Collapse

DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers. Exact inference in DGPs is intractable, and variational inference is often used to approximate the posterior with a parametric distribution tuned by minimizing the Kullback-Leibler divergence. Moreover, finding a good VI approximation is challenging. In particular, a problem of VI is posterior collapse, where VI converges to a variational posterior that matches the prior. In variational DGPs, this implies explaining the data as noise. This work studies posterior collapse in DGPs and identifies its connection to the DSVI algorithm and the widely used linear prior mean function employed in all but the last layer. We show that the benefit of the linear prior mean does not arise from avoiding the non-injective pathology in very deep DGPs, as previously believed, but from improving the conditioning of the optimization problem at initialization. Thus, we propose an alternative initialization of a zero prior mean DGP that mimics a DGP with a linear prior mean at initialization. This enables successful training of DGPs without imposing optimization-driven constraints on the prior, allowing to choose the prior based on modeling assumptions rather than optimization convenience. Our analysis considers three common parameterizations of DGPs and shows that not all of them benefit from a linear prior mean. We also explain why a whitened parameterization of the \DGP provides more stable convergence, something often assumed from experience, but lacking a rigorous analysis. Furthermore, we show that this stability is also beneficial to avoid the posterior collapse problem. Extensive experiments validate our findings: the proposed initialization prevents posterior collapse, improves stability, and achieves performance comparable to (and sometimes better than) DGPs with a linear prior mean.

The physical anastylosis of collapsed architectural monuments -- the meticulous reassembly of fallen stone elements into their original structural configuration -- represents one of the most intellectually demanding challenges in conservation science. Traditional approaches depend heavily on expert archaeologist judgement and manual block-by-block correspondence, a process that is both labour-intensive and inherently subjective. Inspired by the combinatorial complexity of this problem as manifested in the game of Jenga, we present Jenga Inverse Predictor , a GPU-accelerated deep learning framework that addresses structural anastylosis as an inverse prediction task. Given an image of a collapsed block assembly, JIP-2 reconstructs the most probable prior tower configuration by: (1) implementing a complete rigid-body physics engine with OBB/SAT collision detection and a Projected Gauss-Seidel (PGS) contact solver accelerated with Numba JIT and CuPy CUDA; (2) applying the analytical force thresholds of Ziglar (CMU, 2006) -- F_app = 3mu_smg (Y-axis, torque-free) and F_app = 4mu_smg (X-axis, torque risk) -- over three friction levels (mu_s in {0.25, 0.40, 0.60}) across 450 simulated episodes; (3) training a dual-stream ResNet-18 that injects a friction one-hot vector and jointly predicts block removal count, per-position removal probabilities, centre-of-mass imbalance, and Ziglar torque risk; and (4) generating a smooth 3-D video of the block-by-block reverse reconstruction. We discuss implications for computer-assisted anastylosis at the UNESCO Maya site of Uxmal, Yucatan, and provide a detailed technical description of the full pipeline, architecture, and loss formulation.

Accuracy degradation is the standard metric for Catastrophic Forgetting (CF), however, it records only whether forgetting occurred or not. It saturates at the extremes and collapses discretely at task boundaries, hiding the internal structure of what is being forgotten. We introduce six softmax-derived metrics spanning true-label rank (TLR), predictive confidence, and distributional divergence that characterize forgetting continuously, each normalized to [0, 1] with no modification to training. On CIFAR-100, these metrics carry information where accuracy does not: at 0% accuracy, the Confusion Margin spans an IQR of [0.32, 0.50] across classes that accuracy treats identically. We demonstrate that this richer signal is actionable in mitigating catastrophic forgetting. Per-sample metric scores used as loss weights reduce forgetting by 1.3 percentage points over uniform experience replay (ER) on CIFAR-100. Furthermore, the slope of a metric over a small window provides a stable sampling criterion: at a small-window size (e.g. 3 epochs), accuracy-trend degrades to 34.79% (std. = 2.32) while log-TLR achieves 41.07% (std. = 0.57). This gap is structural since reliable small-window trend estimation requires a continuous signal. On TinyImageNet, log-TLR trend sampling reduces forgetting by 7.7 percentage points over the ER baseline.

Large Transformer models function as Dense Associative Memories (DAMs), retrieving knowledge via high-dimensional attractor dynamics driven by the self-attention mechanism \citep{ramsauer2020hopfield, wu2024attention}. However, adapting these frozen memory systems to new tasks presents a fundamental ``Plasticity-Stability'' dilemma. Current methods either risk catastrophic interference by modifying synaptic weights directly (e.g., LoRA) \citep{hu2021lora} or degrade associative capacity by clogging the retrieval buffer with static prompt tokens (e.g., VPT) \citep{jia2022vpt}. In this work, we propose \textbf{H-Res} (Hierarchical Residual Steering), a mechanism that modulates the effective energy landscape of the Transformer without altering its global equilibrium or expanding its sequence length. By formulating adaptation as a control problem on the activation manifold \citep{chen2018neuralode}, H-Res learns a state-dependent vector field that steers token trajectories into task-specific basins of attraction. We formally prove that H-Res preserves the attention entropy of the foundation model and facilitates Neural Collapse \citep{papyan2020prevalence}. Empirically, Manifold Steering outperforms global weight modification by 26% on associative retrieval tasks and eliminates the computational overhead of prompt-based methods, scaling effectively to structured domains \citep{zha2023vtab}.

Discrete diffusion language model (DLM) fine-tuning inherits inexpensive diagnostics from denoising-time confidence monitors, but their PEFT-training meaning is untested. We test top-1 argmax concentration as a collapse warning. Across 816 LoRA/PEFT configurations from three DLM families, the warning fires for every configuration while logs record 0/816 actual collapses at the 200 step horizon, giving zero precision. The cause is pre-equilibrium saturation: top-1 concentration is already high before optimization and quickly becomes insensitive to final training stability. We then evaluate max LoRA gradient norm, a parameter-side signal that samples gradient routing rather than token concentration. On a pooled held-out LLaDA-family split, a train-optimized threshold identifies top-decile final-loss configurations with precision 0.68 and F1=0.79, above the all-positive top-1 baseline even at the lower split-bootstrap confidence bound. Autoregressive controls and cross-family threshold failures bound the result to short-horizon DLM-LoRA inspection rather than a universal collapse detector. Workflow: drop top-1 as a PEFT alarm, log max-gradient early in training, and calibrate thresholds per DLM family before routing runs for inspection.

Self-organized criticality (SOC), a dynamical regime associated with maximal information processing, offers a promising foundation for reservoir computing. Recent work has shown that neural cellular automata (NCA) can be evolved toward critical avalanche dynamics and employed as effective reservoirs for memory and classification tasks. Here, we investigate whether mass conservation -- a local redistribution rule that preserves total lattice mass -- serves as an inductive bias toward SOC in evolved NCA reservoirs. We compare mass-conserving and standard NCA across multiple independent runs and evaluate both on three downstream benchmarks: 5-bit sequential memory, MNIST digit classification, and CartPole-v1 temporal control. Mass-conserving NCA consistently exhibit stronger criticality, with more runs achieving perfect power-law fits across avalanche distributions, while also being 1.27$\times$ faster during evolution. Importantly, conservation does not impair downstream utility: both variants achieve comparable performance across all three tasks. Furthermore, the reservoir with perfect criticality achieves the highest temporal control score, suggesting a positive link between SOC quality and sequential computation. Our results demonstrate that mass conservation is a simple, effective mechanism for promoting robust criticality in evolved NCA reservoirs without sacrificing downstream performance.

