Mnist

Prototype reduction replaces a training set with a smaller representation, and the established methods return a finite set of points. We propose Skeletal Prototypes on Iterative Nerve Expansions (SPINE). The model for each class is an embedded 1-complex rather than a point set. Its initial edge set is a class-conditional Mapper graph, so the data decide which localized clusters are joined. Later phases fit the vertices under a classification objective, and an observation is assigned to the class whose complex is nearest. The segments therefore enter the decision rule and not only the fitting. We evaluate SPINE on seventeen benchmark datasets under stratified 10-fold cross validation, against seven other prototype reduction methods at a matched budget. SPINE attains the highest mean accuracy and the best average rank. It is significantly better than five of the seven competitors under Wilcoxon signed-rank tests with Holm correction. A budget sweep shows that the decision rule using the entire graph segments contribute most when prototypes are scarce, while the method as a whole competes best at moderate budgets. Construction cost places SPINE with the discriminative methods, and it is faster than generalized learning vector quantization on fourteen of the seventeen datasets.

Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.

Evolvable-Substrate HyperNEAT (ES-HyperNEAT), a bio-inspired indirect encoding that determines neuron placement and connection weights from spatial coordinates, exhibits a failure mode on MNIST as a diagnostic benchmark. Because input pixels map to a coordinate space centered at the origin, evolved networks converge on a small central cluster of input pixels, a spatial-concentration bias; prior work observed only 21% mean accuracy in this regime. Is this bias an optimization artifact or an architectural ceiling? Inspired by Mixture-of-Experts (MoE) principles, we partition the input into non-overlapping spatial segments, each assigned to a separately evolved specialist network. With 13 such experts, this design reaches 43% mean accuracy, a 106% relative improvement over the baseline. The architectural gain does not depend on data-driven aggregation: equal-weighted averaging, which uses no validation data, already yields a 70% improvement; the gain comes from partitioning, not the weighting. Receptive-field analysis shows the mechanism: partitioning forces evolution to discover features across the entire image, expanding active pixel coverage from 4% to 79%. Absolute accuracy stays below gradient-trained baselines, but the relative gain points to central bias, not the evolutionary search. Two tools are designed to generalize beyond MNIST: a receptive-field diagnostic for silent input-coverage collapse, and a spatial-partitioning remedy that restores coverage.

This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.

AI agents in partially observable environments need to coordinate active sensing with working memory to maintain an evolving perceptual state. However, existing benchmarks struggle to isolate this perceptual-state construction and interpretation capability because they introduce physical and control complexities. We address this with MNIST-PRO, a benchmark that isolates agentic perception by converting MNIST digit recognition into a sequential, glimpse-based search task with lookback constraints. We evaluate ten multimodal models across four memory representations, including raw visual history, textual states, structured metric grid maps, and a consolidated visual canvas. While models excel under full observability, partial observability exposes a clear performance gap. We identify three distinct bottlenecks. First, perceptual-state construction and interpretation present a challenge, as agents struggle to integrate fragmented glimpses. Second, agents often stop exploring before they see the full sequence. Third, models often fail to revise early, incorrect beliefs even when faced with subsequent contradictory evidence. These results show that simply acquiring visual evidence is not enough. Agents must also be able to build and update a reliable perceptual state.

The OWL 2 EL profile is used in some of the largest production ontologies, including the Gene Ontology and SNOMED CT. Existing neuro-symbolic (NeSy) learning methods accept propositional theories or Datalog, and reasoning-shortcut (RS) awareness has not been investigated in ontology settings. We present Moose, a method that compiles an $\mathcal{EL}^{++}$ TBox and finite ABox to a Sentential Decision Diagram (SDD). The SDD acts as a differentiable weighted-model-counting layer, and we add closure clauses outside the $\mathcal{EL}^{++}$ profile on declared exhaustive families to overcome the limited expressivity of $\mathcal{EL}^{++}$ under partial supervision. We show termination, soundness, completeness, and polynomial intermediate sizes, and validate the proofs in Lean. We then define the first formal partial-supervision latent-concept-learning task over an OWL EL ontology, i.e., learning per-individual classifiers for latent concepts from observed ABox literals, and evaluate Moose on MNIST-with-ontology and Pizzaïolo. Moose improves over propositional-NeSy, fuzzy-logic, and ontology embedding baselines, and presents the first reasoning-shortcut analysis in an OWL EL setting.

Intensity-image reconstruction from event streams remains a challenging problem due to the binary, sparse, and asynchronous nature of event data. This work proposes eBIRD, an event-guided reconstruction framework that combines a DDPM with ControlNet-based conditioning. We analyze generic and specialized diffusion learning strategies for handwritten digit (N-MNIST) and face (RGBE-Gaze) reconstruction using 33ms event windows. On N-MNIST, the general model achieves the best reconstruction quality (MSE 0.0052, SSIM 0.8982, PSNR 23.34dB), whereas the specialized model performs best on RGBE-Gaze (MSE 0.0161, SSIM 0.7605, PSNR 19.08dB). These preliminary results suggest that controllable diffusion models are a promising approach for event-guided intensity-image reconstruction, while highlighting that the preferred learning strategy depends on the reconstruction domain.

