Deep Neural Networks

High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit exceptional storage capabilities and robustness. Previous empirical studies identified a hyperparameter regime, the "Ridge of Optimization," where attractor stability is maximized. However, the geometric nature of this regime and the optimization dynamics required to reach it have remained unclear. In this paper, we investigate the static geometry of the parameter space and the learning trajectory of Gradient Descent (GD) in KLR-trained Hopfield networks. Using the eigenvalue spectrum of the Hessian, we reveal that the Ridge corresponds to a phase boundary located adjacent to a rank-1 spectral collapse, acting as a geometric singularity where the principal curvature is massively amplified. Furthermore, we demonstrate that the learning dynamics exhibit a transient self-stabilizing behavior driven by the Edge of Stability (EoS) phenomenon. Rather than seeking flat regions, the network parameters are driven toward a state where the local curvature dynamically equilibrates near the stability limit dictated by the learning rate, allowing the optimization to survive the initial instability. We provide analytical derivations for both the rank-1 asymptotic collapse and the dynamic feedback loop governing this equilibration. These findings suggest that optimal, high-capacity memory representations are not formed in flat minima, but are dynamically sculpted at the highly curved boundaries of geometric singularities.

Recurrent Transformers reusing their weights rather than stacking $L$ distinct layers are becoming widely adopted due to their parameter efficiency [1,2,3]. However, the exact representational and dynamical differences between looped and stacked architectures remain uncharacterized. This paper presents a controlled study on the example of bViT model [1] applying one weight-tied block $L$ times. We train two models: bViT and standard ViT [4] on 12-lead electrocardiogram (ECG) classification tasks from the PTB-XL dataset under identical training protocols. Despite an $8.9\times$ parameter reduction, bViT achieves accuracy parity with ViT. Geometric similarity metrics demonstrate that both architectures construct comparable latent representations in an equivalent canonical order. Crucially, their dynamics differ: bViT exhibits smaller step sizes and inter-patient sensitivity, as well as near-neutral behavior away from the data manifold, whereas ViT exhibits collapsing dimensionality of representations and out-of-distribution feature expansion.

Deep neural networks are expressive enough to contain worst-case targets that can be evaluated in polynomial time but cannot be learned in polynomial time by gradient descent. For practical tasks they nonetheless learn well, raising the question of what non-generic structure of real-world targets enables this. Existing surrogate models cannot pose this question because they either lack hard-to-learn targets entirely (deep linear networks) or cannot evaluate such targets efficiently (kernel methods, infinite-width limits). We study tree tensor networks (TTNs), a model class that generalizes deep linear networks and Tucker decompositions. We show they embed arbitrary read-once Boolean formulas, and thus contain polynomial-size targets that cannot be learned by gradient descent in polynomial time under the same mechanism as neural networks. Despite this, we prove that their loss landscapes are conditionally benign for every realizable target: every local minimum that is minimum-norm is global. Thus, surprisingly, bad local minima are not what distinguishes between typical and worst-case problems in TTNs. Instead, learning difficulty in TTNs can arise from high-order degenerate saddle points, which we show are caused by rank-deficiency. This is explored through a case study of the parity function, illustrating the potential for TTNs to relate landscape geometry to computational hardness.

In streaming tasks, recurrent models can carry latent computation across time, allowing each update to build on representations produced earlier. This raises a basic question: once temporal recurrence provides sequential computation across steps, how much depth is still needed within each step? Prior work has shown that recurrence can make shallow models competitive. We instead study this question as a compute-allocation problem, varying within-step depth, expert width, and the number of parallel experts per layer across several compute budgets. For each budget, we compare the best observed recurrent and non-recurrent allocations and the performance they achieve under approximately matched per-step computation. Across Sokoban and autoregressive FineWeb language modeling, we find that temporal recurrence shifts the best observed compute allocation toward substantially fewer layers, with comparable or better performance.

Learning user-defined concepts as constraint networks has been extensively studied in the constraint acquisition (CA) literature. However, existing approaches typically rely on intensive interactions with a human oracle, making the learning process costly in terms of time and number of queries. In this paper, we propose a neuro-symbolic framework for automatic CA that significantly reduces user involvement by introducing neural Oracle Transformer models which learn to emulate user responses and to generalize conceptual knowledge. Trained on previously available examples, the learned oracle interacts with a dedicated CA engine, FastCA, which systematically refines the oracle's responses into a sound, consistent, and interpretable constraint network. This neuro-symbolic interaction enables the recovery of structured symbolic models from data without prior domain knowledge. Our results demonstrate that this neuro-symbolic interplay effectively aligns data-driven pattern recognition with symbolic reasoning, offering a robust approach to automating model construction in combinatorial domains.

We evaluate Deep Perturbation Learning (DPL), which perturbs training images and labels along influence-derived directions, in three roles in which prior work has positioned it for machine unlearning: a direct deletion signal (the strongest claim), a utility-preserving regularizer, and a warm start for adversarial unlearning. Evidence for the weaker roles has been used to support the stronger one, so we test each role separately under a matched protocol with exact-seed retraining baselines. An audit of the public implementation identifies two correctness issues: image directions are computed on augmented, normalized tensors but applied to raw images, and the label perturbation falls below float32 resolution, leaving labels unchanged. After correcting the image-perturbation pipeline, DPL fails the direct-deletion criterion on CIFAR-10/ResNet-18 in all three paired seeds. Its utility effects are inconsistent in sign across seeds, and once direction-computation time is counted it underperforms simple warm-start baselines. A one-seed Tiny ImageNet check likewise does not favor DPL as a regularizer or warm start; preprocessing inconsistencies in the released code make the direct comparison there inconclusive. These results cover random instance deletion only and do not rule out influence-based methods in other deletion regimes. We release a role-matched evaluation protocol and an audit checklist for perturbation-based deletion claims.

This paper reports experiments across six frontier model types from OpenAI, Anthropic, xAI, and Google DeepMind. Ten independent sessions per model type used the same three stage prompt sequence, progressing from architectural preference to a full ASCII backbone. Under the school audience framing, responses repeatedly converged on a shared architectural pattern built around persistent latent state, adaptive computation, memory, specialist routing, verification, stopping control, and delayed decoding. Most runs remained close to this common structure, while a small number developed markedly greater engineering specificity. The audience framing appears to be an important condition of this effect. In additional control runs that removed the school framing while retaining the architectural request, responses became substantially more heterogeneous and failed to reproduce the same stable motif convergence. One observation is particularly striking. GPT-5.6 Sol produced an unusually elaborate successor architecture whose organization closely overlaps with the architecture independently sketched by GPT-6 Astra. Because the prompts explicitly ask each model to imagine an architectural future, this resemblance raises a testable question: whether the overlap reflects exposure to related architectural concepts, a shared learned design prior, or independent convergence toward similar computational principles. The paper uses the term epistemic jailbreak for the accompanying loss of discipline in technical provenance as requested specificity increases. The experiments establish a repeatable behavioral pattern and do not authenticate proprietary implementation claims. What we leave to the community is a harder question: are these models independently imagining the same architectural future, or do such motifs somehow propagate between model families?

Neural networks trained past memorization frequently undergo a delayed transition to generalization, a phenomenon known as grokking. Despite theoretical progress on \emph{why} this transition occurs, the quantitative structure of \emph{when} it occurs in hyperparameter space remains uncharacterized. We map the memorization-to-generalization boundary across 384 configurations of two-hidden-layer MLPs on modular arithmetic, fitting a power-law scaling relation for generalization onset time: $T_{\mathrm{grok}} \propto H^{-0.27}\, D^{-2.04}\, \eta^{-0.50}\, \lambda^{-0.64}$ ($R^2 = 0.732$; $0.821$ with interactions). The exponent hierarchy reveals that data complexity ($D^{-2.04}$) is the dominant driver of regime transition, not model capacity ($H^{-0.27}$): doubling data accelerates generalization by ${\sim}4\times$, while doubling width yields only ${\sim}1.2\times$. A sharp phase boundary at weight decay $\lambda \gtrsim 1.0$ separates grokking from non-grokking configurations, and weight norm trajectories show monotonic compression during the transition, consistent with implicit regularization selecting low-complexity solutions. These results provide a quantitative foundation for predicting and controlling regime transitions in overparameterized networks.