Since 2023, computer scientists have warned against model collapse -- the contamination of training sets with AI-generated outputs that progressively degrade model performance. Exemplifying a positive-feedback-driven failure, it produces effects such as word repetition or pixel noise, ultimately leading to a loss of meaning and coherence -- at least from an engineering standpoint. From a creative one, however, collapse is not merely a breakdown: it also functions as a recursive mirror that recalls early analog video feedback experiments, raising once again the question of what happens when a system turns inward and sees itself. In such cases, so-called machine vision no longer transmits the world (as in tele-vision) but increasingly generates worlds from within. Drawing on media archaeology through case studies of both historical video synthesis techniques and contemporary artistic uses of machine learning, this paper examines what recursive training reveals about the dependent nature of AI-generated data. It argues that the potential effects of collapse challenge transhumanist ideals while inviting an aesthetic perspective, positioning noise and recursion as key concepts for understanding both artmaking and the AI ecosystem. Distributing agency across scales and networks, the latter currently remains reliant on new human-produced content, particularly within foundation models trained on massive datasets.

Long-term memory has become increasingly important for LLM agents that operate across extended interactions and evolving task contexts. Recent memory systems have made past experiences more persistent, compact, and retrievable, but retrieval alone does not ensure that a memory provides valid evidence for the current query. When experiences are compressed into reusable fragments, memories from different situations may appear equally relevant if they involve recurring entities or user states. We refer to this failure as context collapse: memories lose the surrounding context needed to judge whether they provide valid evidence for the current query. To address this problem, we propose Contextual Reinstatement for Agentic Memory (RaMem), a framework that turns retrieved memory fragments into contextually verifiable evidence. RaMem operates through four coordinated stages: (i) evidence anchoring grounds each memory in its original episodic conditions, especially event time, mention time, session span, and participants; (ii) recall condition induction derives the evidence conditions implied by the query; (iii) validity-aware retrieval uses these conditions to prioritize context-compatible memories while retaining content-relevant candidates as fallback evidence; and (iv) context-preserved synthesis keeps the selected memories' structured context available to the generator. Experiments on long-term memory benchmarks show that RaMem consistently improves performance over strong memory baselines, with average F1 gains of more than 10% across several backbones.

Attention sinks, representation collapse, and norm stratification are treated as transformer-specific pathologies. We show they are not specific to attention: they are what content-based routing does under a fixed similarity metric. We give a reframing identity: softmax attention is Boltzmann-weighted aggregation over Euclidean distances with constant key norms, so its score omits a $-\|k\|^2$ term and is blind to key magnitude. This predicts that any router whose metric is ill-matched to its representations should compensate, by concentrating its routing and collapsing the routed representations. We test it on routers that score and aggregate over different axes: softmax attention over tokens (nine pretrained transformers), graph attention over nodes, a selective state-space model and a recurrent mixer over time, and learned residuals over depth. All develop the same signature, and two within-model ablations show it is caused by the routing mechanism rather than by incidental dynamics. The form is contingent, set by the strength of the positional brake each router carries alongside its content score; we sweep that brake and move the onset across its whole range. The mechanism is not contingent, and it does not require norm stratification: a router with norm-normalized keys concentrates just the same. We do not claim these models implement Riemannian geometry; the geometric view is a diagnostic that names the inadequacy of the flat, norm-blind metric.

Deep neural models for click-through rate prediction often exhibit a sharp decline in validation performance immediately after the first training epoch despite continued improvement in training loss. This instability restricts effective learning and limits model performance. In this study, we analyze this behavior using large-scale industrial datasets and evaluate practical mitigation strategies. While reducing the learning rate provides only incremental gains, controlling feature sparsity yields substantial improvements. Removing highly sparse features and aggregating infrequent feature values stabilizes training, extends useful learning beyond a single epoch, and improves both offline evaluation metrics and online system performance.

Reinforcement learning (RL) has become the dominant paradigm for improving the reasoning capabilities of large language models, but it requires expensive training, curated data, and reward signals. Recent work shows that sampling from sharpened base-model distributions at test time recovers much of the RL gain, yet existing methods rely solely on output-layer likelihoods and ignore the transformer's internal forward-pass dynamics. We introduce Depth-Entropy Guided Sampling (DEGS), a training-free, test-time method that exploits layer-wise entropy collapse as an intrinsic quality signal. We observe that stronger reasoners -- including RL-posttrained variants -- exhibit a distinctive "late collapse": logit-lens decoded entropy stays elevated until deeper layers before converging. We define a per-sequence collapse depth $D(\mathbf{x})$ and a joint objective $π(\mathbf{x}) \propto p(\mathbf{x})^α\exp(βD(\mathbf{x}))$ that combines sequence likelihood with this depth-entropy structure, instantiated inside an MCMC power-sampling framework (DEGS-MCMC). Across three open-weight models and four reasoning benchmarks, this near-chance per-candidate signal compounds over the sampling trajectory into state-of-the-art training-free accuracy, with gains largest out of domain and on the harder splits -- exactly where likelihood alone falls short -- at single-digit-percent wall-clock overhead. DEGS narrowly trails an in-house GRPO reference on the math splits GRPO was trained for, yet surpasses it out of domain on GPQA for all three models, without any training, reward model, or labeled data.

Multimodal time series forecasting, which pairs numerical sequences with domain-relevant textual reports, promises to inject world knowledge into forecasting pipelines. However, we uncover a critical failure mode in existing frameworks that we term text collapse: the text branch converges to a content-independent transformation, contributing negligible discriminative signal regardless of the input description. We argue that text collapse is a consequence of a fundamental asymmetry in time series forecasting: the numerical input is strongly autocorrelated with the output, making the numerical backbone inherently dominant, while the text branch, despite carrying complementary and often critical information, is insufficiently utilized, leading to its systematic underexploitation. To address this, we propose \textbf{REST-TS} (\textbf{R}esidual-\textbf{E}xclusive \textbf{S}upervision for \textbf{T}ext in \textbf{T}ime \textbf{S}eries), which turns the asymmetry into a design principle: the numerical backbone produces its own independent numerical forecast, and the text branch is exclusively supervised to predict the structured components of the residual, the prediction gap that numbers cannot explain. Because no numerical pathway can reduce these losses, the text branch must extract genuine content from the input description. Evaluated across diverse real-world domains and backbone architectures, REST-TS achieves state-of-the-art performance and consistently demonstrates greater text-branch utilization than existing frameworks, providing strong empirical evidence that supervising the text branch on the residual compels it to extract genuine content from the input.

The standard heuristic of selecting the SFT checkpoint with the highest pass@1 for GRPO can fail when SFT compresses the rollout distribution. For binary rewards, the expected within group advantage variance is $p(1{-}p)(g{-}1)/g$; when early GRPO drives $p$ below $p^*(g)$, most groups have identical rewards and provide no group relative signal. We study SFT depth ladders for Qwen2.5-Coder-3B and DeepSeek-Coder-6.7B. We test Qwen2.5-Coder-3B across five depths and three seeds, and DeepSeek-Coder-6.7B across four matched depths and three seeds. On Qwen, pre RL pass@1 rises with SFT depth, but peak GRPO pass@10 falls from $0.806$ to $0.481$ (3 seed mean, $n{=}20$); pre RL entropy is positively associated with the GRPO outcome ($ρ{=}{+}0.69$). On DeepSeek, pass@1 remains far above $p^*(8){=}0.083$, and GRPO outcomes compress rather than invert. A two stage diagnostic, combining pre RL entropy triage with an early GRPO entropy monitor, flags high risk checkpoints and can stop failing runs early. Simple KL to reference regularisation and label smoothing variants do not rescue the collapsed Qwen checkpoint in our setting, suggesting the failure is not a trivial GRPO hyperparameter artefact.

