Saturation

We identify a diagonal saturation principle in modal inverse problems: when truncation noise is isotropic, the Bayes-optimal Tikhonov shape is a closed-form power law Gamma_k proportional to lambda_k^|s| set by the prior alone, independent of the domain. Berry's random-wave conjecture decorrelates the truncation noise across modes, and Weyl's eigenvalue counting law supplies enough modes for the conclusion to survive empirical Berry violations. Together they predict an approximately flat loss landscape across the per-mode family, leaving narrow scope for a diagonal regularizer to robustly beat the closed form. On FEM-simulated acoustic rooms, the closed form is near-optimal relative to per-room oracle tuning across observation windows, and three diagonal architectures trained on the same data match its reconstruction error within 1 pp despite learning qualitatively different spectra. The framework extends to heat diffusion via a known exponential Green's function correction with no new free parameters. Saturation is restricted to the diagonal family: Learned Iterative Ridge crosses the boundary by exploiting cross-mode coupling, locating where learning starts to help.

Clinical prediction can saturate for two different reasons: a fitted learner may fail to extract available information, or the recorded variables may impose a population frontier. We separate these quantities through the \emph{learner gap} and the \emph{measurement-channel ceiling}. Optimal balanced accuracy is characterized by total-variation separation, yielding architecture invariance, a sharp partial-identification result under replacement contamination, a cross-fitted ceiling estimator, and exact conditions for multimodal decision improvement. We add two finite-sample diagnostics, namely a label-permutation optimism floor and an underfit curve, and validate the audit on three real cohorts: UCI readmission ($n=99{,}343$), BRFSS diabetes ($n=253{,}680$), and NHANES HbA1c ($n=10{,}219$). Well-tuned gradient boosting nearly reaches the estimated frontier in UCI and BRFSS, whereas deliberately or practically deficient learners retain large gaps. NHANES yields a null difference between questionnaire and measured marginal frontiers but a significant joint complementarity gain, refining the simplistic claim that an objective modality must dominate. Across all cohorts, modest AUROC gains coexist with substantially larger Bayes decision-flip rates, and several architectures estimate similar frontiers while their achieved balanced accuracy differs sharply. A PRISMA-guided synthesis of 104 clinical tasks then shows that the same channel-level regularities recur across more than 18 disease categories: a broad but non-universal structured-clinical region, diminishing same-channel gains across model families, and higher performance when measurement channels change. The framework converts saturation from an empirical observation into an auditable decision: improve the learner when headroom remains; improve measurement when it does not.

Low-light imaging often introduces color bias caused by the low signal-to-noise ratio and the image formation process. Although recent low-light image enhancement methods have achieved strong brightness recovery, faithful color restoration remains challenging, manifesting as overall color bias together with local under- and over-saturation. To address this issue, we propose CAGE, a cylindrical color correction framework with adaptive color debiasing and gamut-harmonized saturation rectification for color-faithful low-light image enhancement. We first introduce AdaLAB, a cylindrical adaptive LAB color space that provides a decoupled and image-specific basis for uniform color correction. Building on this color space, we further develop AdaCCT, an adaptive cylindrical color transform with forward and inverse transforms for the conversion between RGB and AdaLAB color space, as well as necessary color debiasing and saturation rectification. The forward transform suppresses embedded color bias before backbone enhancement by reorganizing the chromatic distribution through chromatic-plane shifting and scaling, while the inverse transform achieves faithful saturation rectification through out-of-gamut lightness compensation. Extensive experiments on multiple benchmarks show that CAGE achieves more faithful color restoration, specifically reduces color bias and saturation abnormality, and delivers better overall visual quality across different low-light enhancement backbones. The code is available at https://yangzhichen763.github.io/CAGE/.

Language descriptions in source-free cross-domain few-shot learning (SF-CDFSL) are often selected according to zero-shot accuracy obtained with a frozen vision--language model. This paper asks whether that ranking remains valid after target-domain visual adaptation. Under a strictly paired protocol, we compare a generic class-name template with fixed detailed class descriptions before and after visual Low-Rank Adaptation (LoRA) on EuroSAT, CropDisease, ISIC, and ChestX. Let $\deltazero$ and $\deltalora$ denote the Detailed-minus-Base accuracy before and after adaptation, respectively. Two recurring regimes emerge. In \emph{semantic saturation}, $\deltazero>0$ but $0<\deltalora\ll\deltazero$: on EuroSAT and CropDisease, initial gains of 8.13--21.54 percentage points contract to 0.69--2.96 points after LoRA. In \emph{semantic emergence}, $\deltazero\leq0$ but $\deltalora>0$: on ISIC and ChestX, detailed descriptions become more useful only after the visual representation is updated. Training trajectories and sample-level decomposition show that saturation is driven mainly by Base-LoRA recovering errors already solved by detailed semantics, whereas emergence is associated with prediction turnover and newly formed Detailed-only correct decisions. Fixed-point-free shuffled-semantic controls, a second CLIP backbone, and multiple random seeds support the broad pattern while identifying ChestX 1-shot as a weak boundary case. These findings establish that zero-shot prompt quality is an incomplete proxy for adaptation-anchor quality and motivate evaluating language on both sides of the adaptation boundary.