Contemporary machine learning struggles to learn continually, reuse prior knowledge, and expose a comprehensible internal structure. A recently proposed developmental, gradient-free learning framework addresses these limitations by learning a discrete, topological model of its inputs through local variation and selection, yielding an inherent continual-learning guarantee: new observations refine existing structure without overwriting past knowledge, and without replay buffers or predefined task boundaries. Its extension to visual inputs demonstrated this principle on shape recognition, but relied on a feature representation of limited expressivity that capped recognition accuracy. We introduce a new visual feature representation that encodes shape structure across multiple scales, capturing edge and contour features together with their spatial relations, and integrate it with the network-refinement learning process; we further improve the learning dynamics and the read-out used to predict from the learned model. The study targets two-dimensional shape, with class-incremental MNIST as a controlled, interpretable benchmark in which continual-learning behavior can be measured directly. Our approach substantially increases accuracy over the prior representation, matching or exceeding replay- and regularisation-based baselines at comparable storage while storing no past data, and preserves the framework's defining behavior: earlier-learned classes are retained as new ones are introduced, with no destructive adaptation, and the learned representations remain human-interpretable. What separates the methods is retention: the baselines surrender most of a just-trained class within its own cycle and relearn it afterwards, which ours does not. The significance lies in the manner of learning. The system integrates information one sample at a time while provably preserving its responses to...

Optical scattering has conventionally been regarded as an impediment in imaging research due to the degradation of image quality during reconstruction. Nevertheless, this study explores two cases in which optical scattering may serve a beneficial role in image reconstruction tasks. We compared the No Scattering MNIST dataset with three Scattering MNIST datasets, each generated under distinct scattering conditions. To assess the information content of the resulting speckle patterns, we employed a Variational Autoencoder (VAE) approach which achieves accuracy comparable to state-of-the-art deep learning approaches, but has an interpretable latent space. We find that scattering can enhance data robustness against spatial pixel loss by effectively distributing information. We also demonstrate that scattering can enable distinctions of focal depth information. We anticipate that these findings will contribute to more efficient imaging techniques, particularly in the presence of obstacles and three-dimensional signals.

Common practice when training Convolutional Neural Networks (CNNs) is to use randomly shuffled mini-batches. This creates two limitations: slower convergence, and a diminishing learning signal, since many samples are quickly classified as easy during training. We address these inefficiencies with A*-Inspired Batch Selection (A*-BS), a lightweight, model-agnostic strategy that formulates mini-batch scheduling as a heuristic search problem. Each batch is treated as a node in a search space and ranked using an A*-like score combining a loss-based difficulty measure with a reuse penalty. This encourages informative gradient updates and batch diversity throughout training, without modifying network architectures or optimization algorithms, so it integrates seamlessly into existing pipelines. We evaluate A*-BS on the twelve 2D classification tasks of the MedMNIST-v2 benchmark, using a deliberately simple architecture of approximately 2.25x10^5 parameters, compared against the ResNet-18 and ResNet-50 baselines reported by the benchmark. On half of these tasks, the lightweight model with A*-BS reaches higher accuracy and AUC than both ResNet baselines, with relative gains of up to 15%. An ablation under identical architecture and hyperparameters shows A*-BS outperforms random batch shuffling on all twelve tasks. Wall-clock measurements further show the lightweight CNN with A*-BS trains substantially faster than ResNet-18 and ResNet-50 on identical hardware. These results indicate that intelligent batch ordering can partially compensate for reduced architectural complexity, offering a computationally efficient alternative to deeper models, with reliability reinforced by strong performance even against deeper, more sophisticated architectures.

We introduce a novel method for both partial and full optimization of the connections in deep differentiable logic gate networks (LGNs) and lookup table networks (LUTNs). Our training method utilizes a probability distribution over a set of connections per gate/lookup table (LUT) input pin, selecting the connection with highest merit, all whilst the optimal gate types or LUT-entries are learned in parallel. We show that the connection-optimized LGNs outperform standard fixed-connection LGNs on the Yin-Yang, MNIST Handwritten Digits and Fashion-MNIST benchmarks, while requiring only a fraction of the number of logic gates. We achieve 98.92% on the MNIST dataset with two layers of 8000 gates. With only one layer of 8000 gates, we obtain 98.45%, showing that our method requires almost 50 times fewer gates compared to fixed-connection LGNs. Training stability up to ten layers has been ensured by employing a high learning rate, straight-through estimators and trimming constant-output gate types. Additionally, we present a LUT neuron description that enables stable training with backpropagation, tested up to 6-layer deep networks. The model requires four times fewer trainable parameters and still achieves a higher accuracy compared to the fixed-connection LGN training algorithm. Our connection-training algorithm also works well for the LUTNs, achieving an accuracy of 98.88% for two layers of 2000 6-input LUTs.

