Ravid Shwartz-Ziv

Ravid Shwartz-Ziv, Randall Balestriero, Kenji Kawaguchi et al. · mit

Variance-Invariance-Covariance Regularization (VICReg) is a self-supervised learning (SSL) method that has shown promising results on a variety of tasks. However, the fundamental mechanisms underlying VICReg remain unexplored. In this paper, we present an information-theoretic perspective on the VICReg objective. We begin by deriving information-theoretic quantities for deterministic networks as an alternative to unrealistic stochastic network assumptions. We then relate the optimization of the VICReg objective to mutual information optimization, highlighting underlying assumptions and facilitating a constructive comparison with other SSL algorithms and derive a generalization bound for VICReg, revealing its inherent advantages for downstream tasks. Building on these results, we introduce a family of SSL methods derived from information-theoretic principles that outperform existing SSL techniques.

Ravid Shwartz-Ziv, Yann LeCun

Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory, and notably the information bottleneck principle, has been pivotal in shaping deep neural networks. This principle focuses on optimizing the trade-off between compression and preserving relevant information, providing a foundation for efficient network design in supervised contexts. However, its precise role and adaptation in self-supervised learning remain unclear. In this work, we scrutinize various self-supervised learning approaches from an information-theoretic perspective, introducing a unified framework that encapsulates the \textit{self-supervised information-theoretic learning problem}. We weave together existing research into a cohesive narrative, delve into contemporary self-supervised methodologies, and spotlight potential research avenues and inherent challenges. Additionally, we discuss the empirical evaluation of information-theoretic quantities and their estimation methods. Overall, this paper furnishes an exhaustive review of the intersection of information theory, self-supervised learning, and deep neural networks.

Ravid Shwartz-Ziv, Micah Goldblum, Hossein Souri et al.

Deep learning is increasingly moving towards a transfer learning paradigm whereby large foundation models are fine-tuned on downstream tasks, starting from an initialization learned on the source task. But an initialization contains relatively little information about the source task. Instead, we show that we can learn highly informative posteriors from the source task, through supervised or self-supervised approaches, which then serve as the basis for priors that modify the whole loss surface on the downstream task. This simple modular approach enables significant performance gains and more data-efficient learning on a variety of downstream classification and segmentation tasks, serving as a drop-in replacement for standard pre-training strategies. These highly informative priors also can be saved for future use, similar to pre-trained weights, and stand in contrast to the zero-mean isotropic uninformative priors that are typically used in Bayesian deep learning.

Jonas Geiping, Micah Goldblum, Gowthami Somepalli et al.

Despite the clear performance benefits of data augmentations, little is known about why they are so effective. In this paper, we disentangle several key mechanisms through which data augmentations operate. Establishing an exchange rate between augmented and additional real data, we find that in out-of-distribution testing scenarios, augmentations which yield samples that are diverse, but inconsistent with the data distribution can be even more valuable than additional training data. Moreover, we find that data augmentations which encourage invariances can be more valuable than invariance alone, especially on small and medium sized training sets. Following this observation, we show that augmentations induce additional stochasticity during training, effectively flattening the loss landscape.

Ravid Shwartz-Ziv, Randall Balestriero, Yann LeCun

In this paper, we examine self-supervised learning methods, particularly VICReg, to provide an information-theoretical understanding of their construction. As a first step, we demonstrate how information-theoretic quantities can be obtained for a deterministic network, offering a possible alternative to prior work that relies on stochastic models. This enables us to demonstrate how VICReg can be (re)discovered from first principles and its assumptions about data distribution. Furthermore, we empirically demonstrate the validity of our assumptions, confirming our novel understanding of VICReg. Finally, we believe that the derivation and insights we obtain can be generalized to many other SSL methods, opening new avenues for theoretical and practical understanding of SSL and transfer learning.

Jiachen Zhu, Katrina Evtimova, Yubei Chen et al.

Transfer learning plays a key role in advancing machine learning models, yet conventional supervised pretraining often undermines feature transferability by prioritizing features that minimize the pretraining loss. In this work, we adapt a self-supervised learning regularization technique from the VICReg method to supervised learning contexts, introducing Variance-Covariance Regularization (VCReg). This adaptation encourages the network to learn high-variance, low-covariance representations, promoting learning more diverse features. We outline best practices for an efficient implementation of our framework, including applying it to the intermediate representations. Through extensive empirical evaluation, we demonstrate that our method significantly enhances transfer learning for images and videos, achieving state-of-the-art performance across numerous tasks and datasets. VCReg also improves performance in scenarios like long-tail learning and hierarchical classification. Additionally, we show its effectiveness may stem from its success in addressing challenges like gradient starvation and neural collapse. In summary, VCReg offers a universally applicable regularization framework that significantly advances transfer learning and highlights the connection between gradient starvation, neural collapse, and feature transferability.