Emerging workloads, such as Multi-Agent Reinforcement Learning (MARL), large-scale neuromorphic computing, and probabilistic graphical models, intrinsically exhibit parallel-sequential computing patterns. While these tasks demand massive parallelism to achieve high throughput, they are severely bottlenecked by irregular data access patterns centralized to main memory. Consequently, conventional architectures face fundamental limitations when executing these workloads, primarily manifesting as global buffer saturation and memory-bound bottlenecks. To address these challenges, we propose the Memory-Centric Hierarchical Architecture (MCHA), a reconfigurable hardware solution tailored for parallel-sequential execution. MCHA leverages a hierarchical communication strategy that facilitates distributed, inter-core data routing, thereby significantly reducing the bandwidth burden on the global memory. Complementing the hardware, MCHA introduces a novel parallel-sequential programming model that utilizes event-driven conditional triggers to effectively hide data transmission latency within the execution pipeline. We benchmark MCHA against a diverse suite of parallel-sequential tasks, including MARL, motor variable control, and Markov random fields. Validated through our open-source, cycle-accurate simulator, MCHA demonstrates performance speedups ranging from 153.06$\times$ to 2456.96$\times$ over NVIDIA A100 GPUs on MARL workloads, while maintaining robust programming flexibility across other application domains. Furthermore, the architecture successfully reduces main memory access from 96% to 5.44%. When synthesized in a 28 nm process, the MCHA implementation occupies an area footprint of 2.92mm$^2$ and consumes 115.36 mW of power at 200 MHz. MCHA is open-sourced at https://github.com/carabdis/MCHA.

Large hyperparameter sweeps for deep neural networks spend substantial compute on configurations that are effectively doomed from the first few epochs. We study whether a single training run's own early telemetry - per-epoch loss, training accuracy, gradient signal-to-noise ratio, weight-norm growth, and an activation-saturation snapshot - together with its sampled hyperparameters, can predict that run's eventual outcome without reference to other runs. We evaluate three prediction tasks: final test accuracy, relative performance within a domain, and training-dynamics failure, including numerical divergence. Across 23,788 training runs spanning six architecture/dataset combinations, gradient-boosted trees using only the first five epochs of telemetry achieve R^2 = 0.92-0.99 for final-accuracy regression and ROC-AUC = 0.983-0.998 for relative classification on a permanently held-out set of hyperparameter configurations. Useful prediction is already available after a single epoch. A paired ablation shows that gradient- and weight-level telemetry provides a statistically consistent improvement over loss and accuracy curves alone, although the practical gain varies by domain. Transfer is strong between similar architectures, while cross-dataset transfer is limited mainly by differences in accuracy scale rather than loss of the underlying relationship. These results suggest that early-training telemetry can provide a practical decision-support signal for compute allocation while motivating human oversight for any automated intervention.

Distributed target tracking in multi-agent networks plays a critical role in cooperative sensing and autonomous navigation. However, it faces significant challenges in highly dynamic and adversarial setups. This study aims to enhance the resilience of decentralized target tracking algorithms against measurement faults and cyber-physical threats, especially false data injection attacks. We propose a consensus-based estimation algorithm that integrates a nearly-constant-velocity model with saturation-based filtering to suppress impulsive measurement variations and promote robust, distributed state estimation. To counteract adversarial conditions, we incorporate a dynamic false data injection detection and isolation mechanism that uses innovation thresholds to identify and disregard suspicious measurements before they can degrade the global estimate. The effectiveness of the proposed algorithms is demonstrated through a series of simulation-based case studies under both benign and adversarial conditions. The results show that increased network connectivity and higher consensus iteration rates improve estimation accuracy and convergence speed, while properly tuned saturation filters achieve a practical balance between fault suppression and accurate estimation. Furthermore, under localized, coordinated, and transient false data injection attacks, the detection mechanism successfully identifies compromised agents and prevents their data from corrupting the distributed global estimate. Overall, this study illustrates that the proposed algorithm provides a simplified fault-tolerant solution that significantly enhances the accuracy and resilience of distributed target tracking without imposing excessive communication or computational burdens.