Recent progress has shown promise in distilling multi-step video diffusion models into efficient few-step students. Among them, Distribution Matching Distillation (DMD) and its successor DMD2 achieved strong generation quality and fast convergence. However, due to the nature of the reverse Kullback--Leibler (KL) objective, these methods exhibit two persistent failure modes: a substantial drop in sample diversity, and visibly over-saturated outputs that deviate from real-video appearance. In this work, we propose Data-Forcing Distillation (DFD), a simple post-training framework that restores diversity and fidelity in DMD with only a single-line of code change. At its core is the teacher score discrepancy to guide the student toward the real-data distribution, pulling it to missing modes (mitigating mode collapse) and away from problematic modes absent in real data (avoiding over-saturation). We provide an in-depth theoretical analysis of our framework and validate our approach on text-to-video, image-to-video, and autoregressive video generation. With only 100--300 steps of finetuning, DFD effectively restores diversity and fidelity on both Wan2.1-1.3B and Cosmos-Predict2.5-2B model, resolving the over-saturation artifacts with significantly better video dynamics and appearance, and even outperforms the teacher model.

SWave is a complex-valued recurrent language model (169.26M parameters, D=384, L=16, T=2048) trained on FineWeb-Edu using 2xH100 NVL. It was designed around three founding premises: that representing language as complex waves rather than real-valued numbers enables richer information encoding; that a Cayley-parameterised unitary transition provides a mathematical guarantee against state decay or explosion; and that a hidden state which rotates rather than shrinks preserves signal integrity over arbitrarily long contexts. The core of SWave evolved substantially across three development phases. The Resonance Head was found to structurally admit imaginary-channel collapse as a global loss minimum (a failure mode we term cos-domination collapse) and was superseded by an untied head with independent real and imaginary embedding tables from the Phase-Associative Memory (PAM) architecture. This resolved the degenerate minimum and enabled stable 200,000-step training (best-step PPL 22.0 at step 89,861). ComplexNorm and the Wave Propagation Scan proved load-bearing throughout all three phases and were retained to the final architecture. ProtectGatedScan was reframed as a structural prior rather than a learned behaviour. The four multi-scale retention concepts showed no measurable improvement under controlled evaluation and were found non-load-bearing. The ComplexGatedUnit was superseded by a real-valued squared-ReLU channel mixer with fewer parameters. The auxiliary training objectives showed no benefit once structural constraints were resolved. The investigation yields a formal characterisation of cos-domination collapse, a parallel scan with a log-space backward pass for numerical stability, six transferable engineering principles for complex-valued recurrent training, and a plan-to-code traceability methodology for catching structural divergences that conventional test suites miss.

As LLM-driven multi-agent systems (MAS) transition from lab to production, system behavior exhibits nonlinear degradation. We introduce the Intelligence Entropy Principle: probability-driven systems spontaneously drift toward disorder, formalized as S(t) = S0 * exp(alpha*t/Cm), where Cm is a model capability coefficient we propose. Lyapunov analysis yields the stabilization condition lambda > alpha/Cm. We construct the ADE (Agent Delivery Engineering) four-layer framework (L1 Physical Laws through L4 User Adaptation) with 23 core components. Validation spans 100K-scale experiments and 33.6 days of production monitoring. We propose a Five-Layer Disorder Taxonomy unifying failures under structural collapse, and present Elastic Organization as an original MAS morphology. Results: channel fracture reduced from 69-98% to near 0%; system death probability below 0.02%.

When AI agents use language models to evaluate their own outputs in a feedback loop, systematic biases emerge. We show that Evaluator Preference Collapse (EPC) is dramatically amplified in multimodal settings. Using GPT-4o to evaluate DeepSeek-chat across text and visual tasks, we find that a single strategy (step_by_step) absorbs 48.4% of all weight -- 3.2x the collapse observed in text-only self-evaluation -- while three visual-domain strategies receive only 9.1% combined weight. We then demonstrate a novel phenomenon we term cross-modal coupling: evaluator preferences acquired on one modality transfer to and corrupt strategy selection on another. Through a four-phase isolation training paradigm, we measure coupling coefficients and document strategy inversion -- the optimal strategy for a modality reverses after cross-modal exposure. A Phase 3 statistical validation across five evaluator configurations (N=80 total independent repetitions, 35,000 API calls) with both text-proxy and real-image visual tasks finds: cross-model evaluation produces strong coupling (JSD0.19-0.34), real-image inputs yield the most directionally consistent signal (mean gamma_{T->V}=1.145, gamma_{V->T}=0.937, 70% T->V, Cohen's d=0.56), and self-evaluation provides near-complete immunity -- 97% of runs (N=30) yield zero coupling (JSD=0.003, d=0.07). Three methodological ablations and multi-executor validation confirm the effect is not a structural artifact. We introduce the coupling matrix indexed by evaluator identity, release the MM-EPC framework, and identify cross-model evaluator architecture as the primary risk factor for preference drift. Code and data: https://github.com/aidless/mm-epc.

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to $0$ asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

The proliferation of recursive training on synthetic data can alleviate data scarcity but risks model collapse, where repeated training erodes distributional tails and homogenizes outputs. Data selection is widely viewed as a remedy, yet its reliability depends critically on the reference distribution used by the verifier. We show that in low-resource verification regimes, where each verifier observes only a small, fragmented, and biased slice of the target manifold, selection itself becomes biased. This situation naturally arises in low-resource data silos such as healthcare consortia or proprietary financial institutions, where raw data cannot be pooled and local references are inherently incomplete. As a result, selection preferentially retains samples aligned with the local manifold while pruning globally relevant tail modes, turning from a safeguard against collapse into a mechanism that precipitates it. We theoretically prove that such siloed selection accelerates collapse and induces power-law diversity decay. As an initial mitigation, we construct Wasserstein proxy references from multiple silos without sharing raw data. Empirical results confirm that local-reference selection fails on skewed distributions, whereas collaborative proxy references mitigate diversity degradation, suggesting that recursive synthetic-data pipelines require particular caution when real-data coverage is fragmented or scarce.

Generative listwise ranking with Large Multimodal Models (LMMs) aims to capture global list context in a single forward pass, but its effectiveness degrades in long-context multimodal scenarios. We identify a recurring failure mode, parse collapse, where the autoregressive decoder produces fluent yet incomplete rankings by silently omitting candidates and terminating early. This failure stems from limited context utilization rather than simple formatting mistakes, making prompt engineering and constrained decoding insufficient. We propose PRISMR (Parameterized Representation Internalization for Semantic Multimodal Ranking), a framework that replaces transient in-context list processing with parametric structural conditioning. PRISMR uses a lightweight hypernetwork to encode multimodal candidates in parallel and generate item-specific LoRA weights, which are synthesized into an instance-specific adapter for a LMM. This paradigm enables more robust internalization of list structure while preserving the base model. We further introduce a large-scale multimodal review-ranking benchmark for evaluation. Experiments demonstrate that PRISMR substantially reduces parse collapse, improves listwise ranking performance, and transfers effectively across domains and instruction-tuned backbones.

While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a layerwise non-uniform training mechanism: downstream classifier weights are driven by dense cross-entropy gradients into a rank-2 equiangular configuration before upstream embeddings fully reorganize, and once this classifier plane forms, backpropagated feature gradients constrain embedding motion to the same plane while weight decay suppresses orthogonal components. Second, after this subspace locking, the induced in-plane dynamics admit an entropy-regularized transport interpretation on $S^1$; combined with modular-addition labels, this reduces embedding formation to phase alignment, whose minimizers are single-frequency characters of $\mathbb{Z}/P\mathbb{Z}$ and hence equal-angle points on a circle. Third, we quantify why this solution prevails over NC: a simplex ETF gains only an $O(1)$ advantage in cross-entropy, whereas the cyclic rank-2 solution enjoys a $Θ(K)$ advantage under Schatten or weight-decay surrogates, yielding a critical threshold $λ_{\mathrm{crit}} = Θ(1/K)$. Our results explain both why classifier weights move first and why embeddings subsequently align with them, showing that grokking on modular arithmetic is governed not by maximal separation alone but by a task-structured trade-off between separation, symmetry, and complexity.