Backpropagation (BP) dominates deep learning training, but its reliance on gradients brings inherent troubles -- vanishing and exploding gradients. The pursuit of gradient-free methods has long been a goal in the field of artificial intelligence. This paper shows that indeed the simplest Monte Carlo algorithm implemented on a single GPU -- randomly mutate a parameter, keep it if the loss decreases, otherwise retry -- can practically train deep networks. This gradient-free method does not even need common techniques such as batch normalization or residual connections to directly train sufficiently deep networks. More remarkably, its flexibility extends to several nontrivial scenarios: it enables pure pruning training, supports discrete weights, accommodates unconventional transfer functions such as Gaussian, and reveals the substantial redundancy of deep networks. We have demonstrated its feasibility on deep networks with more than 20 layers, single-hidden-layer wide networks with up to 16,384 hidden neurons, and even a simple Transformer architecture trained on both image classification (MNIST) and character-level language modeling (Tiny Shakespeare). This simple gradient-free method may offer a complementary perspective for understanding the self-organization and learning mechanisms of neural networks, and also provides an alternative route for building physically inspired deep learning systems.

We present a general neurosymbolic reasoning and learning methodology based on a modular integration of answer set programming with an energy based model substrate. Key contributions are: (1) supporting joint optimisation in the continuous latent space through explicit ASP-based declarative semantics fully incorporating background knowledge, constraints, non-monotonic inference; and (2) advancing recent works at the interface of answer sets, probabilistic logic, and answer set modulo theories by providing a generalised model and practical platform for ASP-centric robust, end-to-end training for applications in dynamic domains (e.g., involving perception and interaction). We provide a practical implementation, and demonstrate basic use and application (with MNIST), and evaluate with the visual question-answering benchmark Clevr and the multi-object tracking benchmark MOT.

This study investigates the presence and propagation of bias within Neural Networks through a comprehensive multi-level analysis spanning the learned latent space, layer activations, and the network's parameters. Based on this taxonomy, we propose three bias detection approaches: 1) SpaceBias (new method), which characterizes the latent space prior to the final classification layer using neighbor-probability distributions and quantifies bias with the two-sample Kolmogorov-Smirnov test on the per-group distributions. 2) ActivationBias (extension of the existing method InsideBias), which analyzes the activations of neural network filters and quantifies bias via a Mann-Whitney U test, based on the observed fact that underrepresented groups exhibit lower activation levels in the final convolutional layers. 3) WeightBias (extension of the existing method IFBiD), which uses a secondary neural network trained to identify biased patterns directly in the parameters of task-specific models. Unlike conventional methods, which assess neural network outcomes and treat the model as a black box, our proposed techniques provide insight into how biases manifest within the network architecture itself at different levels, offering a more nuanced and detailed understanding. Experiments are conducted on two complementary applications: gender classification in the DiveFace dataset (72,000 face images) and digit classification on a colored-MNIST benchmark with controlled bias severity. In total, more than 127,000 models with varying degrees and types of bias were trained and evaluated. The severity sweep shows that the internal disparity, and with it the detection performance, decreases smoothly as the training distribution approaches balance. The results highlight the importance of methods that provide deeper insight into the behavior of AI models.

Siamese verification networks are widely used to compare items such as faces, cars, or signatures. In these scenarios, the network is trained to learn an embedding space in which similar objects are mapped closer together, while dissimilar objects are mapped further apart. Two objects are considered to belong to the same class (e.g., the same person in two different images) when the distance between their embeddings falls below a predefined threshold. Defining this threshold, however, is a non-trivial task and typically requires labeled data. In this work, we assume that the distribution of distances produced by a siamese verification network can be approximated by a bimodal function. Based on this assumption, we propose an unsupervised method to determine the verification threshold by identifying the minimum point between the two modes. The proposed approach does not require annotated samples, enabling the verification threshold to be updated directly in the deployment environment without the cost of manual labeling. We evaluate our method on four datasets: MNIST, CIFAR-10, LFW, and PKLot. The results indicate that the proposed approach achieves an average verification accuracy of 94%, comparable to the Equal Error Rate method, while eliminating the need for labeled data.