Error-penalized scoring rules ($+1$ for a correct answer, $-λ$ for a wrong one, $0$ for abstaining) are increasingly prescribed against hallucination: a rational agent facing such a rule answers exactly when its correctness probability exceeds Chow's threshold $t^\ast=λ/(1+λ)$. We prove that a KL-anchored gradient learner can do the opposite. When abstention is a discrete action, the reward gradient and the anchor's restoring force are throttled by the same gate-saturation factor and die together: under explicit conditions (among them, blanket answering loses score in expectation and prompts share a bounded readout) the model drifts toward refusing everything, its mean training reward rising to zero like $1/t$ in training time $t$, so the curve reads as improvement while coverage collapses. The advantage estimator compounds the failure: in its sparse-answer regime, group normalization silently replaces every designed penalty with an effective penalty of one, moving the learned threshold from $t^\ast$ to $1/2$. The repair is structural: train a mandatory confidence report with a strictly proper score plus a correctness reward, and abstain only at deployment by thresholding the report. The always-emitted report has no gate to saturate, so no shared factor can kill its reward gradient and its anchor together, and its calibrated optimum is attracting. Simulations confirm every prediction, and experiments on language models at two scales confirm the mechanism live: the rule silences questions the models demonstrably still solve within ten optimizer steps, an ablation isolates the cause, and report-level training raises coverage, accuracy, and calibration together.

PPO and the GRPO baseline studied here use clipped surrogate objectives whose favorable-direction saturation introduces an abrupt change in the scalar objective's derivative. We ask whether Output Reset (OR), a smooth one-sided saturation rule, offers a useful alternative for large language model post-training. PPO-OR and GRPO-OR replace the clipped policy term with an OR squared-margin loss in rollout-relative token log-ratio space; the advantage sign determines the update direction, and a token contributes zero direct OR residual after crossing the favorable margin. We compare PPO-clip with PPO-OR under generalized advantage estimation (GAE), and GRPO with GRPO-OR under group-relative advantages, using \texttt{Llama-3.2-1B-Instruct} on Anthropic \texttt{hh-rlhf} with one shared reward model and three seeds per method. Under GAE, PPO-OR has a mean final training-time reward-model score $0.305$ higher than PPO-clip, with a larger observed across-seed spread. Under group-relative advantages, GRPO-OR does not have a higher mean score, but shows a smaller observed spread, a near-zero terminal OR residual, and a declining overshoot fraction, while the matched GRPO clipped-objective trace remains variable. Both group-relative methods exhibit substantially larger rollout-to-current log-ratio displacement than the GAE methods, and OR does not consistently reduce it. Thus, OR changes optimization behavior in both matched comparisons, but the observed reward effect differs between them. At $G=2$, the GRPO-OR diagnostics do not translate into a reward-score gain. Whether larger groups change this outcome remains open. The reported scores are training-time reward-model measurements, not held-out human-preference performance.

Feedback-driven loops support iterative improvement in large language models, reinforcement learning, and autonomous discovery, yet their gains often diminish under repeated internal feedback. We study why closed-loop knowledge systems saturate and what external information can move them beyond their current attractors. We introduce a three-level operational framework in which knowledge states $x_t$ evolve through transition kernels $K_θ$ indexed by a structural parameter $θ$. The governing structure is defined as the observational equivalence class of $θ$ induced by these kernels, while attractors and basins are properties of the fixed-$θ$ dynamics. A structural intervention changes $θ$ and produces a detectable kernel discrepancy on pre-specified probe states, making structural change falsifiable. Using a Lyapunov drift condition, we show that stable internal dynamics approach bounded stability regions with exponentially attenuated transients and a noise-controlled residual floor. We characterize escape through a metric condition on intervention-induced attractor displacement and a baseline-relative KL lower bound for increasing escape probability. This analysis also explains why conditional mutual information alone cannot certify escape: it measures variation among intervention-conditioned updates rather than departure from the no-intervention law. Case studies in LLM code repair, sparse-reward reinforcement learning, and Bayesian optimization use matched continuation controls to illustrate how feedback strength and alignment affect quality-improving escape. Our contribution is an operational connection among stability tools, measurable intervention effects, and cross-domain diagnostics.

