Accurately differentiating between what are truly unpredictably random and systematic changes that occur at random can have profound effect on affect and cognition. To examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels. Both R-W model and the Bayesian approach reflected an individual's estimation of the environmental volatility, and there is a strong correlation between the learning rate in R-W model and the belief of stationarity in the Bayesian approach in different volatility conditions. In a low volatility condition, R-W model indicates that learning rate positively correlates with lose-shift rate, but not choice optimality (inverted U shape). The Bayesian approach indicates that the belief of environmental stationarity positively correlates with choice optimality, but not lose-shift rate (inverted U shape). In addition, we showed that comparing to Expert learners, individuals with high lose-shift rate (sub-optimal learners) had significantly higher learning rate estimated from R-W model and lower belief of stationarity from the Bayesian model.

Neural Information Processing Systems http://nips.cc/

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither allow connections that are not dyadic nor permit relationships between sets of nodes. We thus turn to simplicial complexes for connecting more than two nodes as well as modeling relationships between simplices, such as edges and triangles. Our data then consist of signals lying on topological spaces, represented by simplicial complexes. Much recent work explores these topological signals, albeit primarily through deterministic formulations. We propose a probabilistic framework for random signals defined on simplicial complexes. Specifically, we generalize the classical notion of stationarity. By spectral dualities of Hodge and Dirac theory, we define stationary topological signals as the outputs of topological filters given white noise. This definition naturally extends desirable properties of stationarity that hold for both time-series and graph signals. Crucially, we properly define topological power spectral density (PSD) through a clear spectral characterization. We then discuss the advantages of topological stationarity due to spectral properties via the PSD. In addition, we empirically demonstrate the practicality of these benefits through multiple synthetic and real-world simulations.

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels.

Accurate electricity forecasting is crucial for grid stability and energy planning, especially in Benghazi, Libya, where frequent load shedding, generation deficits, and infrastructure limitations persist. This study proposes a data-driven approach to forecast electricity load, generation, and deficits for 2025 using historical data from 2019 (a year marked by instability) and 2023 (a more stable year). Multiple time series models were applied, including ARIMA, seasonal ARIMA, dynamic regression ARIMA, exponential smoothing, extreme gradient boosting, and Long Short-Term Memory (LSTM) neural networks. The dataset was enhanced through missing value imputation, outlier smoothing, and log transformation. Performance was assessed using mean squared error, root mean squared error, mean absolute error, and mean absolute percentage error. LSTM outperformed all other models, showing strong capabilities in modeling non-stationary and seasonal patterns. A key contribution of this work is an optimized LSTM framework that integrates exogenous factors such as temperature and humidity, offering robust performance in forecasting multiple electricity indicators. These results provide practical insights for policymakers and grid operators to enable proactive load management and resource planning in data-scarce, volatile regions.

Hebbian and anti-Hebbian plasticity are widely observed in the biological brain, yet their theoretical understanding remains limited. In this work, we find that when a learning method is regularized with L2 weight decay, its learning signal will gradually align with the direction of the Hebbian learning signal as it approaches stationarity. This Hebbian-like behavior is not unique to SGD: almost any learning rule, including random ones, can exhibit the same signature long before learning has ceased. We also provide a theoretical explanation for anti-Hebbian plasticity in regression tasks, demonstrating how it can arise naturally from gradient or input noise, and offering a potential reason for the observed anti-Hebbian effects in the brain. Certainly, our proposed mechanisms do not rule out any conventionally established forms of Hebbian plasticity and could coexist with them extensively in the brain. A key insight for neurophysiology is the need to develop ways to experimentally distinguish these two types of Hebbian observations.

Accurately differentiating between what are truly unpredictably random and systematic changes that occur at random can have profound effect on affect and cognition. To examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels. Both R-W model and the Bayesian approach reflected an individual's estimation of the environmental volatility, and there is a strong correlation between the learning rate in R-W model and the belief of stationarity in the Bayesian approach in different volatility conditions. In a low volatility condition, R-W model indicates that learning rate positively correlates with lose-shift rate, but not choice optimality (inverted U shape). The Bayesian approach indicates that the belief of environmental stationarity positively correlates with choice optimality, but not lose-shift rate (inverted U shape). In addition, we showed that comparing to Expert learners, individuals with high lose-shift rate (sub-optimal learners) had significantly higher learning rate estimated from R-W model and lower belief of stationarity from the Bayesian model.

R-W model and the Bayesian approach reflected an individual's estimation of the