This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework. Finally, experiments and empirical analysis show the effectiveness of the collapsibility for causal estimations in CPDAGs. Code is available at https://github.com/Jamyang-D/strongly-convex.

Dominant web data curation pipelines for pretraining collapse document quality into a single composite score, systematically missing high-value content along dimensions the scorer underweights. We present a taxonomy-driven framework that recovers this value by filtering along semantically meaningful dimensions that composite scores fail to capture. First, building on the ESSENTIAL-WEB taxonomy, we introduce two novel dimensions: timeliness and cultural specificity, both of which show low pairwise NMI with existing ones. We annotate 14M documents using Qwen2.5 32B and distill into a lightweight 0.5B model. To enable rapid corpus-wide annotation, we additionally train a 73M multi-task MLP on E5 embeddings, achieving 50x inference throughput. Second, to navigate the combinatorial explosion of filter configurations, we introduce a compute-efficient two-pass framework: Pass 1 identifies the strongest dimension signals at small scale; Pass 2 constructs and evaluates conjunctive and disjunctive compound filters from the top performers - identifying high-performing configurations at a fraction of full scaling-law cost. Applying the selected filters to deprioritized web data, taxonomy-filtered subsets outperform their unfiltered baselines and even surpass the highest-quality tier. On mid-tier data, our best filter improves over its unfiltered baseline by 12.1% on reasoning, 9.5% on coding, and 2.0% on knowledge benchmarks, exceeding unfiltered top-tier data by 6.7% on reasoning and 13.7% on coding. Furthermore, filtered data from two tiers below the typical production threshold improves by 22.3% on reasoning and 19.5% on coding over its unfiltered baseline, surpassing top-tier data on coding benchmarks. These results establish that vast latent value remains locked in deprioritized web data, and that multi-dimensional taxonomy filtering is a principled, compute-efficient key to unlocking it.

Synthetic histopathology image generation addresses critical challenges in computational pathology, including patient privacy and the growing need for large-scale training data for foundation models. Latent diffusion models have dominated the image generation domain, with recent works emphasizing that the choice of latent space is critical to the quality of generated images. Existing state-of-the-art generative models in histopathology use pretrained Vision Foundation Models (VFMs) as conditioning signals, and we observe that this leads to "conditioning collapse," where the conditioning signal dominates the latent space and lowers the quality and diversity of generated samples. Therefore, we instead use pretrained histopathology VFMs as the latent space itself, leveraging their patch-token features that encode rich semantic information. We empirically show that these features are $\ell_2$-normalized and lie on the unit hypersphere $\mathcal{S}^{d-1}$ with strong angular dominance and intrinsic curvature, making them naturally suited for a Riemannian formulation. We therefore present STREAM, the first framework to apply Riemannian flow matching in the pathology domain. STREAM consists of two stages: 1) a bridge-type stochastic perturbation that establishes per-token rectifiability on $\mathcal{S}^{d-1}$ for training a Diffusion Transformer (DiT) in latent space, and 2) a novel anisotropic decoder that allocates robustness to low-energy directions of the velocity-field Jacobian while preserving fidelity along its high-energy directions. Together, STREAM achieves state-of-the-art reconstruction and generation performance on breast and colorectal cancer datasets. The code will be publicly released upon acceptance.

Catastrophic forgetting is commonly interpreted as the irreversible erasure of previously acquired knowledge during sequential learning. In this work, we investigate an alternative perspective: that forgetting may arise not from complete destruction of task representations but from a loss of accessibility to preserved information. We introduce a three-level framework separating knowledge storage, representation, and accessibility, and evaluate each component through a series of continual-learning experiments on sequential CIFAR-100 classification using ResNet-18. Our analysis combines checkpoint persistence, linear probing, representation geometry, classifier-reset recovery, and layer-wise recoverability experiments. We observe complete behavioral forgetting of earlier tasks, with task accuracy collapsing from 54.8% to 0%, while linear probe performance retains approximately 76% of the original representational information. Furthermore, retraining only the final classifier restores 75.7% of the original task performance without modifying the backbone network. Layer-wise analysis reveals that early and intermediate layers preserve highly recoverable task information despite severe degradation at later stages. Projection-energy and principal-angle analyses indicate that retained knowledge persists as distributed high-dimensional representations rather than through preservation of a small dominant subspace. These findings suggest that catastrophic forgetting is better characterized as an accessibility failure than complete representational erasure, and that substantial task-relevant information remains embedded within neural representations even after functional forgetting has occurred.

Few-shot class-incremental learning (FSCIL) in synthetic aperture radar imagery presents unique challenges due to severe data scarcity and SAR-specific variability. In particular, strong azimuth sensitivity in SAR induces large intra-class variation and inter-class confusion, and FSCIL sequential updates further lead to catastrophic forgetting of previously learned classes. Inspired by neural collapse, we propose an optical-guided SAR FSCIL framework, which derives orthogonal feature subspaces from a data-rich optical ATR dataset and uses them as geometric priors to guide SAR feature learning. SAR features are projected onto these orthogonal subspaces via principal angle constraints, effectively transferring discriminative structure from the optical to the SAR domain. Specifically, our projection loss and the classifier loss optimized with a frozen simplex-ETF geometry jointly induce neural collapse by concentrating features around class means while maintaining large inter-class angles. We evaluate the approach on a benchmark comprising an optical ATR dataset and a SAR ATR dataset with 24 target classes, organized into a base training session and seven incremental sessions. Compared with recent FSCIL methods including NCFSCIL and so on, our method achieves the highest final accuracy and a favorable trade-off between final performance and performance degradation. Moreover, neural collapse metrics show improved intra-class compactness and inter-class separability, indicating that the learned features more closely approximate the ideal simplex-ETF geometry.

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block S->N->F aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield LimiX-2M, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.

We present AAD-1, an Asymmetric Adversarial Distillation framework for One-step autoregressive image-to-video generation. State-of-the-art methods adopt adversarial distillation but suffer from motion collapse and training instability, resulting in static videos. AAD-1 addresses these challenges through two key designs in architecture and training strategy. Our key architectural insight is to break the symmetry between generator and discriminator. While the generator remains causal to preserve autoregressive sampling capability, the discriminator attends bidirectionally over the full spatiotemporal context and produces a single holistic realism score for the entire video sequence. This asymmetric design enables the discriminator to effectively detect global temporal failures and long-range drift that cause motion collapse in autoregressive generation. To stabilize training, we introduce a phased strategy that first uses distribution matching to bootstrap a stable one-step generator, providing a warm-up phase that brings the student distribution closer to the teacher before adversarial distillation begins. Extensive experiments on VBench demonstrate that AAD-1 achieves state-of-the-art performance in one-step autoregressive video generation.

Objective: Consumer face camera remote photoplethysmography (rPPG) enables passive cardiovascular monitoring, but whether single-cycle waveform morphology encoding arterial stiffness biomarkers is recoverable from this measurement has not been characterised. Methods: We evaluated 16 architectures spanning six families on 153 subjects across three datasets, introducing cross-subject Pearson r to distinguish subject-specific recovery from template collapse. Results: No architecture recovered subject-specific morphology (cross-subject r range 0.773--0.9999; ground-truth ceiling 0.601). Supervised Contrastive (SupCon) converged to log N = 4.844, constituting the strongest available empirical evidence that no discriminative morphological structure is extractable from single-cycle rPPG by the encoder families tested. The VAE decoder restores population-level harmonic content absent from the rPPG input (H2/H1: 0.310 output vs. 0.275 input), generalising zero-shot to UBFC (r = +0.708); a directional hallucination gap (p = 0.150) suggests partial signal reading. Anti-collapse objectives fail when input carries no discriminative structure. Significance: Consumer cameras cannot encode individual arterial morphology; cross-subject r is a necessary collapse diagnostic for waveform reconstruction benchmarks.

