leveraging Unpaired Data for Vision-Language Generative Models via Cycle ConsistencyTianhong Li, Sangnie Bhardwaj, Yonglong Tian et al.
Current vision-language generative models rely on expansive corpora of paired image-text data to attain optimal performance and generalization capabilities. However, automatically collecting such data (e.g. via large-scale web scraping) leads to low quality and poor image-text correlation, while human annotation is more accurate but requires significant manual effort and expense. We introduce $\textbf{ITIT}$ ($\textbf{I}$n$\textbf{T}$egrating $\textbf{I}$mage $\textbf{T}$ext): an innovative training paradigm grounded in the concept of cycle consistency which allows vision-language training on unpaired image and text data. ITIT is comprised of a joint image-text encoder with disjoint image and text decoders that enable bidirectional image-to-text and text-to-image generation in a single framework. During training, ITIT leverages a small set of paired image-text data to ensure its output matches the input reasonably well in both directions. Simultaneously, the model is also trained on much larger datasets containing only images or texts. This is achieved by enforcing cycle consistency between the original unpaired samples and the cycle-generated counterparts. For instance, it generates a caption for a given input image and then uses the caption to create an output image, and enforces similarity between the input and output images. Our experiments show that ITIT with unpaired datasets exhibits similar scaling behavior as using high-quality paired data. We demonstrate image generation and captioning performance on par with state-of-the-art text-to-image and image-to-text models with orders of magnitude fewer (only 3M) paired image-text data.
CVDec 6, 2023Code
Return of Unconditional Generation: A Self-supervised Representation Generation MethodTianhong Li, Dina Katabi, Kaiming He
Unconditional generation -- the problem of modeling data distribution without relying on human-annotated labels -- is a long-standing and fundamental challenge in generative models, creating a potential of learning from large-scale unlabeled data. In the literature, the generation quality of an unconditional method has been much worse than that of its conditional counterpart. This gap can be attributed to the lack of semantic information provided by labels. In this work, we show that one can close this gap by generating semantic representations in the representation space produced by a self-supervised encoder. These representations can be used to condition the image generator. This framework, called Representation-Conditioned Generation (RCG), provides an effective solution to the unconditional generation problem without using labels. Through comprehensive experiments, we observe that RCG significantly improves unconditional generation quality: e.g., it achieves a new state-of-the-art FID of 2.15 on ImageNet 256x256, largely reducing the previous best of 5.91 by a relative 64%. Our unconditional results are situated in the same tier as the leading class-conditional ones. We hope these encouraging observations will attract the community's attention to the fundamental problem of unconditional generation. Code is available at https://github.com/LTH14/rcg.
LGFeb 24, 2025Code
Fractal Generative ModelsTianhong Li, Qinyi Sun, Lijie Fan et al.
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.
LGFeb 4
Generative Modeling via DriftingMingyang Deng, He Li, Tianhong Li et al.
Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.
CVMar 3
DREAM: Where Visual Understanding Meets Text-to-Image GenerationChao Li, Tianhong Li, Sai Vidyaranya Nuthalapati et al.
Unifying visual representation learning and text-to-image (T2I) generation within a single model remains a central challenge in multimodal learning. We introduce DREAM, a unified framework that jointly optimizes discriminative and generative objectives, while learning strong visual representations. DREAM is built on two key techniques: During training, Masking Warmup, a progressive masking schedule, begins with minimal masking to establish the contrastive alignment necessary for representation learning, then gradually transitions to full masking for stable generative training. At inference, DREAM employs Semantically Aligned Decoding to align partially masked image candidates with the target text and select the best one for further decoding, improving text-image fidelity (+6.3%) without external rerankers. Trained solely on CC12M, DREAM achieves 72.7% ImageNet linear-probing accuracy (+1.1% over CLIP) and an FID of 4.25 (+6.2% over FLUID), with consistent gains in few-shot classification, semantic segmentation, and depth estimation. These results demonstrate that discriminative and generative objectives can be synergistic, allowing unified multimodal models that excel at both visual understanding and generation.
CVJan 29
One-step Latent-free Image Generation with Pixel Mean FlowsYiyang Lu, Susie Lu, Qiao Sun et al.
Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.
