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Title: ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.
Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst more »
using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special = architectural re-design. « less
Kuan-Lin Chen; Ching-Hua Lee; Harinath Garudadri; Bhaskar D Rao(
, Advances in neural information processing systems)
Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that widemore »ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special architectural re-design.« less
Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MORmore »that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back« less
Shawki, N.; Elseify, T.; Cap, T.; Shah, V.; Obeid, I.; Picone, J.(
, Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB))
Obeid, Iyad
Selesnick
(Ed.)
Electroencephalography (EEG) is a popular clinical monitoring tool used for diagnosing brain-related disorders such as epilepsy [1]. As monitoring EEGs in a critical-care setting is an expensive and tedious task, there is a great interest in developing real-time EEG monitoring tools to improve patient care quality and efficiency [2]. However, clinicians require automatic seizure detection tools that provide decisions with at least 75% sensitivity and less than 1 false alarm (FA) per 24 hours [3]. Some commercial tools recently claim to reach such performance levels, including the Olympic Brainz Monitor [4] and Persyst 14 [5]. In this abstract, we describemore »our efforts to transform a high-performance offline seizure detection system [3] into a low latency real-time or online seizure detection system. An overview of the system is shown in Figure 1. The main difference between an online versus offline system is that an online system should always be causal and has minimum latency which is often defined by domain experts. The offline system, shown in Figure 2, uses two phases of deep learning models with postprocessing [3]. The channel-based long short term memory (LSTM) model (Phase 1 or P1) processes linear frequency cepstral coefficients (LFCC) [6] features from each EEG channel separately. We use the hypotheses generated by the P1 model and create additional features that carry information about the detected events and their confidence. The P2 model uses these additional features and the LFCC features to learn the temporal and spatial aspects of the EEG signals using a hybrid convolutional neural network (CNN) and LSTM model. Finally, Phase 3 aggregates the results from both P1 and P2 before applying a final postprocessing step. The online system implements Phase 1 by taking advantage of the Linux piping mechanism, multithreading techniques, and multi-core processors. To convert Phase 1 into an online system, we divide the system into five major modules: signal preprocessor, feature extractor, event decoder, postprocessor, and visualizer. The system reads 0.1-second frames from each EEG channel and sends them to the feature extractor and the visualizer. The feature extractor generates LFCC features in real time from the streaming EEG signal. Next, the system computes seizure and background probabilities using a channel-based LSTM model and applies a postprocessor to aggregate the detected events across channels. The system then displays the EEG signal and the decisions simultaneously using a visualization module. The online system uses C++, Python, TensorFlow, and PyQtGraph in its implementation. The online system accepts streamed EEG data sampled at 250 Hz as input. The system begins processing the EEG signal by applying a TCP montage [8]. Depending on the type of the montage, the EEG signal can have either 22 or 20 channels. To enable the online operation, we send 0.1-second (25 samples) length frames from each channel of the streamed EEG signal to the feature extractor and the visualizer. Feature extraction is performed sequentially on each channel. The signal preprocessor writes the sample frames into two streams to facilitate these modules. In the first stream, the feature extractor receives the signals using stdin. In parallel, as a second stream, the visualizer shares a user-defined file with the signal preprocessor. This user-defined file holds raw signal information as a buffer for the visualizer. The signal preprocessor writes into the file while the visualizer reads from it. Reading and writing into the same file poses a challenge. The visualizer can start reading while the signal preprocessor is writing into it. To resolve this issue, we utilize a file locking mechanism in the signal preprocessor and visualizer. Each of the processes temporarily locks the file, performs its operation, releases the lock, and tries to obtain the lock after a waiting period. The file locking mechanism ensures that only one process can access the file by prohibiting other processes from reading or writing while one process is modifying the file [9]. The feature extractor uses circular buffers to save 0.3 seconds or 75 samples from each channel for extracting 0.2-second or 50-sample long center-aligned windows. The module generates 8 absolute LFCC features where the zeroth cepstral coefficient is replaced by a temporal domain energy term. For extracting the rest of the features, three pipelines are used. The differential energy feature is calculated in a 0.9-second absolute feature window with a frame size of 0.1 seconds. The difference between the maximum and minimum temporal energy terms is calculated in this range. Then, the first derivative or the delta features are calculated using another 0.9-second window. Finally, the second derivative or delta-delta features are calculated using a 0.3-second window [6]. The differential energy for the delta-delta features is not included. In total, we extract 26 features from