While 3D Scene Graphs (3DSGs) provide crucial structured representations for embodied agents, conventional Ahead-of-Time, build-everything-then-filter pipelines conflict with the real-time, low-latency demands of edge platforms, inducing a perceptual saturation effect via severe observation redundancy. To resolve this, we present JITOMA (Just-In-Time On-demand Memory Activation), a closed-loop framework that unifies task reasoning, perception, and memory into a just-in-time growth process. Instead of exhaustively mapping the entire environment, JITOMA leverages a top-down task heatmap at the frontend to filter continuous observations, routing minimal streams to maintain a global foundation of low-cost, dormant anchors. Upon a cognitive query, the backend Large Language Model (LLM) parses the robotic intent to dynamically awaken task-relevant anchors, triggering resource-intensive operations -- such as dense node captioning and functional inference -- exclusively within the activated local subgraph. To evaluate these dynamic capabilities and study perceptual saturation trade-offs, we introduce JITOMA-Bench, a comprehensive suite for long-horizon multi-tasking and complex multi-step reasoning. Extensive experiments demonstrate that JITOMA substantially reduces active graph size and captioning latency, while maintaining stable processing time under long-horizon task switching.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss $f(S)$ from quantizing a layer set $S$ as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93% of the variance of $f$ is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces $f$'s ranking of configurations, misordering at most 2% of pairs. We propose the coverage model $f(S)=c\bigl(1-\prod_{i\in S}(1-a_i)\bigr)$, which reproduces the measured variance profile of $f$ to within a few percent from its $L$ fitted break-rates. This structure supports two predictors of a configuration's loss, each with $L+1$ parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of $f$ left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

We study robust generalization under spurious correlations: tasks where a shortcut feature is correlated with the true label in training but anti-correlated in an adversarial held-out split. Varying the spurious ratio $r$ (the fraction of training examples where shortcut = true label) and model capacity, we find a counterintuitive result: data imbalance promotes generalization in sufficiently capable models. On a synthetic task where the true label is sum parity of an integer sequence and the shortcut is the parity of the maximum-valued element, a 2-layer, 2-head transformer generalized (reached $100\%$ adversarial accuracy) in 0% of seeds at $r{=}0.50$ but 77% of seeds at $r{=}0.90$. The effect is absent in 1-layer models, where imbalance instead traps the model on the shortcut. Through mechanistic analysis -- gradient conflict dynamics, circuit evolution, and QK/OV circuit ablations -- we characterize a mechanistic pathway consistent with imbalance promoting generalization.

Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data. These challenges arise in many scientific and engineering applications, including subsurface flow, climate modeling, and geological carbon storage (GCS). In this work, we propose a scalable operator-learning framework based on the Karhunen-Loeve Deep Neural Network (KL-DNN) and demonstrate its performance for modeling GCS. The model is trained on a dataset comprising 100 samples of large-scale simulations in a three-dimensional domain with 1.7 million cells and 50 time steps. The KL-DNN method constructs latent spaces using low-rank singular value decomposition of static properties and a nested Karhunen-Loeve expansion for dynamic pressure fields, enabling full-resolution predictions without subsampling or spatial coarsening. The KL-DNN model achieves an average root mean square error (RMSE) of 1.1 psi for pressure (0.04% relative error with respect to the average pressure in the domain) and RMSE of 0.0146 for CO2 saturation (5% relative error with respect to the average saturation inside the plume). The model requires 20 minutes of training on a single GPU, representing a 19% reduction in the pressure errors, 7% reduction in the saturation error, and a two-order-of-magnitude speedup compared to DeepONet trained on the same dataset. These results, along with inference time of less than one minute, establish the proposed model as a practical and accurate solution for large-scale PDE problems, enabling rapid uncertainty quantification, history matching, and real-time decision support.

Few-shot label acquisition lacks a label-free signal for when additional labels cease to improve accuracy: existing stopping criteria either require a held-out validation set (violating the few-shot premise) or rely on theoretically ungrounded heuristics, so we introduce the spectral saturation index $S(K)=\mathrm{erank}(\hatΣ_W^{(K)})/K$, the exponential spectral entropy of the pooled within-class covariance normalized by per-class support size $K$, which measures the exploration rate per label and falls below a fixed threshold $τ=0.02$ once the explored spectral subspace saturates and marginal accuracy gains vanish; across 49 real tasks (binary, 5-way, 10-way) and three frozen backbones (PCA-50, CLIP ViT-B/32, DINOv2 ViT-S/14), $S(K)$ correlates strongly with the marginal gain on doubling the support set ($ρ_{\text{pool}}=0.6366$, $p=2.9\times10^{-57}$, cluster-bootstrap 95% CI $[0.551,0.720]$), a fixed $τ=0.02$ classifies stop/continue decisions with cluster-bootstrap $\mathrm{AUC}=0.787$ (95% CI $[0.713,0.860]$) with high recall on meaningful gains ($ΔA>1\%$), and a partial correlation controlling for $\log K$ yields $ρ_{\text{partial}}=0.324$ ($p=1.65\times10^{-13}$), confirming $S(K)$ carries spectral information beyond shared $K$-dependence; theory predicts this from first principles, since the population effective rank sets the saturation scale $K_{\text{sat}}\approx\mathrm{erank}(Σ_W)/τ$, $τ=0.02$ sits at the boundary between the first and second descent (Nakkiran et al., 2021), and $O(1/K)$ bias in the sample effective rank explains the small-$K$ hump in $S(K)$; for unregularized linear probes ($C=\infty$), practitioners should halt when $S(K)<0.02$ (PCA-50, hard stop) or monitor $S(K)$ dropping from $\sim0.3\to0.05$ (foundation models, diminishing-returns signal), with computation costing $\sim1$ ms at $d=50$.

