Introduces conditional scale entropy (CSE) and reports that metaphorical tokens elicit significantly higher spectral breadth than literal tokens at contiguous layers across multiple decoder-only LLMs.
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Opening the Black Box of Deep Neural Networks via Information
31 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
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.
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Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
JEDI is the first online end-to-end latent diffusion world model that trains latents from denoising loss rather than reconstruction, achieving competitive Atari100k results with 43% less VRAM and over 3x faster sampling than pixel diffusion baselines.
A Markov category framework for language models provides an information-theoretic rationale for speculative decoding and shows that a quadratic surrogate to negative log-likelihood induces generalized CCA alignment in linear-softmax heads after normalization.
Language representations serve as the asymptotic attractor for convergence in independently trained multimodal neural networks due to feature density asymmetry.
Channel importance splits into task relevance and local replaceability; local-axis metrics predict safe removal under pruning better than target-axis metrics across multiple CNNs and datasets.
InfoAtlas is a pretrained neural model for zero-shot mutual information estimation that matches state-of-the-art accuracy with 100x speedup and handles varying dimensions via a single model.
The Shannon Scaling Law treats LLM training as noisy-channel transmission and predicts U-shaped performance degradation when signal-to-noise ratio falls below a threshold, outperforming monotonic scaling laws on Pythia and OLMo2 data.
PromptNCE frames LLM conditional probability estimation as contrastive prompting augmented with an OTHER category, recovering true P(y|x) and achieving up to 0.82 Spearman correlation with human-derived PMI on three datasets.
OmniISR unifies centralized, federated, and hybrid learning by injecting mutual-information supervision and negative-entropy regularization at multiple hidden layers, with supporting convergence and drift bounds.
Representation geometry in language models aligns with the unembedding readout subspace in a scale-dependent manner, preserved throughout training in large models but progressively lost in late layers of small models despite continued loss improvement.
InfoRidge reveals a non-monotonic pattern in which predictive mutual information between hidden states and outputs peaks in intermediate layers before declining in final layers.
CNN feature activations follow long-tailed Weibull-like distributions with increasing tail dependence by depth rather than Gaussian, indicating a Matthew process that concentrates signal in tails.
Effective data transferred from pre-training to fine-tuning is described by a power law in model parameter count and fine-tuning dataset size, acting like a multiplier on the fine-tuning data.
All rank-monotone pruning scorers converge to identical accuracy at fixed sparsity, but non-monotone features with sparsity-dependent complexity can escape this plateau, as shown by the SICS hypothesis on ViT-Small/CIFAR-10.
LLM OOD detectors are length-confounded; a two-pathway embedding-plus-trajectory framework detects covert OOD inputs at 0.721 average AUROC and 0.850 on jailbreaks.
Self-supervised encoders prefer isotropic Gaussian latent states because the Information Bottleneck, recast as rate-distortion over the predictive manifold, makes these states optimal for target-neutral representations.
Introduces integration, metastability, and dynamical stability index measures from layer activations and reports patterns distinguishing CIFAR-10 from CIFAR-100 difficulty plus early convergence signals across ResNet variants, DenseNet, MobileNetV2, VGG-16, and a Vision Transformer.
Language models show good calibration when asked to estimate the probability that their own answers are correct, with performance improving as models get larger.
Ranked preference modeling outperforms imitation learning for language model alignment and scales more favorably with model size.
Intelligence Inertia models the computational resistance to structural change in neural networks via a heuristic relativistic analogy, yielding a J-shaped cost curve that diverges from classical approximations.
Proposes a semantic information theory for LLMs that substitutes the token for the bit as the atomic carrier of meaning, recasts the Transformer as an energy-based model, and derives directed rate-distortion and rate-reward functions using Massey's directed information.
TALE selectively prunes task-detrimental layers in LLMs at inference time to match or exceed baseline performance with lower computational cost across multiple models and tasks.
Binary neural networks exhibit frequent late-stage compression in the information plane, but compressed representations do not reliably correlate with better generalization performance.
citing papers explorer
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Post-Hoc Understanding of Metaphor Processing in Decoder-Only Language Models via Conditional Scale Entropy
Introduces conditional scale entropy (CSE) and reports that metaphorical tokens elicit significantly higher spectral breadth than literal tokens at contiguous layers across multiple decoder-only LLMs.
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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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JEDI: Joint Embedding Diffusion World Model for Online Model-Based Reinforcement Learning
JEDI is the first online end-to-end latent diffusion world model that trains latents from denoising loss rather than reconstruction, achieving competitive Atari100k results with 43% less VRAM and over 3x faster sampling than pixel diffusion baselines.
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A Markov Categorical Framework for Language Modeling
A Markov category framework for language models provides an information-theoretic rationale for speculative decoding and shows that a quadratic surrogate to negative log-likelihood induces generalized CCA alignment in linear-softmax heads after normalization.
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The Wittgensteinian Representation Hypothesis: Is Language the Attractor of Multimodal Convergence?
Language representations serve as the asymptotic attractor for convergence in independently trained multimodal neural networks due to feature density asymmetry.
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Task Relevance Is Not Local Replaceability: A Two-Axis View of Channel Information
Channel importance splits into task relevance and local replaceability; local-axis metrics predict safe removal under pruning better than target-axis metrics across multiple CNNs and datasets.