Hyper-Connections (HC) replace the single Transformer residual stream with multiple streams, introducing a permutation symmetry over stream indices. We study how this symmetry is resolved in practice: whether streams specialize in a balanced way or exhibit dominant-stream usage. Using fine-grained diagnostics for HC-based language models, we trace how multi-stream representations are actually used. We find that after an early seeding stage, residual mixing often remains close to identity, limiting a core HC mechanism for exchanging information between streams. Moreover, both signal and interpretable features concentrate in a dominant stream, and the nominally multi-stream residual connection can underutilize its capacity, behaving closer to a single-stream residual pathway. Finally, we show that breaking symmetry at stream initialization reduces dominant behavior and improves performance across \textit{m}HC variants. Our code is publicly available.

RLHF evaluation should track how failures emerge, where they localize, and which warning signals appear before external quality degrades. We study this problem with a compact RLHF pipeline built for this paper, including PPO, DPO, uncertainty-penalized PPO (UP-PPO), reward-model uncertainty, approximate policy drift, diversity and repetition diagnostics, and two external LLM judges. Rather than treating reward hacking as a single terminal event, we classify matched checkpoint and prompt-level transitions by the directions of learned reward R_phi, judge scores R_dag and R2_dag, and their average R_dag. The main empirical findings are that aggressive PPO produces the clearest localized reward-hacking signal, UP-PPO reduces but does not eliminate that signal, row-level diagnostics reveal failures hidden by checkpoint averages, and pre-transition features partially anticipate future localized reward hacking. The central conclusion is methodological: RLHF failures are training dynamics that can be classified, localized, and partially anticipated, not only final-model pathologies. The repository is available at github.com/zabahana/rlhf-failure-modes-diagnostics. The pipeline is also deployed as a live interactive web demo for model comparison and diagnostic views at rlhf-failures.zelalem.ai.

Despite the remarkable fidelity of generative models, they frequently suffer from mode collapse. Existing strategies for enhancing diversity predominantly focus on intervening during the generation trajectory. We identify a critical oversight that the standard Gaussian initialization often causes trajectories to collapse into dominant modes because it is agnostic to the guidance potential landscape. In this work, we formulate selecting the initial noise from a guidance potential posterior, which effectively re-weights the prior towards diversity-rich regions. To sample from this distribution efficiently, we introduce Diversity-inducing Initialization (DivIn), which leverages Langevin dynamics to actively navigate the initialization landscape, steering initial noise away from collapsing regions while anchoring them to the valid data manifold. Our method serves as an inference-time diversity enhancement compatible with both diffusion and flow matching models. Extensive experiments show that DivIn exhibits a superior performance in both class-to-image and text-to-image scenarios. Furthermore, we highlight that as DivIn is orthogonal to trajectory-based methods, combining them significantly expands the diversity-quality Pareto frontier beyond what either achieves in isolation.

Entropy minimization (EM) is the dominant objective for test-time adaptation, yet its failure mode, model collapse, remains poorly understood. In this work, we show that distribution shifts can cause feature clusters corresponding to distinct classes in the model's representation space to merge, while the decision boundary remains fixed. This induces a systematic skew in the predicted class distribution, referred to as prediction bias. Prediction bias refers to a shift in the predicted class distribution, with some classes overrepresented and others suppressed. We show that entropy minimization amplifies this prediction bias by tightening the existing clusters, reinforcing the incorrect groupings until all predictions collapse to a trivial solution. Next, to demonstrate the significance of prediction bias and mitigate it, we further propose Distribution Shift Bias Reduction (DSBR), a bias-correcting objective that specifically targets this failure mode by equalizing the contribution of each predicted class to the unsupervised entropy minimization loss. To study this failure mode, we design suitable adaptation settings using four medical-imaging datasets and additionally evaluate on ImageNet-C. We find that DSBR consistently stabilizes test-time adaptation, prevents model collapse, and matches or outperforms state-of-the-art methods. Moreover, DSBR operates solely at test-time.

Sign Language Production (SLP) is the task of generating avatar sign language motion from natural language text. The quality of the generated motion is typically evaluated by a motion-space Fréchet distance (FID) and back-translation (BT) BLEU score on benchmarks such as How2Sign. Both metrics can improve substantially while the underlying generator fails to faithfully represent the sign language gestures. In this work we propose to evaluate the generated motion at three independent levels: ($\tau1$) initial-pose conditioning, ($\tau2$) output diversity, and ($\tau3$) target faithfulness. We compute these as pairwise-distance ratios using latent representations of a frozen motion autoencoder (MoAE). We evaluate 14 SLP model checkpoints on the How2Sign dataset, including a re-implemented Neural Sign Actors (NSA), and show that $\tau3$ faithfulness is never attained, while FID varies by nearly two orders of magnitude and is uncorrelated with faithfulness. We show that on the isolated gloss dataset ASL3DWord favorable $\tau3$ can be attained, hence isolating the size of the sentence-level paired-dataset as the bottleneck.

The transition from single-turn models to Multi-Agent Systems (MAS) promises enhanced problem-solving capabilities, yet the centralized orchestration topology remains a critical point of fragility. To analyze this, we propose a Mean-Field Entropy Dynamics framework, modeling the orchestration process as a system governed by the competing forces of task resolution and cumulative context loading. To facilitate validation, we introduce Inverse Workflow Generation (IWG), a multi-agent pipeline that synthesizes process-verifiable, high-complexity benchmarks with dense intermediate checkpoints. We demonstrate that our entropy dynamics model fits empirical trajectories, providing physically interpretable parameters that quantify system stability and performance collapse. Crucially, our analysis uncovers a ``Reasoning Trap": while reasoning-heavy models excel in isolated tasks, they frequently fail as orchestrators due to context squeezing. Elucidating the physical mechanisms underlying the Orchestrator and quantifying systemic uncertainty offers insights for the MASs' architectural design.

We test whether a relational-style intervention delivered during functional collapse in a small language model produces post-collapse behavior distinguishable from technical feedback, from a lexically-matched scrambled control, and from each of the two pragmatic dimensions in isolation. Using Qwen3.5-4B with a deliberately broken bash tool, we run 300 episodes across six conditions in a matched-pairs design (50 tasks): no intervention (A), technical/impersonal (B), relational/first-person (C), scrambled relational (D), technical/first-person (E), and relational/impersonal (F). E and F form a 2x2 factorial with B and C that dissociates relational structure (acknowledgment, absolution, agency restoration, unconditional acceptance) from sender register (first-person vs. impersonal). We report two main findings. First, an attention-behavior dissociation: attention follows lexical surprise (D > F > C > E > B, all q_FDR < 10^{-10}), with the scrambled message capturing the most attention; yet behaviorally A ~ B ~ D < E ~ F << C. Second, the factorial localizes the C effect: neither relational structure alone (F) nor first-person register alone (E) replicates C's behavioral signature; main effects of both dimensions are individually significant, and the structure x register interaction is significant on persistence (p = 0.046). A third dissociation emerges in emotion probes: F tracks C on 7 of 8 probes despite producing only baseline behavior, indicating that relational structure alone installs a probe-level state that only translates into behavior when paired with first-person register. The model's processing decomposes into three dissociable stages: attention (ordered by lexical surprise), probe-level state (ordered by structure), and behavior (ordered by the conjunction of both).