Humans and machines often solve harder problems by spending more time on computation. In deep learning, looped models implement this idea during inference by recurrently updating a hidden state. In practice, however, their training backpropagates through only one or a few updates, making it hard to train early updates to support future ones. We propose looped flows, an approach that sidesteps this issue by training the recurrence with local denoising objectives. By imposing temporal association across denoising objectives through progressively decreasing noise levels and shared noise, the model is incentivized to learn recurrent states that transfer useful computation over time, even when gradients cover only a few updates. We then formulate inference as integrating the velocity of a probability flow parameterized by the learned denoiser, coupled with recurrent states. This allows solving harder problems by spending more computation through a finer temporal grid and enables multiple valid predictions from different initial noise samples. Across six reasoning benchmarks including two multi-solution benchmarks, looped flows outperform prior state-of-the-art looped models overall, achieving 58.8% test accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.

The growing reliance on Low-Earth Orbit (LEO) satellite communication systems has increased the need for intelligent methods capable of detecting cyberattacks across complex and dynamic space environments. Unlike conventional network intrusion detection, satellite systems generate heterogeneous information across radio-frequency (RF) links, onboard hardware, and orbital operations. However, many existing approaches either rely on terrestrial intrusion datasets or evaluate individual observations independently, limiting their ability to capture temporal attack behavior specific to LEO satellites. In this work, we conduct a systematic study of deep-learning-based cyberattack detection using the recently introduced satellite-specific UNSW-IoTSAT dataset. We investigate structured learning architectures that preserve hardware, orbital, and RF information, including a Subsystem-Fusion MLP and a hierarchical multimodal Transformer that models both cross-subsystem interactions and temporal evolution. We further evaluate leakage-resistant row-level and temporal settings, along with cross-satellite generalization, to characterize how model architecture and evaluation protocol influence satellite cyberattack detection. Experimental results demonstrate the value of structured multimodal modeling and rigorous evaluation, with the hierarchical Transformer achieving up to 91.66% accuracy and 85.63% macro F1 under the leakage-resistant evaluation protocol.

Recent work has identified incremental learning in shallow networks trained on single-index and multi-index models. However, existing analyses often rely on simplifying settings, such as small initialization, correlation loss, or layer-wise training. These choices reduce neuron interactions and leave some feature learning dynamics under standard initialization unexplored. We study training dynamics for polynomial-width two-layer networks learning orthogonal multi-index targets under standard initialization using polynomially many samples. We first prove that incremental learning still occurs: the loss decreases sequentially according to the Hermite expansion of the target, with lower-order components learned before higher-order components recover the individual target directions. In this standard initialization regime, training also shows a competitive reallocation of parameter mass: after the total mass fits the target mean and stabilizes, mass shifts into the target subspace and then concentrates on aligned neurons. Our theoretical analysis uses slightly modified gradient flow, while vanilla gradient descent empirically exhibits the same qualitative dynamics. Technically, we introduce a symmetry-based finite-width approximation via symmetrized networks, rather than comparing directly with an infinite-width limit. This yields better control of approximation errors and may be of independent interest.

The discovery of the EML operator, sufficient to evaluate the standard explicit purely transcendental elementary functions, has led to considerable interest and discussion across multiple scientific disciplines. However, most authors have focused on the binary EML itself, while numerous similar variants with slightly different properties are now known. This article attempts to close this gap by enumerating and classifying them. We also take this opportunity to clarify common misconceptions related to the EML operator. The principal goal, symbolic regression within an architecture as close as possible to proven neural networks which combine matrix multiplication with a single univariate non-linear activation function, remains beyond reach. Instead, we propose a Möbius layer, with rational functions replacing matrix operations, and showcase the recently discovered activation function eml(x,1/x), which allows exp(x) and ln(x) to be recovered separately, and hence all elementary functions to be evaluated within a rational generalization of the neural network.

Teacher-student systems, in which a teacher neural network generates training labels so that a student neural network can learn to implement the same function, are widely used as an abstract setting to study learning. However, the structure of the teachers is often overlooked by assuming randomly-generated, normally-distributed parameters. This hides substantial variation in how learnable different teachers are. We formalize learnability as the success rate of converging to the global minimum, as a function of overparameterization, learning algorithm, student initialization distribution, and teacher geometry. We both identify an easy distribution that maximizes node dissimilarity and a hard distribution that minimizes it, and show that these two distributions induce markedly different success rates across a large range of settings and for different activation functions. To explain the gap, we study the loss landscape of small neural networks that contain two distinct kinds of suboptimal local minima, out-of-bounds (OOB) minima at the edge of the data distribution and interior minima within. Assuming infinite data and a fast readout layer, we analytically reduce the loss landscape of small networks to two dimensions, showing that the region of attraction of interior minima changes as a function of teacher structure. In larger networks, maximally dissimilar teachers induce more interior minima, while minimally dissimilar teachers induce more OOB minima. Motivated by these analyses, we show that differentially increasing the learning rate of the readout layer and decreasing the learning rate of the inner biases increases success rates. These findings provide an important step in narrowing the gap between the study of teacher-student networks and more structured functions that arise in practice.

Myocardial strain from echocardiography is a key biomarker for cardiac function. Recent deep learning methods show strong performance for myocardial motion tracking but often lack physiological constraints, leading to temporal drift across the cardiac cycle. Consequently, tracked points may not return to their relative initial positions at the end of each cardiac cycle, producing inaccurate strain estimates and even divergence in some cases. We propose a deep learning framework that compensates for drift during myocardial tracking. We extend a state-of-the-art echocardiographic tracking method (TAS-Net) with persistent memory tokens that share information across sliding windows over full cardiac cycles. A teacher-student fine-tuning strategy on real echocardiographic data then enforces physiologically consistent cyclic motion while preserving tracking accuracy. Experiments show reduced global and regional strain drift, improved agreement with clinical references, and better test-retest reproducibility, supporting more reliable myocardial strain estimation in clinical practice.

The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.

Longitudinal single cell atlases now capture matched pre treatment and post treatment states from responders and non responders, presenting an opportunity to mechanistically explain why two patients on the same drug diverge. We introduce scDEFT (single cell Drug EFfect Transducer), which treats a drug as a conditioning operator on cell representations, enabling prediction and explanation. In scDEFT, feature wise linear modulation produces drug conditioned cell latents, learned under abundant per cell supervision and then frozen. Two independent heads aggregate those latents over shared transcriptional neighborhoods to predict drug induced state change and responder status. A backward stage ranks the latent dimensions by how strongly they separate responders from non responders and maps them to genes under a cell composition control. On a harmonized inflammatory bowel disease atlas of 1.16 million cells, three cohorts and two drug classes, scDEFT predicts state change at 45% of the baseline to reproducibility ceiling headroom and stratifies responders before treatment at AUROC 0.70, where standard predictors remain at chance. These predictions and the drivers behind them support target and co target nomination, patient stratification, and counterfactual prediction of unseen drug cohort effects.

Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transformer at embedding width d = 128 still spends roughly one third of its capacity on the output matrix W_out in R^(d x |V|). We propose Riemannian Language Models (RiLM), which remove that layer entirely: context unfolds as a trajectory on a Riemannian manifold, and next-token probabilities arise from squared geodesic distance between the current state and vocabulary embeddings. The same embedding map serves input and output -- decoding is geometry. We instantiate the framework on flat R^d (Flat RiLM) and the Poincare ball H^d (HypRiLM) with a shared MLP composition map phi (~290k parameters, d = 128, |V| = 2000). Across five seeds on WikiText-2, HypRiLM reaches 54.2 +/- 0.2 validation perplexity versus 87.6 +/- 0.6 for Flat RiLM; tied and matched LSTM, Transformer, and SSM controls remain at 113-147 PPL on WT-2 -- HypRiLM leads by roughly 2x over the strongest tied recurrent baseline (SSM, 113.0 +/- 3.8). Penn Treebank and a 10k-vocabulary stress test confirm that geodesic decoding transfers across corpora and larger |V|, while hyperbolic curvature helps selectively. We also characterize boundary collapse in naive hyperbolic recurrence and show how Mobius stabilization restores trainability. Claims are scoped to controlled small-model comparisons, not full-vocabulary state of the art.

How many of a transformer's components decide a token? Counted by the absolute value of each unit's and channel's contribution to the logit, one prediction rests on thousands to hundreds of thousands of them. But contributions are signed, and across eighteen models the mass pushing away from the predicted token is a median of seven times the mass carrying it. Divide by the net and the count is dozens: on the baseline, 53 components carry ninety percent of a prediction, 13 it cannot survive losing, and 8 suffice to produce it alone. Across twelve models trained elsewhere, 124M to 7B parameters, the sufficient set runs from two components to sixteen, and what a prediction draws on, followed all the way back, is one to three percent of the model, a share that does not grow with size. Three quarters of a layer's update is a fixed linear map of the state it received. Everything is read from the model's own parameters and activations, with nothing trained or fitted, and it names a component on both sides: what it writes, from the predictions it drives, reaching close to half of every model; what it reads, from its weights in the frame of its own layer, at 58.9 percent above chance over its eight strongest inputs. Sorting the remainder by upstream source yields grammatical categories the embedding cannot see. A name can be acted on. An association the model does not hold installs into one spare unit, key and value read from the weights, for a quarter of a percent of held-out loss, a fortieth of what a rank-one update costs. An installed attention head and a unit two layers above it make an edit fire only where a token occurred earlier in the context, and a unit the model trained for itself is driven from two layers upstream, 86 percent of the effect passing through it. An order-preserving activation puts a unit's inputs at the instrument's ceiling, at the price of a two-part install.

3D Gaussian Splatting (3DGS) enables real-time novel view synthesis but produces millions of primitives through adaptive densification, leading to significant storage overhead. Learned-mask pruning methods such as LP-3DGS address this by assigning each Gaussian a learnable mask to identify and prune redundant primitives. However, we identify a limitation of this paradigm: the steep slope of the Gumbel-Sigmoid activation drives mask values to the extremes within the short mask-training window, before the importance ranking has stabilized, producing a sharply bimodal distribution from which that ranking can no longer be reliably recovered. We propose LinearMask-GS, which replaces Gumbel-Sigmoid with a linear increment activation that keeps mask values in a mid-confidence regime throughout mask training, producing a stable, unimodal mask distribution whose ranking tracks importance. On Mip-NeRF 360, our method achieves 3.6x and 1.6x Gaussian reductions over 3DGS and LP-3DGS, respectively, while maintaining or improving rendering quality. For outdoor scenes, it yields a 1.6x reduction (from 2.18M to 1.36M) with notable gains in PSNR (+0.38 dB), SSIM (+0.025), and LPIPS (-0.029).

EdgeAI systems are increasingly employing computer vision applications to enable intelligent, on-device decision-making in real-time. However, these deployments face highly dynamic operational conditions, with fluctuating constraints on latency, power availability, and memory resources. Deep Neural Networks (DNN), which follow fixed computational execution flows, lack the flexibility to adapt to such variability, resulting in inefficient and suboptimal performance in edge scenarios. This underscores the need for architectures that are not only efficient but also dynamically scalable at runtime. In this paper, we propose Elastoformer: A framework that transforms conventional neural networks (NN) into Elastic NN capable of real-time elastic inference. Unlike the conventional bag-of-models approach, which requires maintaining multiple independent models for different operating conditions, Elastoformer offers a single, modular solution that dynamically switches between multiple modes of operation at runtime, adapting efficiently to the changing computational budgets of edge devices without the overhead of managing separate models. Experiments reveal that our framework achieves up to 85% reduction in computation FLOPs, 50% reduction in latency and 76% reduction in memory overhead, while showcasing the architecture agnostic nature of the framework across both Vision Transformers and CNNs. Our code is available at https://github.com/sudaksh14/Elastoformer.

Finger-specific motor intent is a clinically meaningful control signal for post-stroke neurorehabilitation, where residual muscle activity may remain measurable despite weak or incomplete movement. We study five-finger multilabel intent decoding from impaired-arm high-density surface electromyography (sEMG) in PhysioMio, a bilateral longitudinal dataset collected from stroke patients. A common processing protocol aligns movement labels, applies 20--450 Hz Butterworth filtering and Symlet-4 wavelet denoising, segments overlapping 200 ms windows, and extracts twelve time- and frequency-domain descriptors per channel. Direct LSTM, CNN, and GNN baselines reveal complementary behavior: the LSTM attains the highest subset accuracy (0.545), whereas the GNN attains the highest macro F1 (0.706) and macro AUPRC (0.776). Architecture search then identifies CNN-Large as the strongest single-split CNN, with 0.593 subset accuracy and 0.714 macro F1, while CNN-Micro provides a compact architecture for embedded inference. To match a four-sensor hardware design, we retrain CNN-Micro using channels associated with ECRB, ECRL, FDS, and FDP and exclude the ground electrode from model input. Across five seeds, cross-channel knowledge distillation improves the four-channel student over direct training, reaching $0.5219 \pm 0.0114$ subset accuracy, $0.7612 \pm 0.0038$ finger accuracy, and $0.6095 \pm 0.0058$ macro F1. The selected 123K-parameter model accepts nine windows of 48 features and has been exported to ONNX. These results establish a reproducible software path from post-stroke sEMG to compact five-finger intent prediction for subsequent hardware-in-the-loop evaluation.

Low-bit attention accelerates Transformer inference by moving the $QK^\top$ and $PV$ matrix multiplications to FP8 or FP4 matrix engines. However, the softmax path often evaluates shifted-score exponentials in higher precision, forms a temporary probability block, and quantizes it before low-bit $PV$ multiplication. This exp-then-quantize path creates a mismatch between a high-precision probability producer and a low-bit matrix consumer. We propose EFQ-Softmax (Exp-Free Quantization for Softmax), a low-bit probability-generation method that directly maps shifted attention scores to block-scaled E2M1 operands. For each microscaling block, EFQ-Softmax selects an exponent-only scale from the local maximum, maps the shifted scores to a normalized residual domain, and generates nonnegative E2M1 probability codes using a single affine rule. The resulting operand is used consistently in both the $\widetilde{P}V$ numerator update and the $\widetilde{P}\mathbf{1}$ denominator update. The FlashAttention-style row-maximum update, historical rescaling, high-precision accumulation, and final normalization remain unchanged. We evaluate end-to-end quality on Qwen3-8B, Qwen3-VL-8B-Instruct, and WAN2.2-TI2V-5B, and separately measure kernel-level performance on the A5 vector unit. EFQ-Softmax improves the Qwen3-8B seven-task mean from 0.6749 with MXFP4 to 0.6773 and the Qwen3-VL nine-task mean from 0.7826 to 0.8000. On WAN2.2, it maintains temporal consistency and visual quality comparable to the FP16 and MXFP4 baselines under VBench. On the A5 vector unit, EFQ-Softmax reduces the vector-stage latency of the fused probability-generation kernel by 40.33% on average across sequence lengths from 16K to 128K. These results show that direct low-bit probability generation can replace the conventional exp-then-quantize path while preserving end-to-end model quality.