Multimodal large language models (MLLMs) commonly inherit the deep, symmetric Transformer backbone designed for unimodal text modeling, and apply the same computation uniformly to image and language tokens. This design overlooks a key modality asymmetry: image and text tokens differ substantially in information density, redundancy, and required reasoning depth. Through a layer-wise analysis of LLaVA-1.5, we observe that vision tokens tend to saturate in the middle layers. Specifically, text-to-image attention decreases from 0.68 at layer 0 to 0.07 by layer 4, and stabilizes near 0.04 after layer 18, whereas text tokens continue to benefit from deep semantic processing. These findings suggest a mismatch between architectural symmetry and depth-asynchronous modality evolution, resulting in redundant visual computation and possible drift in perceptual representations during deep task-specific adaptation. Motivated by this, we propose Dual-Path Vision Token Routing (DPVR), a modality-asymmetric routing framework for efficient MLLMs. Its core instantiation, DPVR-LF (Late-Layer Fusion), routes vision tokens at the saturation point into a one-layer trainable side branch, runs a thirteen-layer text-only forward that skips image positions in the deep stack, and re-fuses the visual and textual streams only at the final layer. With approximately 3% trainable parameters, DPVR-LF preserves competitive multimodal performance on standard benchmarks while reducing visual computation in the deep Transformer stack. The results challenge the conventional assumption that vision tokens must traverse all deep language-model layers, and indicate that a single late fusion layer can be sufficient for maintaining strong perceptual competence in LLaVA-style MLLMs.

As autonomous AI agents move from conversational systems to long-horizon software execution, runtime safety layers that decide when to interrupt an agent have become essential. We study this timing problem using a continuous 18-dimensional affective-dynamics engine (HEART) as a diagnostic probe, evaluating four intervention trigger families - absolute state thresholds, composite state-action patterns, regex reasoning-feature extraction, and zero-shot LLM-as-judge - against human-annotated intervention points on SWE-bench-Verified debugging traces. We report three findings. First, a State Saturation Trap: agents show no recovery signal under sustained difficulty, so modeled frustration quickly crosses the threshold and stays at its maximum, converting threshold-on-state triggers from moment detectors into near-constant indicators that fire on 39-83% of actions across five trajectories. Second, a capability-and-context floor for LLM judges: a small model (gpt-5.4-mini) never fires, while frontier and cross-vendor models escape the zero-firing floor only with full-trajectory context, and even then reach only F1 0.17-0.40 at up to 90x the cost. Third, and most importantly, the supervised target is not reproducible among humans: three trained annotators using one rubric on a 56-action trajectory agree on where to intervene only slightly above chance (location Krippendorff's alpha = +0.047; best pairwise Cohen's kappa = +0.349) and not at all on intervention type (pause degenerate; clarify below chance; reflect only alpha = +0.226). We conclude that intervention timing is a low-reliability construct, making single-annotator F1 an unsuitable optimization target. Our contribution is the joint mapping of this problem across human inter-rater reliability, four detector architectures, a cross-model LLM-judge sweep, and a reproduced saturation effect, rather than any single detector's accuracy.

Large language models (LLMs) have emerged as powerful representation learners whose internal features increasingly align with human cognition. We study whether modern LLMs can serve as a lens for understanding neural representations in the human brain, focusing on emotional valence in EEG. We first build a one-dimensional valence direction, the V-axis, from modern LLMs using only nine emotion-evocative sentences. We validate it through zero-shot transfer to sentiment benchmarks and cross-model consistency across fourteen LLMs. We then show that this LLM-derived direction maps onto human neural activity. On a public EEG cohort of 123 subjects watching affective videos, a single linear projection on EEG features tracks the V-axis position of each stimulus. Moreover, 36 EEG emotion classifiers trained without exposure to the V-axis spontaneously rediscover the same direction in their internal representations, suggesting that the same valence structure emerges in both language models and human electrophysiology. Yet this convergence does not provide an effective training signal. We test twenty-five alignment strategies, including knowledge distillation, representational similarity, contrastive, and topographic losses; none improve decoding, and sixteen significantly reduce accuracy. We formalize this result as the saturation regularity: once task labels alone drive a brain-decoding network onto the target direction, additional supervision mainly distorts an already-saturated basin, while the load-bearing within-class residual receives little useful gradient. This regularity also indicates where improvement should come from: the residual subspace unreachable by supervision. Motivated by this insight, we ensemble across residual diversity rather than supervising the basin, improving balanced accuracy by 10.5% over the prior best on FACED, with the same effect replicated on SEED-V.