Non-invasive brain-to-speech decoding aims to restore communication to patients suffering from neurodegenerative disease, without the risks of neurosurgery. Existing MEG- and EEG-based methods, while scalable, continue to suffer from high word error rates driven by relatively low signal-to-noise ratios compared to invasive recordings. We propose physiological noise augmentation (PNA), a data augmentation method that explicitly trains decoders to become invariant to task-agnostic artifacts (e.g. ocular and cardiac activity). PNA draws inspiration from automatic speech recognition systems, where environmental noise (e.g. dogs barking, city traffic) is added to clean speech to improve robustness. Analogously, we decompose brain recordings into clean data and noise artifacts using independent component analysis (ICA), before scaling and remixing to generate biophysically realistic, label-preserving training examples. We show that PNA approximates anisotropic regularization, penalizing decoder sensitivity along artifact-dominated directions. On MegNIST, a 12k-trial imagined-digit MEG dataset, PNA with 10-trial averaging improves EEGNet decoding accuracy by 4.7 percentage points (absolute) over training on real data alone. Our results suggest that artifact-aware augmentation and trial averaging are complementary tools for improving robustness in non-invasive speech BCIs.

Learning representations that remain robust across centuries of variation in handwriting is a key challenge in diachronic representation learning. Taking one of the longest continuously used writing systems, ancient Greek, as a case study, we introduce three datasets for diachronic representation learning: Hell-Char, a curated training set spanning the 3rd-1st centuries BCE, and two evaluation sets, PaLit-Char (2nd-5th c. CE) and Med-Char (9th-14th c. CE). To address the challenges of symbolic variation, scarce data, and systematic degradation, we propose: a similarity-weighted supervised contrastive loss that biases embeddings using dynamically estimated inter-class similarities, and a lacuna-driven augmentation scheme that simulates realistic manuscript corruptions. Trained with these strategies, both a lightweight CNN and a pretrained ResNet achieve strong recognition performance and produce embeddings that more coherently separate character classes than PCA or generic pretrained models. These embeddings enable clustering, identification of stylistic subgroups, and construction of prototype images that visualize diachronic evolution and transitional letterforms. Our results demonstrate that respecting intrinsic inter-letter relationships and augmenting with domain-informed corruptions yield robust, interpretable representations, offering a transferable paradigm for representation learning under scarce, temporally evolving, and noisy conditions. Code and data available at: https://github.com/ipavlopoulos/diachronic-greek-letterforms.

Training medical image classifiers on entire datasets is wasteful when annotation budgets are limited: not all samples contribute equally, yet acquiring expert labels is expensive. Active learning reduces annotation cost through iterative querying, but assumes repeated access to an oracle and requires multiple rounds of model training. One-shot geometry-based methods such as facility location avoid retraining but operate on pairwise distances that ignore the local structure of the data manifold. We propose a graph-based one-shot selection method that operates entirely on frozen foundation model embeddings. Given embeddings from a pretrained encoder, we construct a k-nearest neighbor graph over all training samples and derive a two-term coverage kernel from the heat diffusion kernel, capturing both direct and two-hop neighborhood relationships. Greedy facility location on this kernel selects class-balanced subsets that maximize coverage of the data manifold. The two-term kernel matches the full spectral heat kernel in selection behavior while reducing computation to sparse matrix operations with a single hyperparameter. We evaluate on five MedMNIST datasets spanning histopathology, radiology, and microscopy, comparing against both training-dynamics and geometry-based baselines. Our method achieves the highest balanced accuracy on nine of ten dataset-ratio conditions, with the largest gains on class-imbalanced datasets where global graph construction captures cross-class structure that per-class methods miss, all without any model training during selection. Code is available at https://github.com/zahiriddin-rustamov/graph-coverage-selection.

Programmability is a missing first-class interface in fixed-tensor neural networks: editing a relation, freezing a subgraph, auditing a local function, or changing the execution backend should be an operation on the neural program rather than ad-hoc parameter surgery. GrapNet studies this graph-as-network setting. The graph is the architecture and executable program, not an input data graph. Each compute node owns its next-layer child references and a trainable allocation vector aligned with those references; deleting a relation physically removes both the child reference and the corresponding allocation coordinate. Structural rules and execution policies live outside the node core, so the same child-owned graph can be grown, frozen, structurally edited, grouped into trainable family blocks, routed by attention over active relations, or lowered to dense snapshots after topology stabilizes. GrapNet composes with conventional modules through a vector-valued parent interface: dense layers, CNN encoders, ResNet feature extractors, attention blocks, and transformer representations can all feed one sensory GrapNode per coordinate. The evaluation is organized as a programmability stress suite rather than as a new replay benchmark. In a matched ten-seed Split Fashion-MNIST study, a plastic GrapNet+ER head reaches 63.16 percent seen-class accuracy versus 51.08 percent for a parameter-larger dense MLP+ER under the same seen-class loss and replay memory, with paired delta 12.08 points and p=1.3e-5. On Split CIFAR-10 with a frozen ImageNet ResNet-18 encoder, the same substrate improves the online head over MLP-256 by 3.81 points, with p=0.0026. These results support GrapNet as an editable neural graph substrate whose core value is structural programmability with faithful execution views.