97.0CLMay 11
ELF: Embedded Language FlowsKeya Hu, Linlu Qiu, Yiyang Lu et al.
Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.
CVOct 17, 2024
Fluid: Scaling Autoregressive Text-to-image Generative Models with Continuous TokensLijie Fan, Tianhong Li, Siyang Qin et al.
Scaling up autoregressive models in vision has not proven as beneficial as in large language models. In this work, we investigate this scaling problem in the context of text-to-image generation, focusing on two critical factors: whether models use discrete or continuous tokens, and whether tokens are generated in a random or fixed raster order using BERT- or GPT-like transformer architectures. Our empirical results show that, while all models scale effectively in terms of validation loss, their evaluation performance -- measured by FID, GenEval score, and visual quality -- follows different trends. Models based on continuous tokens achieve significantly better visual quality than those using discrete tokens. Furthermore, the generation order and attention mechanisms significantly affect the GenEval score: random-order models achieve notably better GenEval scores compared to raster-order models. Inspired by these findings, we train Fluid, a random-order autoregressive model on continuous tokens. Fluid 10.5B model achieves a new state-of-the-art zero-shot FID of 6.16 on MS-COCO 30K, and 0.69 overall score on the GenEval benchmark. We hope our findings and results will encourage future efforts to further bridge the scaling gap between vision and language models.
CVJun 17, 2024Code
Autoregressive Image Generation without Vector QuantizationTianhong Li, Yonglong Tian, He Li et al.
Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications. Code is available at: https://github.com/LTH14/mar.
99.3CVApr 27
Tuna-2: Pixel Embeddings Beat Vision Encoders for Multimodal Understanding and GenerationZhiheng Liu, Weiming Ren, Xiaoke Huang et al.
Unified multimodal models typically rely on pretrained vision encoders and use separate visual representations for understanding and generation, creating misalignment between the two tasks and preventing fully end-to-end optimization from raw pixels. We introduce Tuna-2, a native unified multimodal model that performs visual understanding and generation directly based on pixel embeddings. Tuna-2 drastically simplifies the model architecture by employing simple patch embedding layers to encode visual input, completely discarding the modular vision encoder designs such as the VAE or the representation encoder. Experiments show that Tuna-2 achieves state-of-the-art performance in multimodal benchmarks, demonstrating that unified pixel-space modelling can fully compete with latent-space approaches for high-quality image generation. Moreover, while the encoder-based variant converges faster in early pretraining, Tuna-2's encoder-free design achieves stronger multimodal understanding at scale, particularly on tasks requiring fine-grained visual perception. These results show that pretrained vision encoders are not necessary for multimodal modelling, and end-to-end pixel-space learning offers a scalable path toward stronger visual representations for both generation and perception.
CVMar 17, 2025
Unified Autoregressive Visual Generation and Understanding with Continuous TokensLijie Fan, Luming Tang, Siyang Qin et al. · deepmind
We present UniFluid, a unified autoregressive framework for joint visual generation and understanding leveraging continuous visual tokens. Our unified autoregressive architecture processes multimodal image and text inputs, generating discrete tokens for text and continuous tokens for image. We find though there is an inherent trade-off between the image generation and understanding task, a carefully tuned training recipe enables them to improve each other. By selecting an appropriate loss balance weight, the unified model achieves results comparable to or exceeding those of single-task baselines on both tasks. Furthermore, we demonstrate that employing stronger pre-trained LLMs and random-order generation during training is important to achieve high-fidelity image generation within this unified framework. Built upon the Gemma model series, UniFluid exhibits competitive performance across both image generation and understanding, demonstrating strong transferability to various downstream tasks, including image editing for generation, as well as visual captioning and question answering for understanding.
CVJul 21, 2025
Latent Denoising Makes Good Visual TokenizersJiawei Yang, Tianhong Li, Lijie Fan et al.