Ori Press, Ravid Shwartz-Ziv, Yann LeCun et al.

Entropy minimization (EM) is frequently used to increase the accuracy of classification models when they're faced with new data at test time. EM is a self-supervised learning method that optimizes classifiers to assign even higher probabilities to their top predicted classes. In this paper, we analyze why EM works when adapting a model for a few steps and why it eventually fails after adapting for many steps. We show that, at first, EM causes the model to embed test images close to training images, thereby increasing model accuracy. After many steps of optimization, EM makes the model embed test images far away from the embeddings of training images, which results in a degradation of accuracy. Building upon our insights, we present a method for solving a practical problem: estimating a model's accuracy on a given arbitrary dataset without having access to its labels. Our method estimates accuracy by looking at how the embeddings of input images change as the model is optimized to minimize entropy. Experiments on 23 challenging datasets show that our method sets the SoTA with a mean absolute error of $5.75\%$, an improvement of $29.62\%$ over the previous SoTA on this task. Our code is available at https://github.com/oripress/EntropyEnigma

Samuel Paech, Allen Roush, Judah Goldfeder et al.

Widespread LLM adoption has introduced characteristic repetitive phraseology, termed "slop," which degrades output quality and makes AI-generated text immediately recognizable. We present Antislop, a comprehensive framework providing tools to both detect and eliminate these overused patterns. Our approach combines three innovations: (1) The Antislop Sampler, which uses backtracking to suppress unwanted strings at inference time without destroying vocabulary; (2) An automated pipeline that profiles model-specific slop against human baselines and generates training data; (3) Final Token Preference Optimization (FTPO), a novel fine-tuning method that operates on individual tokens, surgically adjusting logits wherever a banned pattern has appeared in an inference trace. We demonstrate that some slop patterns appear over 1,000x more frequently in LLM output than human text. The Antislop Sampler successfully suppresses 8,000+ patterns while maintaining quality, whereas token banning becomes unusable at just 2,000. Most importantly, FTPO achieves 90% slop reduction while maintaining or improving performance in cross-domain evals including GSM8K, MMLU, and creative writing tasks. In contrast, DPO suffers significant degradation in writing quality and lexical diversity despite achieving weaker suppression. We release all code and results under MIT license: https://github.com/sam-paech/auto-antislop.

Colin White, Samuel Dooley, Manley Roberts et al.

Test set contamination, wherein test data from a benchmark ends up in a newer model's training set, is a well-documented obstacle for fair LLM evaluation and can quickly render benchmarks obsolete. To mitigate this, many recent benchmarks crowdsource new prompts and evaluations from human or LLM judges; however, these can introduce significant biases, and break down when scoring hard questions. In this work, we introduce a new benchmark for LLMs designed to be resistant to both test set contamination and the pitfalls of LLM judging and human crowdsourcing. We release LiveBench, the first benchmark that (1) contains frequently-updated questions from recent information sources, (2) scores answers automatically according to objective ground-truth values, and (3) contains a wide variety of challenging tasks, spanning math, coding, reasoning, language, instruction following, and data analysis. To achieve this, LiveBench contains questions that are based on recently-released math competitions, arXiv papers, news articles, and datasets, and it contains harder, contamination-limited versions of tasks from previous benchmarks such as Big-Bench Hard, AMPS, and IFEval. We evaluate many prominent closed-source models, as well as dozens of open-source models ranging from 0.5B to 405B in size. LiveBench is difficult, with top models achieving below 70% accuracy. We release all questions, code, and model answers. Questions are added and updated on a monthly basis, and we release new tasks and harder versions of tasks over time so that LiveBench can distinguish between the capabilities of LLMs as they improve in the future. We welcome community engagement and collaboration for expanding the benchmark tasks and models.

Oscar Skean, Md Rifat Arefin, Dan Zhao et al.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on the final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks across various architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features, challenging the standard view on final-layer embeddings and opening new directions on using mid-layer representations for more robust and accurate representations.

Ravid Shwartz-Ziv, Micah Goldblum, Yucen Lily Li et al.

Real-world datasets are often highly class-imbalanced, which can adversely impact the performance of deep learning models. The majority of research on training neural networks under class imbalance has focused on specialized loss functions, sampling techniques, or two-stage training procedures. Notably, we demonstrate that simply tuning existing components of standard deep learning pipelines, such as the batch size, data augmentation, optimizer, and label smoothing, can achieve state-of-the-art performance without any such specialized class imbalance methods. We also provide key prescriptions and considerations for training under class imbalance, and an understanding of why imbalance methods succeed or fail.