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InfoAtlas: A Foundation Model for Zero-Shot Statistical Dependence Estimate
InfoAtlas is a pretrained neural model for zero-shot mutual information estimation that matches state-of-the-art accuracy with 100x speedup and handles varying dimensions via a single model.
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LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws
The Shannon Scaling Law treats LLM training as noisy-channel transmission and predicts U-shaped performance degradation when signal-to-noise ratio falls below a threshold, outperforming monotonic scaling laws on Pythia and OLMo2 data.
-
PromptNCE: Pointwise Mutual Information Predictions Using Only LLMs and Contrastive Estimation Prompts
PromptNCE frames LLM conditional probability estimation as contrastive prompting augmented with an OTHER category, recovering true P(y|x) and achieving up to 0.82 Spearman correlation with human-derived PMI on three datasets.
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OmniISR: A Unified Framework for Centralized and Federated Learning via Intermediate Supervision and Regularization
OmniISR unifies centralized, federated, and hybrid learning by injecting mutual-information supervision and negative-entropy regularization at multiple hidden layers, with supporting convergence and drift bounds.
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Scale Determines Whether Language Models Organize Representation Geometry for Prediction
Representation geometry in language models aligns with the unembedding readout subspace in a scale-dependent manner, preserved throughout training in large models but progressively lost in late layers of small models despite continued loss improvement.
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The Generalization Ridge: Information Flow in Natural Language Generation
InfoRidge reveals a non-monotonic pattern in which predictive mutual information between hidden states and outputs peaks in intermediate layers before declining in final layers.
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Why CNN Features Are not Gaussian: A Statistical Anatomy of Deep Representations
CNN feature activations follow long-tailed Weibull-like distributions with increasing tail dependence by depth rather than Gaussian, indicating a Matthew process that concentrates signal in tails.
-
Scaling Laws for Transfer
Effective data transferred from pre-training to fine-tuning is described by a power law in model parameter count and fine-tuning dataset size, acting like a multiplier on the fine-tuning data.
-
Selection Plateau and a Sparsity-Dependent Hierarchy of Pruning Features
All rank-monotone pruning scorers converge to identical accuracy at fixed sparsity, but non-monotone features with sparsity-dependent complexity can escape this plateau, as shown by the SICS hypothesis on ViT-Small/CIFAR-10.
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How Language Models Process Out-of-Distribution Inputs: A Two-Pathway Framework
LLM OOD detectors are length-confounded; a two-pathway embedding-plus-trajectory framework detects covert OOD inputs at 0.721 average AUROC and 0.850 on jailbreaks.
-
Why Self-Supervised Encoders Want to Be Normal
Self-supervised encoders prefer isotropic Gaussian latent states because the Information Bottleneck, recast as rate-distortion over the predictive manifold, makes these states optimal for target-neutral representations.
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Training Deep Visual Networks Beyond Loss and Accuracy Through a Dynamical Systems Approach
Introduces integration, metastability, and dynamical stability index measures from layer activations and reports patterns distinguishing CIFAR-10 from CIFAR-100 difficulty plus early convergence signals across ResNet variants, DenseNet, MobileNetV2, VGG-16, and a Vision Transformer.
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Language Models (Mostly) Know What They Know
Language models show good calibration when asked to estimate the probability that their own answers are correct, with performance improving as models get larger.
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A General Language Assistant as a Laboratory for Alignment
Ranked preference modeling outperforms imitation learning for language model alignment and scales more favorably with model size.
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Intelligence Inertia: Physical Isomorphism and Applications
Intelligence Inertia models the computational resistance to structural change in neural networks via a heuristic relativistic analogy, yielding a J-shaped cost curve that diverges from classical approximations.
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Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs
Proposes a semantic information theory for LLMs that substitutes the token for the bit as the atomic carrier of meaning, recasts the Transformer as an energy-based model, and derives directed rate-distortion and rate-reward functions using Massey's directed information.
-
TELL-TALE: Task Efficient LLMs with Task Aware Layer Elimination
TALE selectively prunes task-detrimental layers in LLMs at inference time to match or exceed baseline performance with lower computational cost across multiple models and tasks.
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Information Plane Analysis of Binary Neural Networks
Binary neural networks exhibit frequent late-stage compression in the information plane, but compressed representations do not reliably correlate with better generalization performance.
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Human-Centered Learning Mechanics: A Dynamical Framework for Entropy-Regulated Representation Learning
Proposes HCLM framework formalizing entropy regularization via effective information force and geometric surrogates like log-determinant covariance, with experiments claiming stronger stable forces than softmax entropy.
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Learning to Find Correlated Features by Maximizing Information Flow in Convolutional Neural Networks
Introduces IFM loss regularization for CNNs to learn correlated discriminative features, tested on shiftedMNIST dataset.
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Personalization as a Game: Equilibrium-Guided Generative Modeling for Physician Behavior in Pharmaceutical Engagement
EGPF treats physician engagement as an incomplete-information Bayesian game, infers behavioral types via functors, and uses equilibrium strategies to direct generative AI, reporting 34% better AUC and 28% higher relevance than baselines.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
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