When annotators disagree on a label, the disagreement itself carries signal -- and the number of annotators needed to capture it depends on the evaluation metric. We fine-tune NLI models on label distributions subsampled from ChaosNLI, a dataset providing 100 independent annotator judgments per item, and identify metric-dependent saturation. In our 3-class NLI setting, entropy correlation -- whether the model identifies which items elicit disagreement -- requires N ~ 20-50 annotators to converge, while distributional match (KL divergence) saturates by N ~ 10 (87-95% of improvement across five model seeds). This finding rests on a prior observation: soft labels carry item-specific signal that label smoothing cannot replicate. Across five smoothing intensities, entropy correlation clusters at r ~ 0.45-0.49, while soft labels reach r = 0.643 (p < 0.001); per-item analysis traces this gap to smoothing's inability to distinguish ambiguous items from clear ones. The soft-label advantage replicates across two architectures (DeBERTa, RoBERTa), a non-NLI-pretrained baseline, and an exploratory cross-domain evaluation on content safety. These results suggest that annotation budgets should be informed by the target evaluation metric rather than set uniformly.

As Large Language Models (LLMs) evolve into persistent scientific collaborators, context window saturation has emerged as a critical bottleneck. Scientific workflows involving iterative data analysis and hypothesis refinement rapidly saturate even extended contexts with dense technical content, while monolithic approaches suffer from quadratic cost scaling and cognitive degradation. We evaluate a Dual Process Memory Architecture that decouples immediate episodic needs (constant 10-message window) from long-term consolidated knowledge (growing at approximately 3 tokens/message). Unlike prior social agent memory systems, our domain-specific consolidation addresses contradictory parameter evolution, multi-hop reasoning across experimental phases, and precise technical fact retention. Through large-scale evaluation spanning 15,000 messages with cross-model validation across six LLMs from three families (OpenAI, Anthropic, Google), totaling 1,440 queries, we establish three key findings. First, while full-context models fail at 10,000 messages due to context overflow, our system maintains 70-85% accuracy with 1-2 second latency using 62% fewer tokens (45,434 vs 120,000+ limit). Second, cross-model validation reveals architecture-level trade-offs independent of specific LLMs: Dual Process excels at numeric/temporal queries (65-90% accuracy) while RAG excels at historical retrieval (60-85%), suggesting complementary deployment strategies. Third, we identify a "Sim-to-Real" gap where synthetic tests maintain constant memory but realistic workflows exhibit linear growth (about 3 tokens/message), with consolidation quality emerging as the primary scalability bottleneck. The architecture successfully manages profiles with 14,000+ scientific facts (125k tokens), demonstrating that domain-specific memory consolidation enables sustained operation beyond full-context limits.

We investigate growth dynamics in deterministic equational discovery substrates. Across three toy domains (arithmetic, boolean, higher-order list; n=592 trajectories), short-range substrate sizes fit a power-law N(t) proportional to t^b. Within each substrate b is architecture-sensitive (cross-validated R^2 approximately 0.82); the regression does not transfer across substrates (arith+bool to list yields R^2 approximately -0.84). A heuristic mean-field closure model predicts a saturating power-law dN/dt = K N^k exp(-mu N) of which the pure power-law is the short-range approximation. Three robustness checks: bootstrap intervals on (k, mu) are tight in 4/5 toy trajectories and degenerate in 1/5; out-of-sample forecasting on toy data (fit first 100 epochs, predict next 400) is won by pure power-law 5/5, indicating the toy trajectories do not reach saturation; on two real-world growth proxies the result splits. New Mathlib/*.lean file additions per month (mathlib4, 60 months, 9701 files) support the saturating form on OOS forecasting by approximately 7x over pure power-law; Coq mathcomp monthly commits (129 months, 3083 commits) favour pure power-law on both tests with mu collapsing to zero. The dynamics are substrate-conditional at two levels: within-substrate architecture-to-b regressions do not transfer, and the preferred functional family for N(t) itself (pure vs. saturating power-law) differs by substrate. We propose "saturating power-law growth with substrate-conditional (k, mu), observable when the substrate has reached its saturation regime" as a working framing.

Recent studies have reported $\textit{saturation effects}$ and $\textit{multiple descent behavior}$ in large dimensional kernel ridge regression (KRR). However, these findings are predominantly derived under restrictive settings, such as inner product kernels on sphere or strong eigenfunction assumptions like hypercontractivity. Whether such behaviors hold for other kernels remains an open question. In this paper, we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previously associated with inner product kernels on sphere, including: $i)$ the $\textit{minimax optimality}$ when the source condition $s\le 1$; $ii)$ the $\textit{saturation effect}$ when $s>1$; $iii)$ a $\textit{periodic plateau phenomenon}$ in the convergence rate and a $\textit {multiple-descent behavior}$ with respect to the sample size $n$.