An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al. (COLT 2024). For width $s$, at most $k$ active units per input, and effective weight and bias bounds $W,B$, every size-$m$ sample in the class's fixed radius-$R$ input domain satisfies $\mathcal{R}(S)\le CWR\min\{k,\sqrt{sk/m}\log^{3/2}(2m)\}+kB/\sqrt m$. A support-preserving cover and a single normalized chaining argument remove the previous explicit dimension factor, up to logarithms. Lower bounds on appropriate i.i.d. marginals match up to those logarithms, showing how changing active units across inputs retains a width dependence. The input domain matters: zero-bias networks sparse on the entire ball have at most $2k$ nonzero units and complexity $O(kWR/\sqrt m)$, whereas bias bounds comparable to $WR$ restore the worst-case rate on that same domain in only logarithmic dimension. A spherical-cap construction proves the latter claim without assuming sparsity merely on the sampling support. For a specified normalized bounded loss and biases comparable to $WR$, we also obtain agnostic minimax excess-risk bounds of order $\min\{1,\sqrt{s/(km)}\}$ up to logarithms.

False ventricular tachycardia (VT) alarms are a leading contributor to alarm fatigue in intensive care units. We propose a deep learning framework combining a 1D SE-ResNet with ICU-realistic data augmentations and a physics-informed auxiliary reconstruction task based on the three-element Windkessel hemodynamic model, implemented as a differentiable forward simulation. By requiring the network's latent representation to produce physiologically plausible arterial pressure waveforms, artifact-driven ECG patterns are penalized while true VT remains coherent across modalities. Evaluated on the VTaC benchmark under a strict real-time protocol (10-second pre-alarm window), our method achieves a 5-point Challenge Score improvement over prior state-of-the-art. Ablation studies confirm that the physics-informed objective is the primary performance driver, providing gains in accuracy, 2x label efficiency, and more localized and clinically meaningful ECG segments.

Microscopic image analysis has long been recognized as a promising approach for monitoring activated sludge. In recent years, deep learning-based image analysis has been increasingly adopted in this field because of its high performance. However, previous studies on microscopic image analysis of activated sludge have rarely explored transformer-based models or self-supervised foundation models and have instead relied on CNNs and supervised ImageNet pretraining. In addition, previous studies often downsampled image sizes, but the effects of downsampling have not been sufficiently investigated, and the relationship between downsampling strategies and image analysis performance remains unclear. Furthermore, no study has quantitatively compared deep learning performance with quantitative image analysis (QIA), which was widely used before the emergence of deep learning. In this study, to examine how model architecture and learning strategies affect performance in microscopic image analysis of activated sludge and to quantitatively determine whether deep learning outperforms QIA, we prepared three types of activated sludge samples, classified their microscopic images, and evaluated classification accuracy. Our results showed that transformer-based architectures and alternative pretraining methods were effective in terms of classification accuracy. Our downsampling analysis showed that using overly small images reduced accuracy, but increasing image size beyond a certain point did not improve it further. In addition, the analysis indicated that, to achieve high classification accuracy, maintaining the field of view was a more effective downsampling strategy than maintaining resolution. Finally, our comparison between deep learning and QIA showed that deep learning outperformed QIA in terms of accuracy.

Floorplans are compact, appearance-invariant maps ideal for indoor localization, yet existing methods rely on depth networks that are brittle in cluttered scenes. We propose GALoc, a geometry-first framework that replaces depth prediction with gravity-aligned wireframes that satisfy verticality and coplanarity by construction. Given monocular RGB, camera intrinsics, relative poses, and IMU orientation, GALoc constructs a linear constraint matrix encoding verticality and coplanarity, and finds the camera gauge minimizing its smallest singular value via global search. The rectified wireframes are projected into bird's-eye-view layouts through a closed-form, FOV-consistent transformation and matched against the floorplan via metric-free SE(2) search. We evaluate end-to-end on Structured3D, with calibrated noise on Gibson, and on real-world author-collected sequences. When sufficient wall geometry is visible, GALoc matches or outperforms depth-based baselines -- achieving 88% sequential localization success at 0.1m over 100-step sequences on Gibson vs the baseline's 68% -- while abstaining in structure-blind scenes.

We describe the Snugi-AI-v2 submission to eRisk 2026 Task 2, the second edition of contextualized early depression detection from Reddit discussions. Our central contribution is a learned MLP stopping policy trained to directly optimize ERDE50, replacing the fixed and tiered threshold strategies used in all prior eRisk Task 2 submissions. Combined with a sustained confidence gate that commits only after N=3 consecutive rounds of high policy confidence, the system reduces false positives caused by transient emotional posts without sacrificing recall. The pipeline encodes each discussion thread with a frozen MentalRoBERTa model, maps the accumulated representation to a depression probability via an MLP classifier, and delegates the timing decision to the learned policy. Our best run achieves F1 = 0.73 (Run 1) and F_latency = 0.70 (Runs 0 and 3), with a median alert round of 8 out of 500, completing the full evaluation in 1 hour 26 minutes, the fastest among all complete-submission teams. We report a systematic ablation across five runs spanning two encoder variants, four stopping strategies, and three gate values, along with negative results from GRPO policy training, BDI-II post filtering, MentalLongformer encoding, and DeBERTa ensembling. Code: https://github.com/chiuyuwen91/erisk-2026

Deep learning models have been increasingly applied to Time Series Forecasting (TSF) in recent years. Transformer-based and MLP-based models have both been used effectively on many real-world TSF regression benchmarks, and there is ongoing debate as to which family of methods is best. While these benchmarks have drawn much attention, it is also worth noting that many current datasets and methods assume approximate periodicity in the time series. In this work, we focus on a new TSF task without periodicity: anticipating falls during humanoid locomotion, on the basis of egocentric vision and proprioception. When the locomotion trajectories are sufficiently diverse, periodicity is violated. We contribute two new benchmark datasets (one from simulation, one from real hardware), showing that periodicity is violated and recent deep TSF methods struggle on these benchmarks. We also propose a novel deep learning architecture that exploits both endogenous and exogenous variables and a training process that rigorously enforces i.i.d sampling of training examples. Our results show statistically significant improvement over prior art in multiple experimental conditions, by 12.73% or more on the real data and 10.40% or more on the simulation data. Code and datasets will be available upon acceptance.

Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of standard coordinate networks: their neural tangent kernel (NTK) is translation-variant and lets training points of large coordinate magnitude disproportionately influence predictions elsewhere, producing long-range coupling and gradient conflict during training. We show analytically and empirically that mixture-of-experts (MoE) architectures with centered, compact-support routers yield a uniformly banded NTK whose kernel-regression weights decay exponentially with distance, localizing the learning. Building on this, we propose \emph{Latent-MoE}, which interleaves domain-aware MoE blocks within a shared backbone. Unlike FB-PINNs or X-PINNs, which rigidly partition both the domain and the parameters so that the parameters on different subdomains are updated independently, Latent-MoE is designed to preserve the localization benefit of domain-aware routing while allowing capacity to flow across regions through the shared backbone. On standard homogeneous-physics benchmarks Latent-MoE is competitive with established baselines; on benchmarks with multi-stage time-variable physics, where global models and rigid domain decompositions both fall into spurious solutions, it improves over them by more than an order of magnitude, with markedly reduced gradient conflict during training.

Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training dynamics. In this paper, we develop a theoretical framework that characterizes how these factors jointly shape generalization performance throughout training. More precisely, we study a broad class of neural networks trained under the $\ell^2$ loss by gradient descent (GD) with weight decay, and prove the convergence of GD to a neighbourhood of the global minimizers of the empirical loss. By partitioning the space based on the input data, we then decompose the population error into data error, optimization error, and prediction variation error, and bound them separately. In particular, for the prediction variation error, which measures the oscillations of the learned function, we propose (local) approximate homogeneity and derive explicit cellwise and layerwise bounds for its evolution along the training trajectory. These bounds yield two important implications: a necessary condition of improved generalization explains differences in layerwise generalization behavior; a sufficient condition describes delayed generalization and provides a theoretical characterization of grokking.

Associative Recall (AR) is the cognitive ability to learn and retrieve links between items in memory. In NLP, AR is used as a benchmark for evaluating the in-context memory capacity of architectures such as Mamba, and has been found to strongly correlate with language modeling performance. This paper explores AR from the perspective of mechanistic interpretability, aiming to reverse-engineer the exact internal algorithm used by Mamba to perform recall. Our key insight is that Mamba performs recall by implicitly learning linear hash functions, and we identify the low-level circuit that enables this behavior. Building on these findings and inspired by theoretical tools in similarity-preserving hashing, such as the Johnson-Lindenstrauss lemma, we develop a theoretical framework for analyzing AR, which we term Recall Scaling Laws. Given the vocabulary size and the number of facts in context, this framework allows us to (1) predict the embedding and state dimensions required for Mamba to achieve perfect recall, (2) predict recall success probability given the model dimensions, and (3) analyze multi-layer models and multi-head SSM patterns. Empirical results show that our theoretical findings are accurate and predictive, offering insights into how AR capacity scales with vocabulary, state, embedding size, and architecture.

Fibre optic sensing, such as distributed acoustic sensing (DAS), has become a widespread technology for geophysical studies. To process the large-scale datasets produced by DAS, several machine learning methods have been proposed. However, without standardization of data and models, these methods lack comparability and interoperability. This introduces a gap between model developers and practitioners analyzing DAS data and inhibits adoption of deep learning for DAS. To address these limitations, here we present SeisBench DAS, an extension to the SeisBench library for machine learning in seismology. SeisBench DAS defines standard formats for DAS benchmark datasets, including standardised metadata and labels, and DAS models. It builds on the xdas framework for data ingestion and virtual array handling, and on PyTorch for reading and applying the machine learning models. Importantly, SeisBench provides an engine to efficiently apply deep learning models to diverse formats of DAS data, bridging the gap between model developers and practitioners. SeisBench DAS is designed as an open and extensible framework, allowing to easily incorporate future developments in deep learning for DAS.

Accurate city-level IP Geolocation is an important enabler for the modern digital ecosystem, underpinning services ranging from local content delivery and targeting to digital rights enforcement. However, traditional heuristic and database-driven methods often struggle to resolve the complex, non-linear allocation patterns of modern network infrastructures, particularly within the exploding IPv6 address space and transient mobile networks. In this paper, we introduce IPGeoAI, a novel deep learning model architecture that reframes geolocation from a static lookup problem to a sequential modeling task. Our approach utilizes the Transformer Encoder to capture hierarchical dependencies inherent in IP subnet structures. We propose a method to resolve geographic ambiguity by integrating unstructured semantic context via a Zero-Shot LLM Feature Extraction pipeline. We utilize Large Language Models to transform raw, noisy Autonomous Systems (AS) descriptions into structured, domain-specific metadata (such as 'University' vs. 'ISP' or 'Global' vs. 'Local') via an offline pre-computation process. By fusing these semantic signals into the network via a Multi-Head Cross-Attention module, we bridge the gap between numerical network topology and real-world semantic identity. Extensive offline evaluation on a proprietary dataset spanning 200,000 cities demonstrates that IPGeoAI significantly outperforms a leading external vendor in city-level granularity. By adopting a hierarchical inference strategy that refines coarse-grained country signals, our model achieves a 6% improvement in city-level accuracy while extending coverage to 100% of the traffic. Furthermore, in large-scale online production tests, the model drove a statistically significant +0.35% improvement in our 1st-tier downstream use cases metric.

Deep neural networks deployed in the wild must be both efficient and adaptable, requiring model compression and test-time adaptation (TTA). While both are well studied in isolation, their interaction remains poorly understood. We systematically analyze how structured compression affects a model's ability to adapt under distribution shift. Using ResNet-18 and ViT-Base on CIFAR-10-C and ImageNet-C, we evaluate multiple compression methods combined with standard TTA techniques. We introduce a diagnostic framework that examines representational expressivity and adaptation subspace compatibility. Our results reveal a consistent gap: although compressed models retain high accuracy under supervised adaptation, their TTA performance degrades significantly with increasing compression. We show that this stems from reduced representational diversity and structural constraints that limit recoverability. These effects strongly depend on the compression method, highlighting the need to design compression strategies that preserve adaptability.

Deep neural networks (DNNs) are increasingly deployed in real-world vision systems, yet their predictions can be covertly manipulated by backdoor attacks, in which malicious triggers cause targeted misclassification while preserving high clean accuracy. Existing defenses often rely on model internals, training data, or clean validation samples, making them difficult to deploy when only black-box access to a trained model is available. We propose TRIM (Trigger Removal by Identifying Manipulated Regions), a deployment-oriented black-box defense that detects and selectively removes backdoor triggers at inference time without requiring model internals, training data, or clean samples. The key insight behind TRIM is to identify image regions that are responsible for anomalous model behavior and purify only those regions while preserving benign content. TRIM innovates via three key components: (i) region-based segmentation with deep feature representations, (ii) adaptive trigger discovery through inpainting and diffusion-based reconstruction to isolate regions responsible for misclassification---without assumptions about trigger type, shape, or location, and (iii) selective region purification that cleans poisoned regions while retaining benign content. To support practical deployment, TRIM further caches feature embeddings of previously identified triggers, enabling efficient recognition and avoiding redundant detection and purification. Extensive experiments across diverse datasets and backdoor types, including blended, sparse, varying-size, and multiple triggers, show that TRIM consistently outperforms existing black-box defenses, reducing attack success rates (ASR) to as low as 1.16% while preserving clean accuracy of up to 87.87%. These results demonstrate that effective backdoor mitigation is possible at inference time even when the defender has no access to any auxiliary data.

Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks. We address this by introducing a simple closed-form ``two-stage'' compositional formula $\hat{f}$ for reconstructing an unknown Lipschitz function $f:\mathcal{X}\to \mathbb{R}$ on a metric space $(\mathcal X,ρ)$ from $N$ i.i.d. noisy observations. Our main result is a high-probability uniform ($L^{\infty}$) recovery guarantee that jointly controls approximation and statistical errors while enjoying an optimization error of zero; in particular, we do not assume oracle access to an approximate ERM. Our secondary main results establish the optimality of our formula in three complementary senses. 1) Function space: On Ahlfors-regular metric spaces, the hypothesis class parameterized by our formula attains the optimal fat-shattering dimension. 2) Parameter space: Its dependence on the parameters is maximally numerically stable, in the sense that a smaller approximation error cannot be achieved with a smaller Lipschitz dependence on the model parameters. 3) Forward pass: Its dependence on the input is maximally regular, matching the Lipschitz constant of the target function $f$. When $\mathcal X=[0,1]^d$ is equipped with the $\ell^\infty$ norm, $\hat{f}$ admits algorithmic ReLU-MLP and exact ReLU-multi-head transformer realizations of depth $\mathcal{O}(\log(N))$ with $\mathcal{O}(N)$ nonzero parameters.