Parameter-based knowledge editing updates the internal knowledge of large language models (LLMs) via localized weight modifications and has attracted significant attention. However, most existing methods overlook fundamental theoretical limitations and are rarely evaluated under realistic, practice-oriented settings. In this paper, we first present a theoretical analysis based on the dimensional Collapse Hypothesis, explaining how localized parameter edits can propagate along fragile directions in the representation space, inducing global interference and ultimately causing reasoning collapse. Building on this insight, we conduct a comprehensive empirical evaluation by systematically varying knowledge complexity, number of edits, evaluation dimensions, and baseline methods. Our results show that parameter-based editing methods consistently damage core LLM capabilities. In contrast, a simple retrieval-based baseline achieves consistently stronger performance than all parameter-editing methods across all evaluated conditions. These findings highlight that preserving the fundamental capabilities of LLMs after knowledge editing should be a central concern for future research.

Neural collapse is a structural property of the last-hidden-layer activations in neural network classification models, when trained beyond a zero classification error. In this work, we explore the role of label encoding in neural collapse by relying on the unrestricted feature model with mean squared error training loss. We demonstrate that, for one-hot encoded labels and balanced data, the uncentered mean features associated with each class transition from a simplex equiangular tight frame to an orthogonal frame when increasing the bias regularization coefficient associated with the final classifier. These structures are reminiscent of the orthogonal frame structure of one-hot encoded labels. For any arbitrary encoding, we also show that the final classifier's bias aims at centering the labels, compensating for the discrepancy between the global mean of the labels and the origin. We further discuss the role of the encoding in other neural collapse properties.

Modern 3D medical vision-language models (VLMs) can generate fluent radiology-style text while exhibit critically low pathology detection and output diversity, collapsing to generic templates that under-report rare yet critical findings. We identify this failure mode as Template Collapse. This failure stems from the unique constraints of 3D medical imaging, e.g., limited data, severe label imbalance, and weak signals from volumetric encoders. Under these constraints, text-generation objectives encourage shortcut learning and fluent but weakly grounded reports. We systematically diagnose the Template Collapse through clinical fidelity, output diversity, normal-template bias, and rare-finding survival. To mitigate it, we propose CLarGen, a decoupled framework that separates what to say (clinical detection) from how to say it (language synthesis). CLarGen uses (i) a Latent Query Transformer for multi-label pathology detection, (ii) pathology-guided retrieval for clinically matched exemplars, and (iii) a medical language model to synthesize the final report from detected findings and retrieved context. Across state-of-the-art 3D CT report generation baselines, CLarGen mitigates Template Collapse and substantially improves clinical accuracy (macro-F1 0.487 vs. 0.189; CRG 0.472 vs. 0.368) while maintaining fluent reporting. Our results suggest that explicit, measurable clinical grounding is essential for template-collapse-resistant 3D CT report generation. Code is available at https://github.com/ai-med/CLarGen.

Large language models are now adapted through chains of post-training stages rather than through a single instruction-tuning pass. This paper studies whether such sequential post-training gradually compresses internal representations into low-rank, anisotropic, and homogeneous feature spaces. We define a measurement suite for hidden states, logits, token trajectories, and LoRA updates, and we use it to analyze supervised fine-tuning, preference optimization, safety/refusal tuning, math and code specialization, and long chain-of-thought tuning under controlled stage orderings. The central hypothesis is that excessive representation concentration is not merely a geometric curiosity: it predicts reduced plasticity during later adaptation, weaker out-of-domain generalization, and poorer calibration. We further evaluate lightweight interventions, including mixed-domain replay, feature refresh, representation diversity regularization, and LoRA update decorrelation, as ways to preserve future learnability without giving up the behavioral gains of post-training.

We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties of self-attention mechanisms has garnered significant attention in recent years due to their ability to comprehensively analyze token interactions. However, analysis of this simple model suggests that mode collapse, where token distributions degenerate to a single point, occurs during long inferences (i.e., many layers), indicating a discrepancy with reality. This study investigates this mean-field transformer model and demonstrates that the introduction of auxiliary variables, such as positional encoding, acts as a counterforce against theoretical mode collapse. Specifically, we show that in the theoretical scheme, the energy-maximizing distribution does not degenerate to a single point; instead, it is characterized by a pushforward of the auxiliary variable distribution, thereby avoiding concentration in the Dirac measure. Our main examples are the positional encoding and the fixed prompt insertion treated as a parallel auxiliary-variable mechanism. Furthermore, we demonstrate that positional encoding and prompt insertion possess universality of representation in the limit, meaning that the limit distribution of inference can exactly represent a wide class of distributions. We also analyze several key properties of positional encoding and metastability, and validate our theoretical results through mathematical experiments.

Cluster analysis is a widely applied machine learning technique to understand the existing patterns in the population of gamma-ray bursts (GRBs), in order to explore their physical sources. In the present scenario, the number of clusters corresponding to differentiable groups is still under conflict, in spite of numerous attempts with the state-of-the-art clustering procedures. This crucial unknown parameter needs to be evaluated, either directly or indirectly in terms of other tuning parameters, to produce the clusters in GRBs through implementation of an appropriate clustering algorithm. While most of the applied algorithms reached two physically explained groups of merger and collapsar predominated by the short and long bursts respectively, other statistical approaches violated this binary partition. However, physical establishment of any additional cluster(s) is not yet confirmed. Therefore, we propose a new algorithm, from a different stream of clustering referred to as `completely parameter-free', which carries out the classification of GRBs in a manner that has not been tried so far. It indicates two main groups, of short and long duration bursts from the BATSE sample, compatible with the merger-collapsar theory.

Efficient Distillation (EDistill) compresses large language models (LLMs) by structured pruning parameters and tuning lightweight modules with high training efficiency. Although these EDistilled LLMs achieve state-of-the-art (SOTA) performance on general ability benchmarks relative to similarly sized LLMs, we identify a severe degradation in their multi-step reasoning ability, which we term reasoning collapse. We systematically analyze the geometric origins of reasoning collapse and show that the SOTA EDistill method based on width-reducing projection matrices suffers from eRank collapse, in which the effective rank (eRank) of hidden representations drops. We theoretically explain how singular values of randomly initialized projection matrices become unevenly distributed, leading to eRank collapse and thus token indistinguishability. To address this issue, we propose RED (Reasoning-preserved Efficient Distillation) for LLMs, which introduces activation-aware initialization to initialize projection matrices as channel-selection matrices, thus theoretically mitigating eRank collapse. Experiments on Llama and Qwen series demonstrate that RED substantially recovers reasoning while maintaining high training efficiency and SOTA general ability.

Bridging the gap between visual realism and physical understanding is a core challenge for video-based world models. We study the structural identifiability of continuous-time physical laws from raw pixels, focusing on whether an encoder-only pipeline can uniquely recover the parameters of second-order linear ODEs. We prove that a level-set slope-coverage condition ensures the learned latent space is locally affine to the true physical state, enabling exact parameter recovery. Our theory provides the first characterization of minimal data requirements across damping regimes, establishing that underdamped systems are identifiable from a single video clip, whereas other regimes require three diverse trajectories. We further introduce a variance-floor regularizer to stabilize the decoder-free objective and prevent latent collapse. Validated on synthetic and real-world data, our approach demonstrates that interpretable physical constants can be reliably estimated from video without the need for compute-intensive pixel reconstruction, ensuring both physical correctness and transparency. Code is available at https://github.com/wenjiewang3/PhysicsFromVideo.