We audit the multimodal-physics evaluation pipeline end-to-end and document three undetected construction practices that distort how the field measures vision-language reasoning: train-eval contamination, translation drift, and MCQ saturation. (1) Public training pools (UGPhysics-Train, SciInstruct, MMK12) pass single-stage 5-gram-Jaccard audits with zero hits across all six public physics evals; a three-stage audit (Jaccard -> mxbai-embed-large cosine -> Haiku-4.5 LLM-judge) surfaces 134 near-duplicates and 4,846 paraphrase candidates in SciInstruct alone. (2) A 17-pp Sonnet 4.5 delta on 59 paired Estonian-English olympiad problems (30.5% vs. 13.6%; sign test p=0.011, McNemar p=0.021, paired bootstrap 95% CI [+5.1, +28.9] pp). (3) A 46-pp format-and-novelty gradient on identical Sonnet weights between MCQ (79.7% on PhyX) and open-ended olympiad evaluation (33.4% on PhysOlym-A). We release four artifacts addressing these gaps: PhysCorp-A (6,432-record three-stage-audited multimodal corpus), PhysR1Corp (2,268-record closed-form RL pool), PhysOlym-A (500-problem, 99.8% novel-source held-out olympiad eval with native difficulty labels and an EN/ET bilingual subset), and Physics-R1, a reference GSPO+DAPO recipe cold-started from Qwen3-VL-8B-Thinking. Across 3 seeds, Physics-R1 lifts the audited corpus over the 8B base by +18.3 pp on PhysOlym-A liberal (8.0 -> 26.3 +/- 1.7; 7.1 pp behind Sonnet 4.5), +15.7 pp on PhysReason (23.9 -> 39.6 +/- 6.4; ahead of Qwen3-VL-32B and Gemini 2.5 Pro), +6.9 pp on OlympiadBench-Physics (46.2 +/- 1.5), and +4.1 pp on PhyX MCQ (77.8 +/- 0.3).

Compile-pass rate is the dominant evaluation signal for LLM code generation, yet for multi-component domain-specific artifacts it can be actively misleading. We demonstrate this on executable game scene synthesis with a four-axis evaluation protocol (named `Mage') -- compile success, runtime success, structural fidelity, and mechanism adherence -- applied to 858 generation attempts across four open-weight LLMs (7B--30B), 26~hand-crafted Unity goal pattern playable concepts, and two automatically extracted IR granularity levels. Direct NL-to-C# generation achieves the highest runtime-pass rate (43% mean) yet produces structurally vacuous scenes (mechanism $F_1 \approx 0.12$). Structural IR conditioning halves the runtime rate but recovers domain-faithful structure ($F_1$ up to 1.00). Within IR conditioning, behavior-only and full-scene granularity are statistically indistinguishable (McNemar $p = 1.0$), indicating input-level granularity saturation. These results show that compile rate is anti-correlated with functional correctness in this domain and that multi-axis evaluation is necessary to detect the divergence. We release the benchmark, replay logs, and per-record metrics for independent verification.

It has been known for a long time that initializing weight matrices to be orthogonal instead of having i.i.d. Gaussian components can improve training performance. This phenomenon can be analyzed using finite-width corrections, where the infinite-width statistics are supplemented by a power series in $1/\mathrm{width}$. In particular, recent empirical results by Day et al. show that the tensors appearing in this treatment stabilize for large depth, as opposed to the tensors of i.i.d.-initialized networks. In this article, we derive explicit layer-wise recursion relations for the tensors appearing in the finite-width expansion of the network statistics in the case of orthogonal initializations. We also provide an extension of recently-introduced Feynman diagrams for the corresponding recursions in the i.i.d.-case which are valid to all orders in $1/\mathrm{width}$. Finally, we show explicitly that the recursions we derive reproduce the stability of the finite-width tensors which was observed for activation functions with vanishing fixed point. This work therefore provides a theoretical explanation for the stability of nonlinear networks of finite width initialized with orthogonal weights, closing a long-standing gap in the literature. We validate our theoretical results experimentally by showing that numerical solutions of our recursion relations and their analytical large-depth expansions agree excellently with Monte-Carlo estimates from network ensembles.