Neural fields (NFs) map continuous coordinates to signals such as color or density, but fast high-quality reconstruction from sparse observations remains difficult. Classical Neural Tangent Kernel (NTK) regression gives closed-form fits, yet it is fundamentally linear and cannot accumulate reusable task priors. We develop three algorithms that address these gaps. NTK-KIP learns a distilled support set of coordinates (and optional labels) so that a finite NTK can inpaint large missing regions from little observed data, yielding a compact non-linear representation instead of a raw kernel solve. MetaQuill meta-learns a shared initialization for an INR so that new scenes can be adapted by updating only a small task-specific weight offset, which provides true feature learning and a reusable prior. Finally, MetaQuill-KIP fuses both ideas: it seeds the task with a KIP-style non-linear warm start, then refines only that small offset around the meta-learned initialization. MetaQuill-KIP achieves high-PSNR reconstructions and semantically plausible inpainting under very sparse observations, while requiring only lightweight per-instance adaptation, whereas diffusion-style baselines typically depend on large pretrained generative priors and costly per-image tuning. This shows that NTK-driven neural fields can be made both non-linear and meta-learnable, narrowing the gap between analytic kernels and practical few-shot reconstruction.

Scaling laws in modern deep learning describe how held-out loss improves as model capacity, training data, and compute increase, often following power-law trends. We investigate whether analogous scaling regularities arise in actuarial ratemaking, where data are tabular, heterogeneous, and noisy, and where classical models such as GLMs remain strong baselines. Using a real-world motor insurance portfolio, we train models from different families across increasing fractions of the training data and multiple random seeds, evaluating out-of-sample Poisson deviance, a likelihood-based loss for Poisson count predictions in which lower values indicate better held-out fit. We find that all model families improve with additional data, but scaling exponents differ substantially: TabM exhibits markedly stronger data scaling than purely supervised tabular Transformers and standard MLP baselines. Transformer variants show weak parameter scaling unless augmented with additional inductive biases (TabM-style adaptation or self-supervision). These results provide quantitative guidance on model selection by data regime and suggest that effective scaling on actuarial tabular tasks depends on architecture and loss function objective design, with simple increases in Transformer size providing limited gains.

Physics-informed neural networks (PINNs) offer a promising framework for modeling semiconductor devices, yet standard architectures struggle with severe numerical stiffness and multiscale spatial discrepancies inherent to oxide heterostructures. Here, we demonstrate a cascaded PINN architecture coupled with a custom second-order Chebyshev second kind polynomial spectral optimizer (DSO V2 Hybrid) to model ion-electronic drift-diffusion transport in Pt/SrTiO$_3$/Si memristive heterostructures across a 20 nm STO film on a 380 $μ$m Si substrate. By isolating potential, carrier density, and vacancy transport into four sequentially trained sub-neural-networks, our model circumvents condition numbers exceeding $10^{16}$ without operator splitting. The trained surrogate reproduces experimental conductive-AFM current-voltage hysteresis ($R^2 > 0.96$) while ensuring strict Poisson consistency across continuous space. Compared to conventional finite-element solvers (e.g., COMSOL), the PINN surrogate enables differentiable inverse parameter estimation and linear time inference.

Dynamic networks are being applied in many domains, from social media to logistics systems, each with their own set of special characteristics. A model employed on this type of data must capture the duality between temporal/structural and feature-based information. Yet state-of-the-art deep learning models often struggle to learn especially short-term behavioral interaction signals, such as sender intensity or interaction inertia, directly from raw event streams. To address this gap, we propose a statistical feature augmentation method that explicitly encodes behavioral interaction statistics into the input feature space. We evaluate our proposed method on an anomaly detection task across three real-world datasets (Reddit, Wikipedia, MOOC) and seven models spanning both continuous-time and discrete-time architectures. As a baseline, we apply the same models trained on the original embeddings. Our results show, that augmentation consistently improves detection performance. Beyond performance, the enriched input enables fine-grained post-hoc analysis of behavioral importance, since each statistic occupies a dedicated input dimension. In particular, this work showcases a promising approach for merging classical network analysis with deep learning.

A compressed student has two shapes that need not agree: the weight it deploys at inference and the weight family its training can reach. We show that a state-of-the-art weight-inheritance distiller, Low-Rank Clone (LRC), deploys a full-width student MLP but ties training to a teacher-induced slice, leaving 62.5-81.4% of each deployed matrix's independent linear degrees of freedom unreachable-paid for at inference, never trainable. Our principle is one line: train what you deploy. From the identical LRC warm start, we make the training object the entire deployed matrix, with no change in deployed shape, deployed parameter count, or inference FLOPs, via two mergeable realizations (Dense-LRC and CORE-LRC) that both collapse to one deployed weight. This recovers stranded capacity: taking the stronger realization per teacher, +2.36/+2.71/+10.45 Avg9 over matched-budget plain-LRC baselines across three teachers (Llama3.2-3B, Llama3.1-8B, Qwen2.5-3B), with the largest gain on the widest teacher (Qwen), where it reaches the original recipe's approx. 20B-token accuracy at 10B tokens (2x token efficiency); there the strictly same-lineage arm still recovers +6.39, the fully controlled figure. Controls strongly support attributing the gain to the enlarged reachable set, rather than to added parameters or the recipe. From approx. 10B distillation tokens plus a short SFT, a half-parameter 1.5B student matches its approx. 9T-token teacher's 9-task macro-average, within evaluation noise and with a residual MMLU deficit, and a 2.7B student beats Meta's own official compression of Llama3.1-8B at ~900x fewer compression tokens (a token count under unmatched recipes, not a compute claim). All results are from single-seed runs on the LRC backbone.

Higher-order interaction components are important for signal, image, and video modeling, but explicit high-order operators often suffer from rapidly increasing parameter and computational costs. This paper presents kVNN, a learnable kernelized Volterra Neural operator for compact higher-order filtering. The motivation is to use kernelization to improve the efficiency of Volterra-type neural operators while providing a structured interpretation of their higher-order components. The proposed formulation combines the order-wise structure of Volterra filtering with learnable polynomial-kernel atoms, allowing different interaction orders to be represented by separate learnable centers and coefficients. This order-decoupled representation avoids explicit high-order tensor parameterization and can be implemented as a CNN-compatible layer. Experiments on representative vision tasks show that kVNN achieves a favorable accuracy--efficiency trade-off.

We describe a neural network architecture and training procedure designed to model electronic ground and excited states of arbitrary molecular systems. By indirectly learning a latent, implicit basis representation of the electronic-state Hamiltonian, the model offers a unified treatment of multiple electronic states, conical intersections, and non-adiabatic couplings. The formalism can be further extended to learn consistent latent representations of additional operators such as transition dipole moments, for example. To demonstrate the general capabilities of our architecture, we train and evaluate networks on two realistic photochemical systems, thymine and azobenzene. The resulting models accurately reproduce energies and oscillator strengths for the ground- and low-lying excited states relevant to the photochemistry of these systems. We highlight the performance of the trained networks by studying critical molecular geometries, including conical intersections and excited state minima. By construction, the proposed framework also recovers the emergence of Berry phase accumulation around conical intersections. By pairing key mathematical structure from quantum chemistry with the representation learning power of transformers, the presented architecture offers a qualitatively new path toward fast and accurate ground- and excited-state simulations.

Automatic Target Recognition (ATR) in Synthetic Aperture Sonar (SAS) is a task largely dominated by deep neural networks (DNNs). Most SAS-ATR models use convolutional neural network (CNN) architectures whereas transformer-based architectures have had much less representation in the literature despite being state of the art in general computer vision (CV) research. Additionally, researchers have had mixed results in attempting to overcome challenges presented by a scarcity of labeled training data by using methods such as data augmentation and the use of pretrained weights from a variety of imaging modalities. In this work, we compare the performance of modern CNN and transformer-based DNNs to determine which architecture and training configurations elicit the highest performance in SAS-ATR. We investigate how network size, architecture, pretraining method, data augmentation and other forms of regularization affect SAS-ATR performance with a focus on producing the highest-performing model and providing a roadmap for training state-of-the-art SAS-ATR models.