When large language models are fine-tuned to generate persona- or tone-conditioned responses, their output diversity is severely limited--a failure we term Cross-Style Collapse. We trace this collapse to the cross-entropy objective, which under shared representations tends to suppress diverse continuations. We propose Semantic Flow Regularization (SFR), a lightweight auxiliary objective that supervises the backbone with continuous sentence-encoder embeddings of future segments via conditional flow matching. The stochastic flow source preserves multi-modality by construction; the flow-matching head is discarded at inference, adding zero deployment cost. On a large-scale industrial dialogue dataset (Qwen3-32B, 9 personas), SFR improves output diversity, style fidelity, and response quality over SFT. We further validate on the public LiveCodeBench-v5 (Qwen2.5-Coder-7B-Instruct), where SFR consistently improves pass@k, confirming generality beyond stylized dialogue. A controlled comparison on MBPP reveals Multi-Token Prediction to be a degenerate special case of SFR.

Medical RAG needs evidence-grounded claims, so plugging a claim-level NLI checker into retrieval-augmented RL is intuitive. \textbf{We find that the checker's \emph{output distribution} during training, not its held-out accuracy, decides whether it provides trainable gradient.} We compare four NLI checker back-ends as process rewards inside a GRPO-trained medical RAG agent (Qwen2.5-7B, replicated on Qwen3-4B and Llama-3.1-8B) across four held-out medical QA benchmarks. Three diagnostic findings emerge. \textbf{(i)} Signal collapse is log-prob-specific: LLM log-probability scoring labels over 97% of claims neutral -- collapsing the RL gradient to zero -- while a calibrated MedNLI classifier scores the same pairs non-degenerately. \textbf{(ii)} Moderate signal beats strong signal on answer quality: a strong proprietary checker triggers a three-step reward-hacking cascade -- ultra-short answers, search avoidance, language collapse -- so a moderate-signal local classifier trains a higher-quality model (\textbf{+12% BERTScore over zero-shot, no GPT dependency}). \textbf{(iii)} Signal strength is policy-dependent: the same checker registers as moderate on one policy but strong on another without triggering the cascade end-state. We frame these as boundary conditions for verifier-as-reward systems.

Visual agents employ external visual tools within visual chains of thought to incorporate fine-grained evidence. While prior work has mainly studied these tools in visual search tasks, their role in more complex visual reasoning remains underexplored. In this paper, we move beyond simple visual search tasks to investigate more challenging tasks, including 3D spatial reasoning and medical visual question answering, where agents must integrate tool-acquired local evidence with the global context. We identify a {tool-use collapse phenomenon: models progressively stop using tools while still achieving higher task accuracy. Moreover, we observe a clear asymmetry: (i) completely eliminating tool use degrades performance, whereas (ii) incentivizing tool use yields only marginal gains despite substantially increasing usage. We find that vanilla training and tool-use encouragement both reduce rollout diversity, explaining why higher tool use does not yield stronger reasoning performance. Motivated by these findings, we add an entropy regularization term to encourage diverse rollout exploration, achieving the best performance despite gradually declining tool usage. Overall, our findings suggest a training-time view of tools as scaffolding, where broader exploration over language generation and visual tool invocation improves reasoning despite tool-use collapse. Project page: https://scaffolded-exploration.github.io

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and unreliable uncertainty quantification. In this paper, we propose Principled Posterior Matching (PPM), a framework that returns to the fundamentals of variational inference, rather than using tricky approximations. Instead of relying on heuristic approximations, we rigorously formulate the exact optimization of the KL divergence via the integration of Fisher divergence. We derive a tractable, equivalent gradient form of this integral, enabling precise optimization without the biases introduced by prior approximations. Our analysis clearly reveals that the mode collapse in previous methods stems directly from this approximation gap. Supported by our theoretical solution, PPM unifies two complementary paradigms: (1) In variational inference, PPM adopts mass-covering divergences that significantly improve the inversion diversity and uncertainty quantification; (2) In amortized inference, it enables the training of an efficient reconstruction network for rapid, single-step reconstruction. Furthermore, our formulation naturally extends to a broader family of divergence measures by generalizing the integral of the Fisher divergence. We validate PPM across challenging computational imaging tasks, including inpainting, super-resolution fluorescent microscopy, and radio interferometric black-hole imaging. In all experiments, PPM achieves superior reconstruction fidelity, faithful multimodal posterior recovery, and well-calibrated uncertainty estimates, establishing a robust framework for scientific imaging.

Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities across a wide range of vision language tasks. However, when applied to large scale image classification, their performance degrades significantly as the label space expands a phenomenon we define as Performance Collapse in Long Sequence Recognition. Through an information theoretic analysis, we reveal that this collapse stems from a fundamental conflict between the escalating information entropy and the prominent attention dilution and decay within attention mechanisms, which impairs the model's ability to maintain a sufficient signal-to-noise ratio when processing extremely long prompts. To mitigate this, we propose Divide-and-Conquer Inference (DCI), a novel test-time scaling strategy for visual recognition with MLLMs. DCI recursively decomposes complex global classification tasks into multiple simpler, localized subproblems and employs a dynamic pruning mechanism to compress the search space. This method effectively improves the local signal to noise ratio and model accuracy by mitigating the inherent weight dilution issues in long-sequence inference. Moreover, while traditional self-attention incurs a prohibitive quadratic computational complexity, DCI achieves more favorable scaling behavior and substantially accelerates inference in large scale classification scenarios. Extensive experiments on benchmarks such as ImageNet-1K and ImageNet-21K demonstrate that DCI consistently improves classification accuracy. This enables lightweight open-source models to rival or even surpass frontier closed-source giants without any additional training or fine-tuning. As a model-agnostic, plug-and-play paradigm, DCI offers an efficient approach for scaling the inferential precision of MLLMs in large-scale scenarios.

High-resolution printed circuit board (PCB) inspection suffers from resolution collapse when full-board images are resized to standard detector inputs: micro-scale defects shrink to a few pixels and are missed. Tile-based inference preserves local detail but introduces boundary artefacts at tile edges, causing split detections and false negatives. We present a systematic comparison of five inference strategies evaluated on two high-resolution PCB defect datasets, PCB-Defect (230 images, 1704 annotations) and HRIPCB (693 images, 2 953 annotations), spanning six defect classes. We show that training-inference scale consistency is critical: a detector trained on full images collapses to mAP@50 = 0.01 under tile inference, while the same architecture trained on 640*640 tile crops achieves 0.72 and 0.94 on the two datasets respectively. We further exploited Topology-Aware Tile Merging (TA-TM), a training-free post-processing method that builds a tile-adjacency graph and adjusts boundary-sensitive detection scores using neighbour-tile agreement before global NMS. Across both datasets, adding 128 px tile overlap raises boundary-zone recall from ~26-63% to ~70-100%, TA-TM achieves the best mAP@50 on both benchmarks, and tile inference recovers 46-100% of small defects missed entirely by full-image methods. Results are consistent across datasets, confirming the generalizability of the proposed strategy. TA-TM requires no retraining and is architecture-agnostic, making it directly applicable to existing PCB inspection pipelines.

Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2 regularization. We study the deep unconstrained feature model (UFM)-equivalent to a deep linear network with orthogonal inputs-trained without regularization, to isolate how gradient descent and depth alone shape NC. We show that depth induces an implicit low-rank bias: low-rank matrices propagate norm more efficiently through successive multiplications, promoting low-rank alternatives to NC. These alternatives, we argue, correspond to softmax codes: max-margin solutions previously found in width-bottlenecked networks. Analyzing training dynamics under spectral initialization, we identify an early-time repulsion among singular values that drives low-rank emergence, and characterize how depth shrinks NC's basin of attraction. Finally, we show that some effects act in the opposite direction: for randomly initialized networks, increasing width biases training toward higher-rank solutions. Our results provide the first asymptotic and dynamic characterization of implicit bias in deep UFMs trained with unregularized multiclass cross-entropy.