A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $σ$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two $σ$-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Types, in the sense of homotopy type theory, preserve this information and turn the functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts. The payoff is concrete: the shortcut-aware concept posterior that recent methods reach by ensembling or expressive density estimation is the only symmetry-invariant point of the confusion-set simplex, computable in closed form by averaging a single model over the symmetry group. On MNIST reasoning-shortcut benchmarks this single-model wrapper is better calibrated than a diversity-trained ensemble, while leaving label accuracy and identifiable concepts untouched. Code is freely available at https://github.com/bio-ontology-research-group/hott-nesy.

Robust, high-fidelity 3D hand capture, while fundamental to digital human creation, remains challenging with practical multi-view systems that balance rich photometry with the geometric ambiguities of reconstruction arising from limited viewpoint density. This paper presents an end-to-end pipeline for dynamic hand performance capture and registration, specifically designed for view-efficient setups ($\sim$20 views). We address key challenges with two primary innovations. First, to overcome reconstruction difficulties like limited view overlap and background clutter, our mask-free neural method robustly extracts detailed hand geometry and appearance from unmasked images using scene parameterization and scenario-specific density regularization. Second, addressing registration challenges such as accurately capturing non-linear skin deformations and ensuring plausible results during severe self-contact, we propose a physics-inspired framework. It aligns reconstructions to a personalized hand model by optimizing intrinsic volumetric offsets within its canonical tetrahedral mesh, alongside pose parameters. This approach, supported by robust losses and optimization, captures fine surface deformations, ensures plausible results under severe articulation and self-contact, and demonstrates strong tolerance to input noise. We demonstrate the scalability and robustness of our automated pipeline on an extensive dataset of over 12,000 sequences, from which we also derive a large-scale, high-quality synthetic 2D/3D hand dataset for training downstream tasks. This showcases its effectiveness for single hands, intricate two-hand interactions, and natural hand-object manipulations. Our method achieves state-of-the-art reconstruction fidelity in view-efficient, unmasked scenarios and highly accurate registration. Our project page are available at https://vephand.github.io/.

Certified local robustness verification for recurrent neural networks (RNNs) is challenging because approximation errors introduced by nonlinear relaxations can propagate through recurrent connections and accumulate over time. As a result, scalable linear bound propagation methods often become overly conservative and fail to certify inputs that are in fact robust, especially when many pre-activation intervals cross zero. We propose an abstraction-refinement framework for RNN verification that partitions such intervals to remove the dominant relaxation error: on each refined branch, ReLU becomes exact, and smooth activations such as tanh and sigmoid admit substantially tighter linear envelopes. To control the combinatorial cost of splitting in long sequences, we introduce a SHAP-guided timestep selection strategy that ranks hidden states by their contribution to the verification objective and refines only the most critical timesteps in temporal order. Experiments on CIFAR10 and MNIST stroke benchmarks demonstrate consistent improvements in verification success and robustness-margin tightness over abstraction-only baselines, while exposing clear runtime trade-offs between ReLU and tanh models.

The automatic processing of handwritten forms remains a challenging task, wherein detection and subsequent classification of handwritten characters are essential steps. We describe a novel approach, in which both steps -- detection and classification -- are executed in one task through a deep neural network. Therefore, training data is not annotated by hand, but manufactured artificially from the underlying forms and yet existing datasets. It can be demonstrated that this single-task approach is superior in comparison to the state-of-the-art two-task approach. The current study focuses on hand-written Latin letters and employs the EMNIST data set. However, limitations were identified with this data set, necessitating further customization. Finally, an overall recognition rate of 88.28 percent was attained on real data obtained from a written exam.

Can neural networks learn abstract algebraic rules, or do they merely memorize training patterns? We investigate this using MNIST digits as states and modular arithmetic operations as actions in a JEPA-style latent world model. Standard supervised baselines and JEPA models with additive operation embeddings fit seen operations but fail to extrapolate reliably to unseen ones. To bridge this gap, we introduce a block-rotation predictor that imposes the circular structure of modulo-10 arithmetic in latent space. This enables strong zero-shot generalization, with the best ResNet-based JEPA block-rotation model achieving 99.46% zero-shot and 99.46% rollout accuracy. Our results suggest that latent world models can learn symbolic transformation rules when architecture matches the structure of the problem. Our code can be \href{https://github.com/DL-World-Models/mnist-math}{accessed here}.