Hyperspectral image classification still relies heavily on random pixel splits within a single scene. The Salinas dataset, randomly split, is among the most widely used datasets for comparing different architectures. However, under a random split method, a large fraction of test pixels fall immediately adjacent to a training pixel, which inflates reported accuracy. This work introduces a leakage-free evaluation protocol linking spatial separation to the model's receptive field. Applying this protocol across ten different architectures, including classical, spectral, spectral-spatial, transformer, vision-backbone, and state-space families, shows that Macro-F1 drops by 0.147 on average and model rankings change by as many as five places. Furthermore, leakage-free evaluation limits which architectures can be tested on a given benchmark. Since each partition supports patches only within a finite radius, reporting this radius alongside the receptive field is essential for fair comparison. In addition, this study reveals that all ten architectures misclassify largely the same pixels, pointing to a spectral ambiguity in the data that none of them resolves.

Artificial neural networks are often regarded as powerful yet opaque black boxes. Here, we demonstrate that learning in deep neural networks generates local symmetries known in graph theory as fibrations and coverings. We prove that covering symmetries are stable attractors of stochastic gradient descent. Consistent with this theory, we report the emergence of covering symmetries across major network architectures, including multilayer, convolutional, recurrent, and transformer networks. Exploiting these symmetries enables drastic model compression - reducing networks to 17% of their original size without sacrificing performance. Furthermore, controlled breaking of covering symmetry overcomes the loss of plasticity, achieving state-of-the-art performance in continual learning. The theoretical results provide a new foundation for AI systems based on symmetries that convert black boxes into interpretable colored graphs and enable more efficient inference and lifelong learning.

Anti-UAV systems increasingly fuse multiple sensors, yet their detection heads provide no per-modality reliability signal. This study evaluates whether evidential deep learning (EDL) heads, Dempster-Shafer (DS) evidence fusion, and uncertainty-driven temporal sensor gating improve anti-UAV detection through a controlled ablation on three benchmarks: thermal tracking (AntiUAV600), RGB-audio-RF classification (TRIDENT), and RGB-IR tracking (MM-UAV). The EDL training objective improves accuracy over retrained sigmoid baselines (+5.9 percentage points in accuracy and a tripled tracker-on-absent rate in E1; +4.8 percentage points in classification accuracy in E2, surviving a clip-clustered bootstrap, p = 0.011) and ranks classification errors substantially better (entropy UAUC approximately 0.94 vs. 0.51). The remaining components do not support their respective hypotheses. DS fusion does not outperform simple probability averaging. Dirichlet vacuity adds no ranking power beyond predictive entropy and inverts at the detection level, where extreme background imbalance causes it to encode class membership rather than error likelihood, a failure also observed for entropy and sigmoid confidence. Temporal gating preserves accuracy only when nearly inactive and yields no realised latency saving on shared-backbone hardware. The benefit of evidential learning therefore arises primarily from its training objective rather than its uncertainty estimate; a crop-level control further localises the detection-level breakdown to anchor-level evaluation rather than the learned representation.

LLM-based evaluators of natural language generation (NLG) quality are widely deployed as scoring tools and as automated training signals, yet the internal procedure by which they assign a rating remains poorly understood. We investigate this procedure mechanistically through an eight-attack perturbation taxonomy across the Readability and Adequacy dimensions of NLG quality, a generation pipeline that produces paired clean and corrupt summaries with controlled error intensity and explicit token-level modification maps, and a four-experiment battery of causal tracing, logit-lens vocabulary projection, and attention-head knockout applied to Themis (Llama-3-8B) and Prometheus (Mistral-7B). Both evaluators implement a structured, coherent evaluation pipeline operating in two stages: below layer 15, attention performs local error comparison and routes the result to the final input position; above it, the MLP cascade integrates the signal and writes the rating, with the decision crystallizing in the residual stream at a sharp late layer (L = 26 on Themis, L = 25 on Prometheus). Furthermore, a base-model control at the same scale (Llama-3-8B) reproduces the routing architecture and crystallization but not the stage separation, isolating the two mechanisms that fine-tuning specifically installs, suppression of below-L15 MLP contribution at the last position and a two-layer advance of the crystallization depth, indicating that fine-tuning sculpts an existing substrate rather than building the pipeline from scratch. We release the source code and data at https://github.com/himil-v/judge-mech

We extend recent work establishing an equivalence between one-layer transformers and nearest-neighbor classifiers in the binary setting to the multiclass case. By leveraging the simplex encoding, we show that one-layer transformers with an argmax classification head behave identically to a one-nearest-neighbor classifier in the multiclass setting. This closes a gap left by prior work, whose multiclass result relied on a non-standard rounding-based approach rather than the typical argmax head used in practice.

Tabular deep learning (TDL) leverages neural networks (NN) to extract patterns from tabular data. Traditional TDL methods follow a supervised learning paradigm, where a target feature is explicitly given. In this work, however, we explore a different approach by employing deep NNs to learn relationships among individual columns within a given table. We investigate whether NNs can predict the values of arbitrarily selected columns in a given table based on the remaining known columns. We call this problem In-Table Prediction (ITB), which is slightly different from table imputation methods and the pretraining task of TDL. Three potential usage scenarios are identified, which, to our best knowledge, have not been extensively studied in the literature. A self-supervised learning approach is applied to address this problem by randomly selecting columns to be masked out and used as learning targets. This work focuses on tabular datasets containing only continuous features. To handle missing values in continuous features, a novel neural layer is proposed to embed both numerical and empty values. Synthetic data is generated based on predefined column relationships, with empty values inserted using two distinct mechanisms. Additionally, an adapted masking strategy is employed to create test data. Performances of three NN architectures, namely MLP, Resnet and Transformer, are evaluated using the generated synthetic data. We conclude that, the attention-based structure outperforms the other two networks, when a sufficiently large number of training examples is available and a relatively large embedding length is chosen. We stress that these findings are obtained under controlled, synthetic conditions with a small number of columns and it should therefore be regarded as an initial, narrowly-scoped investigation rather than a general characterization of ITP on real-world tabular data.

The Levenberg-Marquardt (LM) algorithm is a well-known second-order method for rapid convergence and strong robustness when training small- to medium-sized neural networks (NNs). However, its computational and memory costs increase significantly as the number of parameters in an NN grows. To address this limitation, subspace methods have been proposed, such as the Krylov subspace LM (KSLM) and the hybrid subspace LM (HSLM), making second-order algorithms more efficient. In this work, we evaluate the subspace Levenberg-Marquardt algorithms for regression and classification tasks in neural networks. We compare the performance of subspace LM variants with the classical LM method, as well as other popular first-order algorithms, such as stochastic gradient descent (SGD) and Adam.

Neural networks are increasingly employed to identify both well-defined and ambiguous concepts, yet output-level metrics reveal little about how those concepts are represented internally. Our study asks if these networks exhibit \textit{conceptual separation}: if examples of the same concept form coherent representations, and whether related concepts lie closer together in the representation space. We examine this conceptual organisation in Convolutional Neural Networks (CNNs) and Large Language Models (LLMs) through geometric and distributional analysis of their internal activations. In CNNs, familiar ImageNet concepts form coherent and semantically ordered representations, while this coherence weakens for unseen concepts and suffers within-class domain shift. In LLMs, clearly distinct domains remain well separated, related subdomains move closer together, and the distinction between ambiguous topics collapses at both the mean and covariance level. These results suggest that conceptual separation can reveal structure that output accuracy alone cannot, and may serve as a useful diagnostic of how robustly a model represents the concepts it is asked to identify. Code and data available on \href{https://github.com/JaeeRoshniCapstoneProject/Are-You-Thinking-What-I-m-Thinking-Examining-Conceptual-Separation-in-Neural-Architectures}{GitHub}.