Despite their fundamental role, it remains unclear what properties could make visual tokenizers more effective for generative modeling. We observe that modern generative models share a conceptually similar training objective -- reconstructing clean signals from corrupted inputs such as Gaussian noise or masking -- a process we term denoising. Motivated by this insight, we propose aligning tokenizer embeddings directly with the downstream denoising objective, encouraging latent embeddings to be more easily reconstructed even when heavily corrupted. To achieve this, we introduce the Latent Denoising Tokenizer (l-DeTok), a simple yet effective tokenizer trained to reconstruct clean images from latent embeddings corrupted by interpolative noise and random masking. Extensive experiments on ImageNet 256x256 demonstrate that our tokenizer consistently outperforms standard tokenizers across six representative generative models. Our findings highlight denoising as a fundamental design principle for tokenizer development, and we hope it could motivate new perspectives for future tokenizer design.
QMFeb 13, 2025
CellFlux: Simulating Cellular Morphology Changes via Flow MatchingYuhui Zhang, Yuchang Su, Chenyu Wang et al. · stanford
Building a virtual cell capable of accurately simulating cellular behaviors in silico has long been a dream in computational biology. We introduce CellFlux, an image-generative model that simulates cellular morphology changes induced by chemical and genetic perturbations using flow matching. Unlike prior methods, CellFlux models distribution-wise transformations from unperturbed to perturbed cell states, effectively distinguishing actual perturbation effects from experimental artifacts such as batch effects -- a major challenge in biological data. Evaluated on chemical (BBBC021), genetic (RxRx1), and combined perturbation (JUMP) datasets, CellFlux generates biologically meaningful cell images that faithfully capture perturbation-specific morphological changes, achieving a 35% improvement in FID scores and a 12% increase in mode-of-action prediction accuracy over existing methods. Additionally, CellFlux enables continuous interpolation between cellular states, providing a potential tool for studying perturbation dynamics. These capabilities mark a significant step toward realizing virtual cell modeling for biomedical research. Project page: https://yuhui-zh15.github.io/CellFlux/.
CVNov 17, 2025
Back to Basics: Let Denoising Generative Models DenoiseTianhong Li, Kaiming He
Today's denoising diffusion models do not "denoise" in the classical sense, i.e., they do not directly predict clean images. Rather, the neural networks predict noise or a noised quantity. In this paper, we suggest that predicting clean data and predicting noised quantities are fundamentally different. According to the manifold assumption, natural data should lie on a low-dimensional manifold, whereas noised quantities do not. With this assumption, we advocate for models that directly predict clean data, which allows apparently under-capacity networks to operate effectively in very high-dimensional spaces. We show that simple, large-patch Transformers on pixels can be strong generative models: using no tokenizer, no pre-training, and no extra loss. Our approach is conceptually nothing more than "$\textbf{Just image Transformers}$", or $\textbf{JiT}$, as we call it. We report competitive results using JiT with large patch sizes of 16 and 32 on ImageNet at resolutions of 256 and 512, where predicting high-dimensional noised quantities can fail catastrophically. With our networks mapping back to the basics of the manifold, our research goes back to basics and pursues a self-contained paradigm for Transformer-based diffusion on raw natural data.
NIMay 23, 2023
Reparo: Loss-Resilient Generative Codec for Video ConferencingTianhong Li, Vibhaalakshmi Sivaraman, Pantea Karimi et al.
Packet loss during video conferencing often results in poor quality and video freezing. Retransmitting lost packets is often impractical due to the need for real-time playback, and using Forward Error Correction (FEC) for packet recovery is challenging due to the unpredictable and bursty nature of Internet losses. Excessive redundancy leads to inefficiency and wasted bandwidth, while insufficient redundancy results in undecodable frames, causing video freezes and quality degradation in subsequent frames. We introduce Reparo -- a loss-resilient video conferencing framework based on generative deep learning models to address these issues. Our approach generates missing information when a frame or part of a frame is lost. This generation is conditioned on the data received thus far, considering the model's understanding of how people and objects appear and interact within the visual realm. Experimental results, using publicly available video conferencing datasets, demonstrate that Reparo outperforms state-of-the-art FEC-based video conferencing solutions in terms of both video quality (measured through PSNR, SSIM, and LPIPS) and the occurrence of video freezes.
CVNov 27, 2021
Targeted Supervised Contrastive Learning for Long-Tailed RecognitionTianhong Li, Peng Cao, Yuan Yuan et al.
