Recent advances in Multimodal Large Language Models (MLLMs) have enabled joint reasoning over financial textual and visual inputs. However, they still struggle with financial terminology, logical consistency, and numerical computations. Moreover, while commercial large models perform well on reasoning tasks, their high inference costs limit their scalable usage in real world financial applications. We thus propose a cost-effective framework, CLER, that combines contrastive retrieval with step-wise reflection to improve reasoning performance. Also, the reasoning cost is only generated in the test stage when using commercial large models. CLER leverages FinErrorSet, a dataset of 8,000+ mistake correction pairs from diverse open-source MLLMs. A fine grained retriever is trained to identify structurally relevant errors for self-correction through individual reflection. Experiments on three benchmarks show that CLER consistently outperforms other baselines. To our knowledge, CLER is the first framework to use cross-model errors for financial reasoning.

In this paper, we propose Graph Retention Networks (GRNs) as a unified architecture for deep learning on dynamic graphs. The GRN extends the concept of retention into dynamic graph data as graph retention, equipping the model with three key computational paradigms: parallelizable training, low-cost $\mathcal{O}(1)$ inference, and long-term chunkwise training. This architecture achieves an optimal balance between efficiency, effectiveness, and scalability. Extensive experiments on benchmark datasets demonstrate its strong performance in both edge-level prediction and node-level classification tasks with significantly reduced training latency, lower GPU memory overhead, and improved inference throughput by up to 86.7x compared to SOTA baselines. The proposed GRN architecture achieves competitive performance across diverse dynamic graph benchmarks, demonstrating its adaptability to a wide range of tasks.

Hierarchical time series forecasting in retail requires forecasts that are both accurate and aggregation coherent across multiple levels. Most existing methods follow a two-stage pipeline that first generates base forecasts and then reconciles them, which limits the exploitation of hierarchical structure in learning. We propose an end-to-end graph-based neural reconciliation framework that jointly models hierarchy-aware dependencies, temporal dynamics, and coherent forecasting within a single differentiable architecture. The framework combines graph neural networks and gated recurrent units with an explicit bottom-up reconciliation module that guarantees exact aggregation consistency. We evaluate the framework on two retail datasets, Italian and Walmart, under both without-promotion and with-promotion settings. The strongest variants, TGLP-BUN (Temporal Graph Linear Projection with Bottom-Up Nonlinear reconciliation) and TALP-BUN (Temporal Attention Linear Projection with Bottom-Up Nonlinear reconciliation), achieve the strongest overall performance against strong statistical and end-to-end deep-learning baselines. The gains are concentrated at higher levels on the sparse Italian hierarchy and are more broadly distributed across the Walmart hierarchy, especially when promotional information is included. Node-wise error distributions and Diebold–Mariano tests further show that these improvements are systematic across series rather than driven by only a small subset of nodes.

Theoretical advances of the last decade have led to novel methodologies for probability density estimation by irregular histograms and penalized maximum likelihood. Here we consider two of them: the first one is based on the idea of minimizing the excess risk, while the second one employs the concept of the normalized maximum likelihood (NML). Apparently, the previous literature does not contain any comparison of the two approaches. To fill the gap, we provide in this paper theoretical and empirical results for clarifying the relationship between the two methodologies. Additionally, we introduce a new variant of the NML histogram. For the sake of completeness, we consider also a more advanced NML-based method that uses the measurements to approximate the unknown density by a mixture of densities selected from a predefined family.

In a recent series of papers, it was shown how the periodogram can be smoothed by thresholding the estimated cepstral coefficients either with a carefully designed uniformly most powerful unbiased test (UMPUT), or with the Bayesian information criterion (BIC). In this paper, we devise a fully automatic scheme that selects the threshold by using the Kolmogorov structure function (KSF). For the numerical examples taken from the previous literature, the newly proposed method compares favorably with the existing schemes.

Epilepsy is one of the most common brain disorders and may result in brain dysfunction and cognitive disturbances. Epileptic seizures usually begin in childhood without being accommodated by brain damage and are tolerated by drugs that produce no brain dysfunction. In this study, cognitive function is evaluated in children with mild epileptic seizures controlled with common antiepileptic drugs. Under this prism, we propose a concise technical framework of combining and validating both linear and nonlinear methods to efficiently evaluate (in terms of synchronization) neurophysiological activity during a visual cognitive task consisting of fractal pattern observation. We investigate six measures of quantifying synchronous oscillatory activity based on different underlying assumptions. These measures include the coherence computed with the traditional formula and an alternative evaluation of it that relies on autoregressive models, an information theoretic measure known as minimum description length, a robust phase coupling measure known as phase-locking value, a reliable way of assessing generalized synchronization in state-space and an unbiased alternative called synchronization likelihood. Assessment is performed in three stages; initially, the nonlinear methods are validated on coupled nonlinear oscillators under increasing noise interference; second, surrogate data testing is performed to assess the possible nonlinear channel interdependencies of the acquired EEGs by comparing the synchronization indexes under the null hypothesis of stationary, linear dynamics; and finally, synchronization on the actual data is measured. The results on the actual data suggest that there is a significant difference between normal controls and epileptics, mostly apparent in occipital-parietal lobes during fractal observation tests.

Relying on optimally distinguishable distributions (ODD), it was defined very recently a new framework for the composite hypothesis testing. We resort to the linear model to investigate the performances of the ODD detector and to compare it with the widely used generalized likelihood ratio test (GLRT). As the ODD concept is very new, its application to models with nuisance parameters was not discussed in the previous literature. The present study attempts to fill the gap by proposing a modified ODD criterion to accommodate the practical case of unknown noise variance.

During recent years the advances in stochastic complexity (SC) have led to new exact formulae or to sharper approximations for large classes of models. We focus on the use of the SC to estimate the structure for the model of sine-waves in Gaussian autoregressive noise. Since the evaluation of SC relies on the determinant of the Fisher information matrix (FEM), the computation of FIM is revisited. It is shown for small and moderate sample sizes that SC compares favorably with other well-known criteria such as: BIC, KICc and GAIC.

The paper is focused on the problem of discrete universal denoising: one estimates the input sequence to a discrete channel based on the observation of the entire output signal, and without assuming any particular knowledge on the statistical properties of the input sequence. A 2k + 1 sliding window denoiser (DUDE) has recently been introduced, and its asymptotic optimality was proven in the case of memoryless channels and additive channels with memory. However, DUDE is computationally infeasible for large values of its context parameter k. The purpose of this paper is to further investigate DUDE in the case of channels with memory. First, for the important family of binary additive channels, we propose H-DUDE, a computationally feasible implementation of DUDE. It modifies the DUDE algorithm to exploit the property of the block transition probability matrix to be diagonalized by the Hadamard transform. H-DUDE accommodates large values of k, and we demonstrate this for the particular case of the finite-memory contagion channel. Second, we apply DUDE for a non-additive channel model that was previously used in the design of stack filters to show its favorable performance

We propose the application of a new transform-based coding method in conjunction with Golomb-Rice (G-R) codes to lower significantly the complexity, which can be used in various applications, e.g. the multiple description coding. The theoretical evaluations predict no important loss in compression performance, while the complexity is considerably reduced. Since GR codes are very fast and well suited for exponentially decaying distributions, they were implemented during the last decade in image and audio compressors. In all these schemes, the selection of the code parameter is performed presuming Laplacian distribution of prediction errors. We derive the selection method for the GR code parameter also for the case of Gaussian inputs.