the raw sample windows which add 1.1 seconds of delay to the system. We used the Temple University Hospital Seizure Database (TUSZ) v1.2.1 for developing the online system [10]. The statistics for this dataset are shown in Table 1. A channel-based LSTM model was trained using the features derived from the train set using the online feature extractor module. A window-based normalization technique was applied to those features. In the offline model, we scale features by normalizing using the maximum absolute value of a channel [11] before applying a sliding window approach. Since the online system has access to a limited amount of data, we normalize based on the observed window. The model uses the feature vectors with a frame size of 1 second and a window size of 7 seconds. We evaluated the model using the offline P1 postprocessor to determine the efficacy of the delayed features and the window-based normalization technique. As shown by the results of experiments 1 and 4 in Table 2, these changes give us a comparable performance to the offline model. The online event decoder module utilizes this trained model for computing probabilities for the seizure and background classes. These posteriors are then postprocessed to remove spurious detections. The online postprocessor receives and saves 8 seconds of class posteriors in a buffer for further processing. It applies multiple heuristic filters (e.g., probability threshold) to make an overall decision by combining events across the channels. These filters evaluate the average confidence, the duration of a seizure, and the channels where the seizures were observed. The postprocessor delivers the label and confidence to the visualizer. The visualizer starts to display the signal as soon as it gets access to the signal file, as shown in Figure 1 using the “Signal File” and “Visualizer” blocks. Once the visualizer receives the label and confidence for the latest epoch from the postprocessor, it overlays the decision and color codes that epoch. The visualizer uses red for seizure with the label SEIZ and green for the background class with the label BCKG. Once the streaming finishes, the system saves three files: a signal file in which the sample frames are saved in the order they were streamed, a time segmented event (TSE) file with the overall decisions and confidences, and a hypotheses (HYP) file that saves the label and confidence for each epoch. The user can plot the signal and decisions using the signal and HYP files with only the visualizer by enabling appropriate options. For comparing the performance of different stages of development, we used the test set of TUSZ v1.2.1 database. It contains 1015 EEG records of varying duration. The any-overlap performance [12] of the overall system shown in Figure 2 is 40.29% sensitivity with 5.77 FAs per 24 hours. For comparison, the previous state-of-the-art model developed on this database performed at 30.71% sensitivity with 6.77 FAs per 24 hours [3]. The individual performances of the deep learning phases are as follows: Phase 1’s (P1) performance is 39.46% sensitivity and 11.62 FAs per 24 hours, and Phase 2 detects seizures with 41.16% sensitivity and 11.69 FAs per 24 hours. We trained an LSTM model with the delayed features and the window-based normalization technique for developing the online system. Using the offline decoder and postprocessor, the model performed at 36.23% sensitivity with 9.52 FAs per 24 hours. The trained model was then evaluated with the online modules. The current performance of the overall online system is 45.80% sensitivity with 28.14 FAs per 24 hours. Table 2 summarizes the performances of these systems. The performance of the online system deviates from the offline P1 model because the online postprocessor fails to combine the events as the seizure probability fluctuates during an event. The modules in the online system add a total of 11.1 seconds of delay for processing each second of the data, as shown in Figure 3. In practice, we also count the time for loading the model and starting the visualizer block. When we consider these facts, the system consumes 15 seconds to display the first hypothesis. The system detects seizure onsets with an average latency of 15 seconds. Implementing an automatic seizure detection model in real time is not trivial. We used a variety of techniques such as the file locking mechanism, multithreading, circular buffers, real-time event decoding, and signal-decision plotting to realize the system. A video demonstrating the system is available at: https://www.isip.piconepress.com/projects/nsf_pfi_tt/resources/videos/realtime_eeg_analysis/v2.5.1/video_2.5.1.mp4. The final conference submission will include a more detailed analysis of the online performance of each module. ACKNOWLEDGMENTS Research reported in this publication was most recently supported by the National Science Foundation Partnership for Innovation award number IIP-1827565 and the Pennsylvania Commonwealth Universal Research Enhancement Program (PA CURE). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the official views of any of these organizations. REFERENCES [1] A. Craik, Y. He, and J. L. Contreras-Vidal, “Deep learning for electroencephalogram (EEG) classification tasks: a review,” J. Neural Eng., vol. 16, no. 3, p. 031001, 2019. https://doi.org/10.1088/1741-2552/ab0ab5. [2] A. C. Bridi, T. Q. Louro, and R. C. L. Da Silva, “Clinical Alarms in intensive care: implications of alarm fatigue for the safety of patients,” Rev. Lat. Am. Enfermagem, vol. 22, no. 6, p. 1034, 2014. https://doi.org/10.1590/0104-1169.3488.2513. [3] M. Golmohammadi, V. Shah, I. Obeid, and J. Picone, “Deep Learning Approaches for Automatic Seizure Detection from Scalp Electroencephalograms,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York, New York, USA: Springer, 2020, pp. 233–274. https://doi.org/10.1007/978-3-030-36844-9_8. [4] “CFM Olympic Brainz Monitor.” [Online]. Available: https://newborncare.natus.com/products-services/newborn-care-products/newborn-brain-injury/cfm-olympic-brainz-monitor. [Accessed: 17-Jul-2020]. [5] M. L. Scheuer, S. B. Wilson, A. Antony, G. Ghearing, A. Urban, and A. I. Bagic, “Seizure Detection: Interreader Agreement and Detection Algorithm Assessments Using a Large Dataset,” J. Clin. Neurophysiol., 2020. https://doi.org/10.1097/WNP.0000000000000709. [6] A. Harati, M. Golmohammadi, S. Lopez, I. Obeid, and J. Picone, “Improved EEG Event Classification Using Differential Energy,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium, 2015, pp. 1–4. https://doi.org/10.1109/SPMB.2015.7405421. [7] V. Shah, C. Campbell, I. Obeid, and J. Picone, “Improved Spatio-Temporal Modeling in Automated Seizure Detection using Channel-Dependent Posteriors,” Neurocomputing, 2021. [8] W. Tatum, A. Husain, S. Benbadis, and P. Kaplan, Handbook of EEG Interpretation. New York City, New York, USA: Demos Medical Publishing, 2007. [9] D. P. Bovet and C. Marco, Understanding the Linux Kernel, 3rd ed. O’Reilly Media, Inc., 2005. https://www.oreilly.com/library/view/understanding-the-linux/0596005652/. [10] V. Shah et al., “The Temple University Hospital Seizure Detection Corpus,” Front. Neuroinform., vol. 12, pp. 1–6, 2018. https://doi.org/10.3389/fninf.2018.00083. [11] F. Pedregosa et al., “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011. https://dl.acm.org/doi/10.5555/1953048.2078195. [12] J. Gotman, D. Flanagan, J. Zhang, and B. Rosenblatt, “Automatic seizure detection in the newborn: Methods and initial evaluation,” Electroencephalogr. Clin. Neurophysiol., vol. 103, no. 3, pp. 356–362, 1997. https://doi.org/10.1016/S0013-4694(97)00003-9.« less
Wang, Ping; Padthe, Karthik K.; Vinzamuri, Bhanukiran; Reddy, Chandan K.(
, Proceedings of the 25th ACM International on Conference on Information and Knowledge Management)
Integrating regularization methods with standard loss functions such as the least squares, hinge loss, etc., within a regression framework has become a popular choice for researchers to learn predictive models with lower variance and better generalization ability. Regularizers also aid in building interpretable models with high-dimensional data which makes them very appealing. It is observed that each regularizer is uniquely formulated in order to capture data-specific properties such as correlation, structured sparsity and temporal smoothness. The problem of obtaining a consensus among such diverse regularizers while learning a predictive model is extremely important in order to determine the optimal regularizermore »for the problem. The advantage of such an approach is that it preserves the simplicity of the final model learned by selecting a single candidate model which is not the case with ensemble methods as they use multiple candidate models for prediction. This is called the consensus regularization problem which has not received much attention in the literature due to the inherent difficulty associated with learning and selecting a model from an integrated regularization framework. To solve this problem, in this paper, we propose a method to generate a committee of non-convex regularized linear regression models, and use a consensus criterion to determine the optimal model for prediction. Each corresponding non-convex optimization problem in the committee is solved efficiently using the cyclic-coordinate descent algorithm with the generalized thresholding operator. Our Consensus RegularIzation Selection based Prediction (CRISP) model is evaluated on electronic health records (EHRs) obtained from a large hospital for the congestive heart failure readmission prediction problem. We also evaluate our model on high-dimensional synthetic datasets to assess its performance. The results indicate that CRISP outperforms several state-of-the-art methods such as additive, interactions-based and other competing non-convex regularized linear regression methods.« less
We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large class of models, the transformed time series matrix is (approximately) low-rank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in the time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishingmore »this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method-coupled with a novel, non-standard matrix estimation error metric-to solve the error-in-variable regression problem, which could be of interest in its own right. Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.« less
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Chen, K. L., Lee, C. H., Garudadri, H., and Rao, B. D. ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.. Retrieved from https://par.nsf.gov/biblio/10332322. Advances in neural information processing systems 34.
Chen, K. L., Lee, C. H., Garudadri, H., & Rao, B. D. ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.. Advances in neural information processing systems, 34 (). Retrieved from https://par.nsf.gov/biblio/10332322.
Chen, K. L., Lee, C. H., Garudadri, H., and Rao, B. D.
"ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.". Advances in neural information processing systems 34 (). Country unknown/Code not available. https://par.nsf.gov/biblio/10332322.
@article{osti_10332322,
place = {Country unknown/Code not available},
title = {ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.},
url = {https://par.nsf.gov/biblio/10332322},
abstractNote = {Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special = architectural re-design.},
journal = {Advances in neural information processing systems},
volume = {34},
author = {Chen, K. L. and Lee, C. H. and Garudadri, H. and Rao, B. D.},
}