Real-world data often exhibits long tail distributions with heavy class imbalance, where the majority classes can dominate the training process and alter the decision boundaries of the minority classes. Recently, researchers have investigated the potential of supervised contrastive learning for long-tailed recognition, and demonstrated that it provides a strong performance gain. In this paper, we show that while supervised contrastive learning can help improve performance, past baselines suffer from poor uniformity brought in by imbalanced data distribution. This poor uniformity manifests in samples from the minority class having poor separability in the feature space. To address this problem, we propose targeted supervised contrastive learning (TSC), which improves the uniformity of the feature distribution on the hypersphere. TSC first generates a set of targets uniformly distributed on a hypersphere. It then makes the features of different classes converge to these distinct and uniformly distributed targets during training. This forces all classes, including minority classes, to maintain a uniform distribution in the feature space, improves class boundaries, and provides better generalization even in the presence of long-tail data. Experiments on multiple datasets show that TSC achieves state-of-the-art performance on long-tailed recognition tasks.
LGDec 17, 2020
Addressing Feature Suppression in Unsupervised Visual RepresentationsTianhong Li, Lijie Fan, Yuan Yuan et al.
Contrastive learning is one of the fastest growing research areas in machine learning due to its ability to learn useful representations without labeled data. However, contrastive learning is susceptible to feature suppression, i.e., it may discard important information relevant to the task of interest, and learn irrelevant features. Past work has addressed this limitation via handcrafted data augmentations that eliminate irrelevant information. This approach however does not work across all datasets and tasks. Further, data augmentations fail in addressing feature suppression in multi-attribute classification when one attribute can suppress features relevant to other attributes. In this paper, we analyze the objective function of contrastive learning and formally prove that it is vulnerable to feature suppression. We then present predictive contrastive learning (PCL), a framework for learning unsupervised representations that are robust to feature suppression. The key idea is to force the learned representation to predict the input, and hence prevent it from discarding important information. Extensive experiments verify that PCL is robust to feature suppression and outperforms state-of-the-art contrastive learning methods on a variety of datasets and tasks.
CVAug 25, 2020
In-Home Daily-Life Captioning Using Radio SignalsLijie Fan, Tianhong Li, Yuan Yuan et al.
This paper aims to caption daily life --i.e., to create a textual description of people's activities and interactions with objects in their homes. Addressing this problem requires novel methods beyond traditional video captioning, as most people would have privacy concerns about deploying cameras throughout their homes. We introduce RF-Diary, a new model for captioning daily life by analyzing the privacy-preserving radio signal in the home with the home's floormap. RF-Diary can further observe and caption people's life through walls and occlusions and in dark settings. In designing RF-Diary, we exploit the ability of radio signals to capture people's 3D dynamics, and use the floormap to help the model learn people's interactions with objects. We also use a multi-modal feature alignment training scheme that leverages existing video-based captioning datasets to improve the performance of our radio-based captioning model. Extensive experimental results demonstrate that RF-Diary generates accurate captions under visible conditions. It also sustains its good performance in dark or occluded settings, where video-based captioning approaches fail to generate meaningful captions. For more information, please visit our project webpage: http://rf-diary.csail.mit.edu
CVApr 2, 2020
Learning Longterm Representations for Person Re-Identification Using Radio SignalsLijie Fan, Tianhong Li, Rongyao Fang et al.
Person Re-Identification (ReID) aims to recognize a person-of-interest across different places and times. Existing ReID methods rely on images or videos collected using RGB cameras. They extract appearance features like clothes, shoes, hair, etc. Such features, however, can change drastically from one day to the next, leading to inability to identify people over extended time periods. In this paper, we introduce RF-ReID, a novel approach that harnesses radio frequency (RF) signals for longterm person ReID. RF signals traverse clothes and reflect off the human body; thus they can be used to extract more persistent human-identifying features like body size and shape. We evaluate the performance of RF-ReID on longitudinal datasets that span days and weeks, where the person may wear different clothes across days. Our experiments demonstrate that RF-ReID outperforms state-of-the-art RGB-based ReID approaches for long term person ReID. Our results also reveal two interesting features: First since RF signals work in the presence of occlusions and poor lighting, RF-ReID allows for person ReID in such scenarios. Second, unlike photos and videos which reveal personal and private information, RF signals are more privacy-preserving, and hence can help extend person ReID to privacy-concerned domains, like healthcare.