Deep networks are powerful function approximators, but they typically store many different computations in shared weight matrices, making it difficult to selectively reuse or adapt parts of them when a familiar structure appears in novel combinations. We introduce the Vector Network (VN), a hierarchical recurrent architecture in which each layer replaces a fixed weight matrix with a library of reusable rank-1 weight atoms. For each input, VN minimizes a layer-local energy to infer a sparse set of active weight atoms and their coefficients, jointly constrained by bottom-up input reconstruction and top-down feedback consistency. These weight atom coefficients then compose an input-specific low-rank weight matrix for that sample. After convergence, slow learning updates only the selected weight atoms through local residual signals scaled by the inferred coefficients. We evaluate VN on four compositional benchmarks spanning 1D signals, 2D spatial decoding, N-body dynamics, and compositional MNIST. VN matches strong baselines in distribution while often achieving out-of-distribution error about an order of magnitude lower when familiar factors must be recombined in novel ways. Vector networks thus make compositional generalization a structural property of the architecture and inference process rather than a brittle byproduct of fitting many behaviors into one shared dense parameter substrate.

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94% fewer parameters and $\sim$ 75% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.

The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance allows flexible exploration of latent configurations, enabling embeddings that best match observed dissimilarities. The Gini MDS is shown to be robust to noise and outliers, making it well-suited for real-world applications. We provide experiments on 16 UCI datasets with outliers and on MNIST images with noise to show that the Gini MDS outperforms the Euclidean MDS on noisy data. Finally, a tensor-based implementation in \texttt{PyTorch} provides GPU acceleration and efficient computation compared to the standard MDS of the \texttt{sklearn} library.

Diabetic Retinopathy (DR) is a common complication of diabetes that can lead to blindness of people. Detecting DR at the earliest stage is essential to prevent irreversible eye damage. Microaneurysm dots are the first signs of DR. As the dots are tiny and of low contrast, detecting mild DR is a very challenging task. Federated learning (FL) preserves data privacy, which is a major concern for medical image processing. FL is a collaborative learning method, which shares only the model parameters with a server, without sharing the patient data to a central server. Inspired by classical FL, we propose a federated learning-based quantum neural network (federated QNN) for this task. We implemented the models with limited samples and few learnable parameters from the E-ophtha and Retina MNIST datasets. The crossevaluation efficiency of the proposed federated quantum neural network system for privacy-preserving early detection of diabetic retinopathy (FQPDR) in Kaggle dataset images indicates the robustness of the light weight learning models. FQPDR performances are inspiring while considering existing non-FL and FL methods.

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models typically transition from an initial phase of generalization to memorizing the training set, existing theory assumes homogeneous data, leaving open how class imbalance and heterogeneity reshape these dynamics. In this work, we develop a high-dimensional analytical framework to study class-dependent learning in score-based diffusion models. Analyzing a random-features model trained on Gaussian mixtures, we derive the feature-covariance spectrum to characterize per-class generalization and memorization times. We reveal the explicit hierarchy governing these dynamics: class variance is the primary determinant of learning order-consistently favoring higher-variance classes-while centroid geometry plays a secondary role. Sampling imbalance acts as a modulator that can reverse this ordering and, under strong imbalance, forces minority classes to acquire distinct, delayed speciation times during backward diffusion. Together, these results suggest that diffusion models can memorize some classes while others remain insufficiently learned. We validate our theoretical predictions empirically using U-Net models trained on Fashion MNIST.

Resource-efficient machine learning increasingly uses sparse Mixture-of-Experts (MoE) architectures, where the gate acts as both a learning component and a routing interface controlling computation, communication, and accuracy. Motivated by finite-rate interpretations of MoE gating, we treat the gate as a stochastic channel and use $I(X;T)$ to quantify the routing information available to the selected expert. To make the associated information quantities tractable beyond synthetic examples, we develop a finite-bank MNIST construction using pretrained CNN experts and a discrete, data-dependent selection rule. Since the selected model belongs to a finite candidate set, the algorithmic mutual information $I(S;W)$ admits a closed-form discrete-entropy estimator from the empirical posterior $q(W|S)$. Sweeping a data-dependence parameter $α$, we observe that $\widehat I(S;W)$ monotonically tracks the generalization gap, while the Xu-Raginsky bound exhibits the expected looseness. We also compare with a uniform union-bound baseline and introduce an empirical estimator of $I(X;T)$ together with a Blahut-Arimoto procedure for tracing an accuracy-rate curve over the expert bank. The proposed framework provides a practical tool for analyzing resource-aware MoE inference systems and for interpreting $I(X;T)$ and $D(R_g)$ as design proxies for efficient expert routing.