Model collapse, the progressive degradation of LLMs trained on their own outputs, has been characterized statistically but lacks a linguistic explanation for which structures degrade, in what order, and why. We show that iterated learning theory from cultural evolution fills this gap. We derive five falsifiable predictions, distinguish those uniquely discriminative for the theory from confirmatory ones, and test them by self-training LLaMA-2-7B and Mistral-7B over 10 generations in English, German, and Turkish. The critical discriminative finding: compositionality follows a non-monotonic trajectory (initially rising, then falling) under unfiltered self-training. This signature persists with maximally regular seed data (ruling out noise removal) and is sustained only by task-grounded filtering, not random filtering, providing the first LLM-scale evidence for the compression-communication tradeoff. All predictions are confirmed with large effect sizes (Hedges' $g > 1.6$; $\mathrm{BF}_{10} > 100$), and LLM regularization gradients closely match human behavioral data ($R^2 = 0.94$). These results reframe model collapse as a cultural transmission phenomenon and yield concrete principles for self-training pipeline design.

We show that posterior collapse in $β$-VAEs implements automatic spectral pruning. A latent mode collapses if its contribution to reconstruction is below the cutoff set by $β$. Equilibrium solutions with different $β$ thus reveal a cascade of collapses as latent modes decouple from least to most useful. We derive this as a consequence of the loss via a Landau stability analysis. We define a latent-rescaling-invariant order parameter that ranks active latent modes and whose collapse thresholds identify which effective variables to inspect first. In the linear Gaussian case, the collapse spectrum, utility spectrum, and normalized PCA spectrum coincide, and each collapse follows a mean-field law. We test these predictions on the WorldClim dataset.

Self-play reinforcement learning trains language models on their own generated tasks, co-evolving a proposer and solver without human labels. Recent systems report strong reasoning gains, but collapse and instability are widely observed and poorly understood. The dominant response treats this as a reward-design problem. We argue instead that self-play stability is governed by two distinct levers: a data-level gate that decides which proposer-generated tasks enter the training pool, and the reward signal that updates the policy on tasks already admitted. Through controlled experiments on a Python output-prediction task and a deterministic-DSL twin task that strips pretraining priors, output ambiguity, and executor noise, we find the two levers are asymmetric. A strict gate is sufficient for stability under every reward variant we test, including a self-consistency reward with no access to ground truth; while no reward variant is sufficient once the gate is removed. This asymmetry exposes a counter-intuitive coupling we call the Grounded Proposer Paradox: a proposer with ground-truth access accelerates collapse faster than an ungrounded one when paired with a self-consistency solver, by concentrating training on clean tasks that form the fastest path to a spurious self-consistent attractor. Replacing the binary gate with a continuous strictness parameter $\varepsilon$ further reveals a two-stage phase transition: training-side metrics decouple at low $\varepsilon$, while validation accuracy holds until $\varepsilon$ is much higher. Data-level gating, not reward calibration, is the binding constraint on self-play stability.

Tabular foundation models with different architectures converge in accuracy across a range of classification and regression tasks. This raises questions a leaderboard cannot answer: (i) whether the models execute the same in-context algorithm, (ii) where row, column, and class-permutation invariances originate, and (iii) how robust they are under perturbations engineered against the inferred mechanism. We characterize all three. The model families realize qualitatively distinct similarity-based readouts: from an attention-weighted vote over context labels to a class-conditional mean readout, each confirmed by causal intervention. We find that the representation collapse highlighted in prior work is not a practical concern for them. Each model's permutation invariances trace to specific positional parameters whose removal preserves accuracy and makes approximate invariance exact. Perturbations engineered against each readout reproduce predicted failure modes; hub and rank attacks isolate them from refit baselines. Together these results give a mechanistic account of contemporary tabular foundation models and identify which inductive biases govern both their accuracy and characteristic failures.

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories into a continuous metric space to quantify domain shifts using the Wasserstein-1 distance. Invoking Kantorovich duality, we bound OOD generalization via architectural Lipschitz continuity and functional approximation limits. This exposes two primary constraints. First, position-dependent attention (e.g., Absolute Positional Encoding) fails to preserve shift invariance, yielding an $Ω(1)$ Lipschitz constant and expected risk, whereas shift-invariant mechanisms (e.g., Rotary Embeddings) preserve equivariance and bound the error. Second, by mapping sequential backtracking to a Dyck-$k$ language, we establish a strict circuit depth lower bound for $\text{TC}^0$ Transformers. Scaling physical layer depth is necessary to avert representation collapse -- a constraint that scaling representation width cannot bypass due to irreducible approximation bounds in Barron spaces. Evaluations across 54 Transformer configurations on combinatorial search corroborate these bounds, demonstrating that generalization risk degrades monotonically with the Wasserstein domain shift.

Supervised classification has a theoretical optimum, Neural Collapse (NC), yet neither of its two dominant paradigms reaches it in practice. Cross entropy (CE) leaves radial degrees of freedom unconstrained and converges to a degenerate geometry, while supervised contrastive learning (SCL) drives features toward NC during pretraining but discards this structure in a post hoc linear probing phase. We show that both paradigms are different appearances of the same method that contrasts prototypes on the unit hypersphere, and that closing the gap requires fixing each at its point of failure. From the CE side, we propose NTCE and NONL, two normalized losses that import contrastive optimization's missing ingredients into classifier learning: a large effective negative set and decoupled alignment and uniformity terms. From the SCL side, we prove that SCL's objective already optimizes throughout training for a principled classifier whose weights are the class mean embeddings, making linear probing both redundant and harmful. Empirically, on four benchmarks including ImageNet-1K, NTCE and NONL surpass CE accuracy, closely approximate NC ($\geq 95\%$), and match CE's converged NC on 4/5 metrics in under $7.5\%$ of its iterations, while SCL with fixed prototypes matches linear probing without the hours-long classifier training phase. The learned geometry yields $+5.5\%$ mean relative improvement in transfer learning, up to $+8.7\%$ under severe class imbalance, and improved robustness to corruptions on ImageNet-C. Our work recasts supervised learning as prototype learning on the hypersphere, with NC reached by design.

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Generative artificial intelligence is rapidly transforming the supply side of training data: an increasing share of new tokens, images, and structured records is produced by previous-generation models rather than by human originators. Recursive training on such synthetic content induces a measurable and often irreversible loss of distributional fidelity, a phenomenon known as model collapse. We develop the first unified microeconomic theory of synthetic data markets under model collapse. We introduce the Synthetic Data Contamination Equilibrium (SDCE), prove existence and generic uniqueness, derive a welfare decomposition W = W_prod + W_cons - L_coll - L_info, establish a Wasserstein-gradient-flow mean-field collapse limit, prove an impossibility of information-constrained implementation, and obtain closed-form expressions for the welfare-maximizing provenance subsidy s* = KL(q||p)/(2 kappa) and the welfare-maximizing watermark strength w* = (1 - psi) KL(q||p)/(2 kappa psi). We prove an information-theoretic Cramer-Rao lower bound on any provenance estimator using only producer-side observations and show that the Provenance-Market Iterative Retraining (PMIR) algorithm attains this bound up to constants while converging to an epsilon-SDCE in O(epsilon^-2 log T) iterations. A reduced-form OLS estimation on a C4-synthetic benchmark over ten retraining generations yields a collapse-rate coefficient b-hat = 0.181 (HAC s.e. 0.024), within one standard error of the structural prediction 0.183. Calibrated experiments raise generation-ten model quality by 23.1 percent over the unregulated benchmark while lowering the 2-Wasserstein drift on a held-out diversity probe from 0.318 to 0.142. Scaling experiments over generations t in {1,...,10} recover a logarithmic-in-t collapse law log Q_t = log Q_0 - 0.183 t rho^2 with R^2 = 0.962.