Oscar Skean, Md Rifat Arefin, Yann LeCun et al.

Understanding what defines a good representation in large language models (LLMs) is fundamental to both theoretical understanding and practical applications. In this paper, we investigate the quality of intermediate representations in various LLM architectures, including Transformers and State Space Models (SSMs). We find that intermediate layers often yield more informative representations for downstream tasks than the final layers. To measure the representation quality, we adapt and apply a suite of metrics - such as prompt entropy, curvature, and augmentation-invariance - originally proposed in other contexts. Our empirical study reveals significant architectural differences, how representations evolve throughout training, and how factors like input randomness and prompt length affect each layer. Notably, we observe a bimodal pattern in the entropy of some intermediate layers and consider potential explanations tied to training data. Overall, our results illuminate the internal mechanics of LLMs and guide strategies for architectural optimization and training.

Katrina Drozdov, Ravid Shwartz-Ziv, Yann LeCun

Video representation learning is an increasingly important topic in machine learning research. We present Video JEPA with Variance-Covariance Regularization (VJ-VCR): a joint-embedding predictive architecture for self-supervised video representation learning that employs variance and covariance regularization to avoid representation collapse. We show that hidden representations from our VJ-VCR contain abstract, high-level information about the input data. Specifically, they outperform representations obtained from a generative baseline on downstream tasks that require understanding of the underlying dynamics of moving objects in the videos. Additionally, we explore different ways to incorporate latent variables into the VJ-VCR framework that capture information about uncertainty in the future in non-deterministic settings.

Md Rifat Arefin, Gopeshh Subbaraj, Nicolas Gontier et al.

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model's intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging $5 \times 5$ integer multiplication task, our approach achieves $99.5\%$ exact match accuracy, outperforming models of the same size (which yield $0\%$ accuracy) and GPT-4 with five-shot CoT prompting ($44\%$). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.

Tal Zeevi, Ravid Shwartz-Ziv, Yann LeCun et al.

Accurate uncertainty estimation is crucial for deploying neural networks in risk-sensitive applications such as medical diagnosis. Monte Carlo Dropout is a widely used technique for approximating predictive uncertainty by performing stochastic forward passes with dropout during inference. However, using static dropout rates across all layers and inputs can lead to suboptimal uncertainty estimates, as it fails to adapt to the varying characteristics of individual inputs and network layers. Existing approaches optimize dropout rates during training using labeled data, resulting in fixed inference-time parameters that cannot adjust to new data distributions, compromising uncertainty estimates in Monte Carlo simulations. In this paper, we propose Rate-In, an algorithm that dynamically adjusts dropout rates during inference by quantifying the information loss induced by dropout in each layer's feature maps. By treating dropout as controlled noise injection and leveraging information-theoretic principles, Rate-In adapts dropout rates per layer and per input instance without requiring ground truth labels. By quantifying the functional information loss in feature maps, we adaptively tune dropout rates to maintain perceptual quality across diverse medical imaging tasks and architectural configurations. Our extensive empirical study on synthetic data and real-world medical imaging tasks demonstrates that Rate-In improves calibration and sharpens uncertainty estimates compared to fixed or heuristic dropout rates without compromising predictive performance. Rate-In offers a practical, unsupervised, inference-time approach to optimizing dropout for more reliable predictive uncertainty estimation in critical applications.

Enrique Queipo-de-Llano, Álvaro Arroyo, Federico Barbero et al.

Attention sinks and compression valleys have attracted significant attention as two puzzling phenomena in large language models, but have been studied in isolation. In this work, we present a surprising connection between attention sinks and compression valleys, tracing both to the formation of massive activations in the residual stream. We prove theoretically that massive activations necessarily produce representational compression and establish bounds on the resulting entropy reduction. Through experiments across several models (410M-120B parameters), we confirm that when the beginning-of-sequence token develops extreme activation norms in the middle layers, both compression valleys and attention sinks emerge simultaneously. Targeted ablation studies validate our theoretical predictions. This unified view motivates us to propose the Mix-Compress-Refine theory of information flow, as an attempt to explain how LLMs organize their computation in depth by controlling attention and representational compression via massive activations. Specifically, we posit that Transformer-based LLMs process tokens in three distinct phases: (1) broad mixing in the early layers, (2) compressed computation with limited mixing in the middle layers, and (3) selective refinement in the late layers. Our framework helps explain why embedding tasks perform best at intermediate layers, whereas generation tasks benefit from full-depth processing, clarifying differences in task-dependent representations.