There has been growing interest in studying the complexity of Rectified Linear Unit (ReLU) based activation networks. Recent work investigates the evolution of the number of piecewise-linear partitions (linear regions) that are formed during training. However, current research is limited to examining the complexity of models trained in a supervised way. Self-Supervised Learning (SSL) differs in that it directly optimises the representation space using a loss function to enhance the model's performance across multiple downstream tasks. This study investigates the local distribution of linear regions produced by SSL models. We demonstrate that the evolution of linear regions correlates with the representation quality by utilising SplineCam to extract two-dimensional polytopes near the data distribution. We track the number, area, eccentricity, and boundaries of regions throughout training. The study compares supervised, contrastive, and self-distillation methods over two standard benchmark datasets, MNIST and FashionMNIST. The analysis of the experimental results shows that self-supervised methods create substantially fewer regions to achieve comparable accuracy to supervised models. Contrastive methods rapidly expand regions over time, whereas self-distillation methods tend to consolidate by merging neighbouring regions. Lastly, we can detect representation collapse early within the geometric space of linear regions. Our analysis suggests that polytopal metrics can serve as reliable indicators of representation quality and model performance.

We study whether deep networks for medical imaging learn useful nonrobust features - predictive input patterns that are not human interpretable and highly susceptible to small adversarial perturbations - and how these features impact test performance. We show that models trained only on nonrobust features achieve well above chance accuracy across five MedMNIST classification tasks, confirming their predictive value in-distribution. Conversely, adversarially trained models that primarily rely on robust features sacrifice in-distribution accuracy but yield markedly better performance under controlled distribution shifts (MedMNIST-C). Overall, nonrobust features boost standard accuracy yet degrade out-of-distribution performance, revealing a practical robustness-accuracy trade-off in medical imaging classification tasks that should be tailored to the requirements of the deployment setting.

Reservoir computing (RC) is an emerging recurrent neural network architecture that has attracted growing attention for its low training cost and modest hardware requirements. Memristor-based circuits are particularly promising for RC, as their intrinsic dynamics can reduce network size and parameter overhead in tasks such as time-series prediction and image recognition. Although RC has been demonstrated with several memristive devices, a comprehensive evaluation of device-level requirements remains limited. In this paper, we analyze and explain the operation of a parallel delayed feedback network (PDFN) RC architecture with volatile memristors, focusing on how device characteristics -- such as decay rate, quantization, and variability -- affect reservoir performance. We further discuss strategies to improve data representation in the reservoir using preprocessing methods and suggest potential improvements. The proposed approach achieves 95.89% classification accuracy on MNIST, comparable with the best reported memristor-based RC implementations. Furthermore, the method maintains high robustness under 20% device variability, achieving an accuracy of up to 94.2%. These results demonstrate that volatile memristors can support reliable spatio-temporal information processing and reinforce their potential as key building blocks for compact, high-speed, and energy-efficient neuromorphic computing systems.

In this paper, we introduce a new concept called Artificial Special Intelligence by which Machine Learning models for the classification problem can be trained error-free, thus acquiring the capability of not making repeated mistakes. The method is applied to 18 MedMNIST biomedical datasets. Except for three datasets, which suffer from the double-labeling problem, all are trained to perfection.

In large-scale distributed scenarios, increasingly complex tasks demand more intelligent collaboration across networks, requiring the joint extraction of structural representations from data samples. However, conventional task-specific approaches often result in nonstructural embeddings, leading to collapsed variability among data samples within the same class, particularly in classification tasks. To address this issue and fully leverage the intrinsic structure of data for downstream applications, we propose a novel distributed learning framework that ensures both diverse and discriminative representations. For independent and identically distributed (i.i.d.) data, we reformulate and decouple the global optimization function by introducing constraints on representation variance. The update rules are then derived and simplified using a primal-dual approach. For non-i.i.d. data distributions, we tackle the problem by clustering and virtually replicating nodes, allowing model updates within each cluster using block coordinate descent. In both cases, the resulting optimal solutions are theoretically proven to maintain discriminative and diverse properties, with a guaranteed convergence for i.i.d. conditions. Additionally, semantic information from representations is shared among nodes, reducing the need for common neural network architectures. Finally, extensive simulations on MNIST, CIFAR-10 and CIFAR-100 confirm the effectiveness of the proposed algorithms in capturing global structural representations.

Handwritten mathematical expression recognition (HMER) requires reasoning over diverse symbols and structures, yet autoregressive models struggle with exposure bias and syntax inconsistency. We present GryphOne, a discrete diffusion framework which reformulates HMER as iterative symbolic refinement instead of sequential generation. GryphOne progressively refines symbols and relations, removing autoregression and improving consistency. Symbol-aware tokenization and random-masking mutual learning further enhance robustness to handwriting diversity. On the MathWriting benchmark, GryphOne achieves 5.51% CER and 59.9% EM (ExpRate), outperforming all reimplemented models in the matched setting as well as the commercial HMER system. Held-out evaluation on CROHME 2014-2023 further shows strong cross-dataset generalization.