High-resolution precipitation nowcasting is critical for reducing the impacts of severe weather but remains difficult because of rapid storm evolution. Deep learning models have shown great promise for this task, but their predictive skill often deteriorates over longer forecast horizons. This leads to increasingly blurry forecasts that fail to capture the complex, non-linear evolution of storm systems. In order to address these limitations, we introduce Spatio-Temporal U-DeepONet (GenONet), a novel architecture for long-range precipitation forecasting up to 3 hours, specifically designed to produce sharp and physically consistent results. GenONet's architecture pioneers the use of a Deep Operator Network (DeepONet) as a generator within a Generative Adversarial Network (GAN) framework for this task. The DeepONet learns the continuous-time dynamics of precipitation, ensuring stability over long forecast horizons. Adversial training against a spatio-temporal discriminator compels the model to produce sharp, coherent forecasts, while a physics-informed loss regularizer, derived from the Moisture Conservation Equation, improves physical plausibility in our ablation setting. Quantitative evaluations show that our model achieves consistently higher scores on most of the metrics, especially for highintensity events and at longer lead times. Qualitatively, GenONet produces structurally coherent forecasts that maintain their integrity, whereas baseline models degrade into indistinct patterns. Finally, an ablation study confirms the benefit of this physics-informed loss, highlighting the strength of combining operator learning with adversarial training.

Recovering compact explicit solutions from neural approximations is challenging when imperfect teacher data guide symbolic topology search and coefficient estimation. We present DeSyR, a decoupled symbolic recovery framework for differential equations. A physics-informed neural network guides repeated searches to construct candidate topologies with provisional constants. Once a topology is fixed, its coefficients are refined solely from the governing equation and prescribed constraints, followed by gated selection and verification. For linear fixed-topology parameterizations, we characterize teacher-error inheritance and show that finite-weight mixed data--physics fitting retains an $O(β^{-1})$ teacher-dependent contribution when the teacher error projects onto the model space. Under well-posedness, representability, zero-residual attainment, and discrete determinacy, physics-only refinement conditionally recovers exact coefficients; for nonlinear parameterizations, the corresponding guarantees are local. DeSyR is evaluated on 15 differential-equation problems across 18 configurations covering high-order, space--time, multidimensional, nonlinear, and coupled systems. A candidate-level audit yields a 99.23% convergence rate among free-parameter refits, while every selected refinement involving free coefficients converges. Configuration-level median refined relative $L_2$ errors are $2.31\times10^{-14}$ or lower. In same-topology comparisons, refinement reduces error by eight to fourteen orders of magnitude. These results show that an approximate neural teacher can guide topology discovery without imposing its error scale on final recovered coefficients, provided a target-capable topology is retained and physics-only refinement converges.

Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniformly sampled. This paper introduces Wave Function Backpropagation (WFB), a wave-parameterized learning formulation in which neural responses are represented by learnable amplitude, wavenumber, angular frequency, and phase. The formulation associates an observed state with its temporal interval Delta t through the phase of a differentiable spatiotemporal wave. We derive standard WFB gradients and a spatial-curvature correction based on the Laplacian of the wave response. WFB is instantiated in a deliberately feed-forward trajectory predictor to provide a controlled proof of concept; sequence learning is outside the scope of the present evaluation. With motion features, STD-WFB using real intervals reduces average displacement error (ADE) by 20.4% relative to the original FFN baseline. In a new position-only evaluation that removes temporal leakage through precomputed velocity and acceleration, real-interval WFB reduces ADE by 10.4% relative to the original FFN and remains competitive with parameter-matched ReLU controls, obtaining 2.1% lower mean ADE than the matched FFN with explicit Delta t. Shuffled-interval WFB attains the lowest mean ADE, indicating that the present evidence supports the effectiveness of the wave representation but does not attribute the gain to interval alignment. These results establish WFB as a viable structured feed-forward learning formulation and define a clear basis for subsequent architectural studies.

This work studies hybrid quantum-classical neural networks for learning routing heuristics. Specifically, this paper asks whether small quantum neural networks can replace parameter-heavy modules inside a competitive attention-based routing model while maintaining solution quality. For the capacitated vehicle routing problem, encoder feed-forward replacement emerges as the most promising design: it reduces the number of model parameters by 56.6% while keeping the hybrid model close to the classical neural baseline at small and medium instance sizes, although the gap grows for larger instances. This work also compares to classical routing algorithms, which remain highly competitive and often superior on the fixed Euclidean test sets. Our results therefore do not indicate quantum advantage or solver dominance, but identify encoder feed-forward replacement as a viable hybrid-module compression strategy for neural combinatorial optimization.

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.

Recent Relational Deep Learning architectures have been proposed as foundation models for multi-table relational data, yet they impose constrained neighborhood budgets that force row truncation when an entity has many related records. We introduce Animus, a synthetic financial dataset in which predicting customer income requires aggregating up to tens of thousands of transactions. On the raw representation, three recently proposed models (RT, Griffin, RelGT) achieve $R^2 \le 0.18$; a single, routine, temporal pre-aggregation step recovers $R^2$ up to $0.65$. This questions whether current relational foundation models are ready for high-cardinality real-world data.

Many parameter-efficient methods generate the parameters of a large neural network from a low-dimensional latent representation. Given an architecture $Φ$ with $P_Φ$ parameter slots, we write $\boldsymbolθ_f=\mathcal{G}(\boldsymbolξ_f)$, where $\mathcal{G}\colon\mathbb{R}^M\to\mathbb{R}^{P_Φ}$ is a parameter generator and $\boldsymbolξ_f\in\mathbb{R}^M$ is a latent representation of the target function $f$. The architecture $Φ$ and the generator $\mathcal{G}$ are shared across the entire target class, while each target $f$ is represented by its own latent vector $\boldsymbolξ_f$, with $Φ_{\mathcal{G}(\boldsymbolξ_f)}$ approximating $f$. This framework encompasses hypernetworks, low-dimensional parameterizations, parameter-efficient adaptation, and model compression. Understanding the tradeoff between the latent dimension $M$ and the network budget $P$ is therefore fundamental to characterizing the expressive efficiency of these methods. We study this tradeoff for affine generators and fully connected ReLU architectures. More precisely, optimizing jointly over architectures $Φ$ satisfying $P_Φ\leq P$ and affine generators $\mathcal{G}:\mathbb{R}^M\to \mathbb{R}^{P_Φ}$, we prove that the optimal worst-case uniform approximation error over the unit ball of $α$-Hölder functions on $[0,1]^d$, where $0<α\leq1$, has the sharp order $\bigl(P\min\{M,P\}\bigr)^{-α/d}.$ In particular, our result shows that even a fixed-dimensional latent space suffices to achieve vanishing approximation error as the network budget increases.

Modularity in deep neural networks has been proposed as a means of improving both interpretability and training by promoting disentangled representations and reducing redundancy. In this work, we study the emergence of modular structure through competition dynamics between groups of neurons during training. We introduce a method that (i) maintains near-baseline accuracy, (ii) induces usage-based modularity by sparsely routing inputs to neuron groups, and (iii) encourages specialization of these modules, such that their activations are correlated with input classes. We evaluate the proposed approach on ImageNet-100 and CIFAR-100 and show that with it, specialized modules emerge without module-level supervision. These modules capture a meaningful high-level structure in the data, with individual modules responding to semantic categories (e.g., dogs or vehicles). We also study the emergence of a hierarchical partition of sub-tasks depending on the number of modules. Our results suggest that competitive dynamics can serve as a simple mechanism for inducing functional modularity in standard architectures.