Aadim Nepal, Safal Shrestha, Anubhav Shrestha et al.

Large language models improve at math after instruction tuning, reinforcement learning, or knowledge distillation. We ask whether these gains come from major changes in the transformer layers or from smaller adjustments that keep the original structure. Using layer-wise ablation on base and trained variants, we find that math reasoning depends on a few critical layers, which stay important across all post-training methods. Removing these layers reduces math accuracy by as much as 80%, whereas factual recall tasks only show relatively smaller drops. This suggests that specialized layers for mathematical tasks form during pre-training and remain stable afterward. As measured by Normalized Mutual Information (NMI), we find that near these critical layers, tokens drift from their original syntactic clusters toward representations aligned with tokens less syntactically related but potentially more useful for downstream task.

Alex Reneau, Jerry Yao-Chieh Hu, Zhongfang Zhuang et al.

In deep learning, processing multidimensional inputs (e.g., images, medical scans, and time series) is an important task that often requires flattening the inputs. We introduce $\mathit{NdLinear}$, a drop-in replacement for linear layers that operates directly on tensors, requiring no flattening. By applying transformations separately along each dimension, NdLinear preserves native data structure while achieving dramatic parameter reductions, often by orders of magnitude, with minimal memory overhead. We prove NdLinear maintains expressivity through structured Tucker decomposition while preserving VC-dimension scaling. Extensive experiments demonstrate NdLinear's capacity to achieve significant parameter reductions with substantial wall-clock efficiency gains and minimal memory overhead. For instance, our $\mathit{NdLinear-LoRA}$ matches or exceeds standard LoRA on language reasoning tasks using up to $9\times$ fewer parameters. Experiments across CNNs, RNNs, Transformers, and MLPs on vision, language, time-series, and tabular tasks consistently demonstrate NdLinear's efficiency gains. While excelling at axis-separable tasks, NdLinear has limitations with entangled spatial interactions. By processing data in its original N-dimensional form, NdLinear provides a theoretically grounded, practical component for building more efficient neural architectures.

Ravid Shwartz-Ziv, Micah Goldblum, Arpit Bansal et al.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

Rylan Schaeffer, Victor Lecomte, Dhruv Bhandarkar Pai et al.

Maximum Manifold Capacity Representations (MMCR) is a recent multi-view self-supervised learning (MVSSL) method that matches or surpasses other leading MVSSL methods. MMCR is intriguing because it does not fit neatly into any of the commonplace MVSSL lineages, instead originating from a statistical mechanical perspective on the linear separability of data manifolds. In this paper, we seek to improve our understanding and our utilization of MMCR. To better understand MMCR, we leverage tools from high dimensional probability to demonstrate that MMCR incentivizes alignment and uniformity of learned embeddings. We then leverage tools from information theory to show that such embeddings maximize a well-known lower bound on mutual information between views, thereby connecting the geometric perspective of MMCR to the information-theoretic perspective commonly discussed in MVSSL. To better utilize MMCR, we mathematically predict and experimentally confirm non-monotonic changes in the pretraining loss akin to double descent but with respect to atypical hyperparameters. We also discover compute scaling laws that enable predicting the pretraining loss as a function of gradients steps, batch size, embedding dimension and number of views. We then show that MMCR, originally applied to image data, is performant on multimodal image-text data. By more deeply understanding the theoretical and empirical behavior of MMCR, our work reveals insights on improving MVSSL methods.

Ido Ben-Shaul, Ravid Shwartz-Ziv, Tomer Galanti et al.

Self-supervised learning (SSL) is a powerful tool in machine learning, but understanding the learned representations and their underlying mechanisms remains a challenge. This paper presents an in-depth empirical analysis of SSL-trained representations, encompassing diverse models, architectures, and hyperparameters. Our study reveals an intriguing aspect of the SSL training process: it inherently facilitates the clustering of samples with respect to semantic labels, which is surprisingly driven by the SSL objective's regularization term. This clustering process not only enhances downstream classification but also compresses the data information. Furthermore, we establish that SSL-trained representations align more closely with semantic classes rather than random classes. Remarkably, we show that learned representations align with semantic classes across various hierarchical levels, and this alignment increases during training and when moving deeper into the network. Our findings provide valuable insights into SSL's representation learning mechanisms and their impact on performance across different sets of classes.