CVSep 20, 2019
Making the Invisible Visible: Action Recognition Through Walls and OcclusionsTianhong Li, Lijie Fan, Mingmin Zhao et al.
Understanding people's actions and interactions typically depends on seeing them. Automating the process of action recognition from visual data has been the topic of much research in the computer vision community. But what if it is too dark, or if the person is occluded or behind a wall? In this paper, we introduce a neural network model that can detect human actions through walls and occlusions, and in poor lighting conditions. Our model takes radio frequency (RF) signals as input, generates 3D human skeletons as an intermediate representation, and recognizes actions and interactions of multiple people over time. By translating the input to an intermediate skeleton-based representation, our model can learn from both vision-based and RF-based datasets, and allow the two tasks to help each other. We show that our model achieves comparable accuracy to vision-based action recognition systems in visible scenarios, yet continues to work accurately when people are not visible, hence addressing scenarios that are beyond the limit of today's vision-based action recognition.
LGDec 5, 2018
Few Sample Knowledge Distillation for Efficient Network CompressionTianhong Li, Jianguo Li, Zhuang Liu et al.
Deep neural network compression techniques such as pruning and weight tensor decomposition usually require fine-tuning to recover the prediction accuracy when the compression ratio is high. However, conventional fine-tuning suffers from the requirement of a large training set and the time-consuming training procedure. This paper proposes a novel solution for knowledge distillation from label-free few samples to realize both data efficiency and training/processing efficiency. We treat the original network as "teacher-net" and the compressed network as "student-net". A 1x1 convolution layer is added at the end of each layer block of the student-net, and we fit the block-level outputs of the student-net to the teacher-net by estimating the parameters of the added layers. We prove that the added layer can be merged without adding extra parameters and computation cost during inference. Experiments on multiple datasets and network architectures verify the method's effectiveness on student-nets obtained by various network pruning and weight decomposition methods. Our method can recover student-net's accuracy to the same level as conventional fine-tuning methods in minutes while using only 1% label-free data of the full training data.
LGMar 29, 2017
Multi-Scale Dense Networks for Resource Efficient Image ClassificationGao Huang, Danlu Chen, Tianhong Li et al.
In this paper we investigate image classification with computational resource limits at test time. Two such settings are: 1. anytime classification, where the network's prediction for a test example is progressively updated, facilitating the output of a prediction at any time; and 2. budgeted batch classification, where a fixed amount of computation is available to classify a set of examples that can be spent unevenly across "easier" and "harder" inputs. In contrast to most prior work, such as the popular Viola and Jones algorithm, our approach is based on convolutional neural networks. We train multiple classifiers with varying resource demands, which we adaptively apply during test time. To maximally re-use computation between the classifiers, we incorporate them as early-exits into a single deep convolutional neural network and inter-connect them with dense connectivity. To facilitate high quality classification early on, we use a two-dimensional multi-scale network architecture that maintains coarse and fine level features all-throughout the network. Experiments on three image-classification tasks demonstrate that our framework substantially improves the existing state-of-the-art in both settings.
LGFeb 18, 2017
Quadratic Upper Bound for Recursive Teaching Dimension of Finite VC ClassesLunjia Hu, Ruihan Wu, Tianhong Li et al.
In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$, introduced by Zilles et al. (2011), is a combinatorial complexity measure characterized by the worst-case number of examples necessary to identify a concept in $\mathcal C$ according to the recursive teaching model. For any finite concept class $\mathcal C \subseteq \{0,1\}^n$ with $\mathrm{VCD}(\mathcal C)=d$, Simon & Zilles (2015) posed an open problem $\mathrm{RTD}(\mathcal C) = O(d)$, i.e., is RTD linearly upper bounded by VCD? Previously, the best known result is an exponential upper bound $\mathrm{RTD}(\mathcal C) = O(d \cdot 2^d)$, due to Chen et al. (2016). In this paper, we show a quadratic upper bound: $\mathrm{RTD}(\mathcal C) = O(d^2)$, much closer to an answer to the open problem. We also discuss the challenges in fully solving the problem.