Approximate nearest-neighbor search (ANNS) algorithms have become increasingly critical for recent AI applications, particularly in retrieval-augmented generation (RAG) and agent-based LLM applications. In this paper, we present CRINN, a new paradigm for ANNS algorithms. CRINN treats ANNS optimization as a reinforcement learning problem where execution speed serves as the reward signal. This approach enables the automatic generation of progressively faster ANNS implementations while maintaining accuracy constraints. Our experimental evaluation demonstrates CRINN's effectiveness across six widely-used NNS benchmark datasets. When compared against state-of-the-art open-source ANNS algorithms, CRINN achieves best performance on three of them (GIST-960-Euclidean, MNIST-784-Euclidean, and GloVe-25-angular), and tied for first place on two of them (SIFT-128-Euclidean and GloVe-25-angular). The implications of CRINN's success reach well beyond ANNS optimization: It validates that LLMs augmented with reinforcement learning can function as an effective tool for automating sophisticated algorithmic optimizations that demand specialized knowledge and labor-intensive manual refinement. Code can be found at https://github.com/deepreinforce-ai/CRINN

Background: Federated learning (FL) enables collaborative training of clinical AI models without centralizing patient data, but adoption is limited by privacy concerns, heterogeneous institutional compliance, and resource disparities; standard differential privacy (DP) applies uniform noise to all clients, penalizing well-compliant or under-resourced institutions. Objective: We introduce a compliance-aware FL framework that adapts DP to institutional compliance, letting lower-compliance sites participate without uniformly penalizing others. Methods: A compliance scoring tool aligned with HIPAA, GDPR, NIST, ISO, and HL7/FHIR maps each client score to a per-step Gaussian noise scale for server-side DP-SGD on a small aggregator dataset. The formal $(ε,δ)$ bound applies to the aggregator dataset under a semi-honest aggregator; client-level DP needs secure aggregation (future work). We evaluate five FL strategies on PneumoniaMNIST and BreastMNIST (16 clients, 50 rounds, five seeds); the cumulative aggregator-dataset $ε$ is about 1434 (Breast) and 513 (Pneumonia) at $δ=10^{-5}$. Results: Including 12 lower-compliance clients (Experiment 1) versus a compliant-only baseline (Experiment 4) changed BreastMNIST accuracy by +4.5 (FedAvg), +6.8 (FedMedian), +5.2 (FedProx), +1.6 (FedYogi), and -4.1 (FedAdam) percentage points (pooled +2.8 pp; not significant at n=5; up to +17 pp per configuration); compliance-weighted allocation matched uniform server-side DP at equal mean noise (+0.1 pp), carrying no utility penalty, and first-round noise cost 1.3 pp (Breast) and 2.5 pp (Pneumonia, FedAvg). Conclusions: Compliance-weighted server-side DP lets lower-compliance institutions join FL without degrading performance, giving auditable per-site noise control at no utility cost; formal guarantees apply to the aggregator dataset, with client-level DP requiring secure aggregation.

We present a demonstration of image classification using an extreme learning machine (ELM) based on a unique simulated magnetic tunnel junction (MTJ) delayed in time. As the ground state of the MTJ is a magnetic vortex, we refer to it as a vortex-based spin-torque oscillator (STVO). The dynamics of the magnetic vortex is simulated with a model called the data-driven Thiele equation approach (DD-TEA). This allows to avoid the constraints associated with repeated experimental manipulation for hyperparameters search and benchmarking. We showcase the versatility of our implementation by using it successfully for classification tasks on the MNIST, EMNIST-letters and Fashion MNIST datasets. Through simulations, we show that within an ELM with a sufficient number of parameters, the performance reached using the STVO dynamics as a source of nonlinearity is equivalent to the ones obtained with classical software activation functions such as the reLU and the sigmoid. While achieving state-of-the-art accuracy levels on the MNIST dataset, our model's performance on EMNIST-letters and Fashion MNIST is lower due to the simplicity of the network architecture and the increased complexity of the data. We expect that the DD-TEA framework will enable the exploration of deeper and more complex STVO-based architectures, ultimately leading to improved classification accuracy.

Neuroevolution of Augmenting Topologies (NEAT) and its advanced version, Evolvable-Substrate HyperNEAT (ES-HyperNEAT), have shown great potential in developing neural networks. However, their effectiveness heavily depends on the selection of hyperparameters. This study investigates the optimization of ES-HyperNEAT hyperparameters using the Tree-structured Parzen Estimator (TPE) on the MNIST classification task, exploring a search space of over 3 billion potential combinations. TPE effectively navigates this vast space, significantly outperforming random search in terms of mean, median, and best accuracy. During the validation process, the best hyperparameter configuration found by TPE achieves an accuracy of 29.00% on MNIST, surpassing previous studies while using a smaller population size and fewer generations. The transferability of the optimized hyperparameters is explored in logic operations and Fashion-MNIST tasks, revealing successful transfer to the more complex Fashion-MNIST problem but limited to simpler logic operations. This study emphasizes a method to unlock the full potential of neuroevolutionary algorithms and provides insights into the hyperparameters' transferability across tasks of varying complexity.