Static capabilities benchmarks suffer from saturation and contamination, making it difficult to track capabilities progress over time. We introduce Agent Island, a multiplayer simulation environment in which language-model agents compete in a game of interagent cooperation, conflict, and persuasion. The environment yields a dynamic benchmark designed to mitigate both saturation and contamination; new models can always outperform the current leading player in this winner-take-all game, and agents compete against other adaptive agents rather than face a fixed task set. We rank players with a Bayesian Plackett-Luce model, allowing us to quantify uncertainty in player skill. In 999 games involving 49 unique models, openai/gpt-5.5 dominates its peers with a posterior mean skill of 5.64, compared with 3.10 for the second-ranked model, openai/gpt-5.2, and 2.86 for the third-ranked model, openai/gpt-5.3-codex. We release the game logs as a dataset for analyses of model behavior. As an example, we investigate same-provider preference in final-round votes and find that models are 8.3 p.p. more likely to support a same-provider finalist than finalists from other providers. This preference is not uniform across providers: among separately estimated providers, the effect is strongest for OpenAI models and weakest for Anthropic models.

Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.

Equality saturation (EqSat) is a powerful optimization paradigm that compactly represents many equivalent programs in an e-graph and delays commitment until extraction selects a lowest-cost program. Making EqSat effective, therefore, requires not only domain-specific rewrite rules but also domain-specific strategies. Today, much of this strategy design is still manual, making it a major obstacle to automating e-graph-based compilers. Recent rule-synthesis frameworks can automatically infer large rewrite vocabularies from semantic specifications, but they also enlarge the rewrite space and further exacerbate e-graph explosion. Although large language models (LLMs) make automated strategy synthesis plausible, directly evolving backend code remains ineffective in practice. The search lacks reusable strategy abstractions and actionable feedback, and can easily trigger e-graph explosion or converge to poor designs. We present EggMind, an LLM-guided, end-to-end framework for synthesizing reusable EqSat strategies. At its core, EggMind introduces a domain-specific language, EqSatL, to represent EqSat strategies as explicit and inspectable artifacts. It then proposes an LLM-guided agentic workflow, equipped with novel techniques including proof-derived rewrite motif caching and tractability guidance, to search efficiently for high-quality strategies while keeping synthesis stable under e-graph growth. Evaluation shows that EggMind substantially improves the resource-quality trade-off on vectorization benchmarks, reducing final cost by 45.1% and peak RAM by 69.1% relative to full EqSat. We further show that the same methodology transfers effectively to an XLA-based tensor compiler, and demonstrate its practical potential in a logic-synthesis case study with augmented rewrite spaces.

This paper presents a novel saturation aware space variant blind image deblurring framework designed to address challenges posed by saturated pixels in deblurring under high dynamic range and low light conditions. The proposed approach effectively segments the image based on blur intensity and proximity to saturation, leveraging a pre estimated Light Spread Function to mitigate stray light effects. By accurately estimating the true radiance of saturated regions using the dark channel prior, our method enhances the deblurring process without introducing artifacts like ringing. Experimental evaluations on both synthetic and real world datasets demonstrate that the framework improves deblurring outcomes across various scenarios showcasing superior performance compared to state of the art saturation-aware and general purpose methods. This adaptability highlights the framework potential integration with existing and emerging blind image deblurring techniques.

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Artificial intelligence benchmarks are an important mechanism for measuring model progress and guiding deployment decisions. However, benchmarks quickly "saturate", making it difficult to differentiate models and diminishing their long-term value. In this study, we define benchmark saturation and analyze it across 60 language model benchmarks using 14 properties that relate to saturation. We find that nearly half of the our benchmarks exhibit saturation, with rates increasing with age. Further, we find that resilience to saturation is impacted by expert-curation, not by public test data. Our results suggest that design choices can extend benchmark longevity and inform more durable evaluation approaches.

We establish two related but logically distinct results for shallow ReLU$^k$ neural networks on the unit sphere $\SS^d$. First, for an arbitrary set of inner neural-network parameters, the best $\mathcal{L}^2(\SS^d)$ approximation of a fixed target function with smoothness $r>\tfrac{d+2k+1}{2}$ admits an asymptotic lower bound given by a constant multiple of $n^{-1/2}\underline{h}^{k+1/2}$, where $\underline{h}$ denotes the antipodal separation distance of the normalized inner-parameter set. This lower bound depends explicitly on the parameter configuration through $\underline{h}$ and applies without additional assumptions on the parameters. Second, for antipodally quasi-uniform parameters, $\underline{h}\simeq n^{-1/d}$, and the lower bound establishes the exact saturation order $n^{-\frac{d+2k+1}{2d}}$ for such parameter families: a target function with regularity greater than $\frac{d+2k+1}{2}$ and satisfying the required parity condition can be approximated at this rate, whereas approximation at any strictly faster rate forces the target function to be zero. Our results therefore place linearized neural-network approximation within the classical saturation framework and show that, although ReLU$^k$ network spaces can outperform finite elements of the same degree, this advantage is intrinsically limited.