Ravid Shwartz-Ziv

Although deep neural networks have been immensely successful, there is no comprehensive theoretical understanding of how they work or are structured. As a result, deep networks are often seen as black boxes with unclear interpretations and reliability. Understanding the performance of deep neural networks is one of the greatest scientific challenges. This work aims to apply principles and techniques from information theory to deep learning models to increase our theoretical understanding and design better algorithms. We first describe our information-theoretic approach to deep learning. Then, we propose using the Information Bottleneck (IB) theory to explain deep learning systems. The novel paradigm for analyzing networks sheds light on their layered structure, generalization abilities, and learning dynamics. We later discuss one of the most challenging problems of applying the IB to deep neural networks - estimating mutual information. Recent theoretical developments, such as the neural tangent kernel (NTK) framework, are used to investigate generalization signals. In our study, we obtained tractable computations of many information-theoretic quantities and their bounds for infinite ensembles of infinitely wide neural networks. With these derivations, we can determine how compression, generalization, and sample size pertain to the network and how they are related. At the end, we present the dual Information Bottleneck (dualIB). This new information-theoretic framework resolves some of the IB's shortcomings by merely switching terms in the distortion function. The dualIB can account for known data features and use them to make better predictions over unseen examples. An analytical framework reveals the underlying structure and optimal representations, and a variational framework using deep neural network optimization validates the results.

Ravid Shwartz-Ziv, Amitai Armon

A key element in solving real-life data science problems is selecting the types of models to use. Tree ensemble models (such as XGBoost) are usually recommended for classification and regression problems with tabular data. However, several deep learning models for tabular data have recently been proposed, claiming to outperform XGBoost for some use cases. This paper explores whether these deep models should be a recommended option for tabular data by rigorously comparing the new deep models to XGBoost on various datasets. In addition to systematically comparing their performance, we consider the tuning and computation they require. Our study shows that XGBoost outperforms these deep models across the datasets, including the datasets used in the papers that proposed the deep models. We also demonstrate that XGBoost requires much less tuning. On the positive side, we show that an ensemble of deep models and XGBoost performs better on these datasets than XGBoost alone.

Ravid Shwartz-Ziv, Itamar Ben Ari, Amitai Armon

In this work we present a spatial-temporal convolutional neural network for predicting future COVID-19 related symptoms severity among a population, per region, given its past reported symptoms. This can help approximate the number of future Covid-19 patients in each region, thus enabling a faster response, e.g., preparing the local hospital or declaring a local lockdown where necessary. Our model is based on a national symptom survey distributed in Israel and can predict symptoms severity for different regions daily. The model includes two main parts - (1) learned region-based survey responders profiles used for aggregating questionnaires data into features (2) Spatial-Temporal 3D convolutional neural network which uses the above features to predict symptoms progression.

Zoe Piran, Ravid Shwartz-Ziv, Naftali Tishby

The Information Bottleneck (IB) framework is a general characterization of optimal representations obtained using a principled approach for balancing accuracy and complexity. Here we present a new framework, the Dual Information Bottleneck (dualIB), which resolves some of the known drawbacks of the IB. We provide a theoretical analysis of the dualIB framework; (i) solving for the structure of its solutions (ii) unraveling its superiority in optimizing the mean prediction error exponent and (iii) demonstrating its ability to preserve exponential forms of the original distribution. To approach large scale problems, we present a novel variational formulation of the dualIB for Deep Neural Networks. In experiments on several data-sets, we compare it to a variational form of the IB. This exposes superior Information Plane properties of the dualIB and its potential in improvement of the error.

Ravid Shwartz-Ziv, Alexander A. Alemi

In this preliminary work, we study the generalization properties of infinite ensembles of infinitely-wide neural networks. Amazingly, this model family admits tractable calculations for many information-theoretic quantities. We report analytical and empirical investigations in the search for signals that correlate with generalization.

Itamar Ben-Ari, Ravid Shwartz-Ziv

We propose a semi-supervised model for detecting anomalies in videos inspiredby the Video Pixel Network [van den Oord et al., 2016]. VPN is a probabilisticgenerative model based on a deep neural network that estimates the discrete jointdistribution of raw pixels in video frames. Our model extends the Convolutional-LSTM video encoder part of the VPN with a novel convolutional based attentionmechanism. We also modify the Pixel-CNN decoder part of the VPN to a frameinpainting task where a partially masked version of the frame to predict is given asinput. The frame reconstruction error is used as an anomaly indicator. We test ourmodel on a modified version of the moving mnist dataset [Srivastava et al., 2015]. Our model is shown to be effective in detecting anomalies in videos. This approachcould be a component in applications requiring visual common sense.

Ravid Shwartz-Ziv, Naftali Tishby

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the \textit{Information Plane}; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on {\emph compression} of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer.