Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
WSD schedule improves model training efficiency by adapting learning rates dynamically.
problem Fixed compute budgets limit training efficiency of language models.
method Introduces a WSD schedule that uses a constant learning rate followed by a rapid decay phase.
result WSD schedule generates a non-traditional loss curve with stable and decay phases.
New framework reveals thermodynamic principles for LLM training.
problem Understanding the training dynamics of large language models.
method Introducing Neural Thermodynamic Laws (NTL) under river-valley loss landscape assumptions.
result Key thermodynamic quantities and principles naturally emerge in LLM training.
Quantization-aware training can recover accuracy lost by post-training quantization.
problem Post-training quantization (PTQ) can fail sharply at aggressive bitwidths.
method A unified geometric framework that explains PTQ failure and QAT recovery.
result QAT has a useful bias that steers iterates back into the basin.
This paper explores loss landscapes of sparse neural networks, finding unique characteristics compared to dense networks.
problem Understanding the loss landscape of sparse neural networks, especially one-hidden-layer networks.
method Analyzes sparse networks with dense and sparse final layers, focusing on linear and non-linear models.
result Sparse networks can have no spurious valleys under certain conditions, but spurious valleys and minima can exist for wide sparse networks.
We identify a class of over-parameterized deep neural networks with standard activation functions and cross-entropy loss which provably have no bad local valley, in the sense that from any point in parameter space there exists a continuous path on which the cross-entropy loss is non-increasing and gets arbitrarily clos…
Tilting loss functions improves machine learning performance.
problem Improving machine learning models, especially in under- and over-parameterized networks.
method Using evolving loss functions that emphasize different classes cyclically.
result Dynamical loss functions lead to better generalization and stability in training.
Neural networks provide a rich class of high-dimensional, non-convex optimization problems. Despite their non-convexity, gradient-descent methods often successfully optimize these models. This has motivated a recent spur in research attempting to characterize properties of their loss surface that may explain such succe…
This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenval…
We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning rate and batch-size in DNN optimization and generalization. Specifically we study…
Adaptor 'E' extends gradient-based optimizers to explore loss landscapes, improving generalization.
problem Finding lower and better-generalizing minima in deep learning.
method Proposes an adaptor 'E' to extend gradient-based optimizers, encouraging exploration along landscape valleys.
result Adapted optimizers increase test accuracy by an average of 2.5% in large-batch training tasks.
Study identifies new stable climate states in climate model.
problem Understanding multistability and transitions in climate models.
method Combination of quasipotential theory and manifold learning.
result Discovery of a third stable climate state not previously known.
Study the landscape of Lipschitz functions between manifolds using persistent homology.
problem Understanding the structure of homotopy paths between maps with high Lipschitz constants.
method Using persistent homology to analyze the landscape of Lipschitz functions between manifolds.
result First results on the persistence of higher-dimensional cycles in function spaces.
Large SGD step sizes lead to sparse feature learning in neural networks.
problem Sparse feature learning in neural networks with large step sizes.
method Empirical observations and theoretical analysis of SGD dynamics.
result Large step sizes induce implicit regularization leading to sparse predictors.
Paper presents a GAN model for realistic river image synthesis.
problem Generating high-quality river images for hydrological research.
method Used a Progressive Growing GAN (PGGAN) architecture to overcome training challenges.
result Demonstrated the effectiveness of GANs in generating high-resolution river images.
Artificial Neural Network (ANN) based model is a computational approach commonly used for modeling the complex relationships between input and output parameters. Prediction of the flow rate of a river is a requisite for any successful water resource management and river basin planning. In the current survey, the effect…
Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…
We solve the optimization of two-layer ReLU networks using convex math.
problem Optimizing two-layer ReLU neural networks.
method Exact characterization of optimal solutions via convex optimization.
result We prove that all globally optimal solutions can be found via convex optimization.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
HydroNets use river structure to improve hydrologic predictions.
problem Scalable and accurate hydrologic models are needed for climate change impacts.
method HydroNets are deep neural networks that incorporate river network structure.
result HydroNets improve predictions with fewer data, especially at longer horizons.
New method SF-AdamW trains large models without decay phases or memory overhead.
problem Inadequate fixed compute budgets for large-scale training.
method Schedule-Free (SF) method revisited and refined.
result SF-AdamW effectively navigates loss landscape without decay phases or memory overhead.
We study the phenomenon that some modules of deep neural networks (DNNs) are more critical than others. Meaning that rewinding their parameter values back to initialization, while keeping other modules fixed at the trained parameters, results in a large drop in the network's performance. Our analysis reveals interestin…
Online algorithms for identifying river pollution sources.
problem Real-time estimation of river pollution sources from downstream data.
method Gradient-based online learning algorithms with adaptive step sizes and escaping from saddle points module.
result High estimation accuracy in three dimensions, superior to existing methods.
Deep learning improves probabilistic river discharge forecasting for hydroelectric power.
problem Uncertain river discharges due to climate variability.
method Modified recurrent neural network architecture conditioned on global circulation model projections.
result Generates parameterized probability distributions for realistic long-term discharge scenarios.
We consider remodeling the planar search patterns, in the presence of the river-type perturbation represented by the weak vector field, basing on the time-optimal paths as Finslerian solutions to the Zermelo navigation problem via Randers metric.
Study uses AUVs and RL to map river plumes over multiple days.
problem Long-term mapping of dynamic river plumes with multiple AUVs.
method Multi-agent reinforcement learning with spatiotemporal GPR.
result Multi-agent approach outperforms single-agent and benchmarks.
Modeling daily river flow distribution with seasonal and long-term trends.
problem Capturing both seasonal and gradual long-term changes in environmental variables.
method Distributional regression using GAMLSS framework to estimate daily distribution of river flows.
result Model successfully captures seasonal variation and long-term trends in river flow data.
Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to solutions that generalize well. Here we show that for overparameterized networks wit…
New algorithm ATENT improves adversarial robustness in neural networks.
problem Improving neural network robustness against adversarial attacks.
method Proposes a new loss function with entropic regularization for training robust neural networks.
result ATENT achieves competitive robust classification accuracy on benchmark datasets.
Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is to learn a policy that is able to optimize over classes of functions that are fa…
This paper shows that every sublevel set of the loss function of a class of deep over-parameterized neural nets with piecewise linear activation functions is connected and unbounded. This implies that the loss has no bad local valleys and all of its global minima are connected within a unique and potentially very large…
Despite the non-convex nature of their loss functions, deep neural networks are known to generalize well when optimized with stochastic gradient descent (SGD). Recent work conjectures that SGD with proper configuration is able to find wide and flat local minima, which have been proposed to be associated with good gener…
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
problem Challenges in estimating epistemic uncertainty in LoRA-based Bayesian inference.
method Introduces LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with free and anchored configurations.
result Empirically shows that connecting independent LoRA optima through continuous low-loss valleys improves mutual information of the predictive distribution.
A new pruning method reduces neural network computation without retraining.
problem Efficiently reduce neural network computation while maintaining accuracy.
method Structured directional pruning via perturbation orthogonal projection.
result Achieves state-of-the-art pruned accuracy without retraining.
A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a Restricted Boltzmann Machine (RBM). A handwritten digit OptDigits data set having 8x7 pixels of visible units was used to train the RBM using a classical Contrastive Divergence. E…
A new Kolmogorov-Arnold network improves function approximation and optimization.
problem Approximating potentially irregular functions in high dimensions.
method Proposes a new Kolmogorov-Arnold network (KAN) and provides error bounds and universal approximation theorems.
result Outperforms multilayer perceptrons in accuracy and convergence speed for irregular functions.
The study analyzes river water quality using statistical and machine learning methods.
problem Analyzing spatio-temporal dynamics of dissolved oxygen in the River Thames.
method Superstatistical methods and machine learning (e.g., Light Gradient Boosting Machine, Informer model).
result The Informer model outperforms others in long-term dissolved oxygen concentration forecasting.
A common difficulty in applications of machine learning is the lack of any general principle for guiding the choices of key parameters of the underlying neural network. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear…
This paper examines SVB's failure and its impact on bank stocks.
problem SVB failure and its contagion effects on bank stocks.
method Analyzed bank-specific vulnerabilities and stock performance.
result Uninsured deposits and unrealized losses were key factors in SVB's impact.
Delivering useful hydrological forecasts is critical for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among others. In this work, we present and appraise a new simple and flexible methodology…
Flooding is a destructive and dangerous hazard and climate change appears to be increasing the frequency of catastrophic flooding events around the world. Physics-based flood models are costly to calibrate and are rarely generalizable across different river basins, as model outputs are sensitive to site-specific parame…
Learning hydrologic models for accurate riverine flood prediction at scale is a challenge of great importance. One of the key difficulties is the need to rely on in-situ river discharge measurements, which can be quite scarce and unreliable, particularly in regions where floods cause the most damage every year. Accordi…
Proposes a method to partition univariate data into unimodal subsets.
problem Partitioning univariate multimodal data into unimodal subsets.
method Recursive splitting around valley points of the data density using properties of critical points on the convex hull of the ecdf plot.
result Obtains a hierarchical statistical model of the initial dataset as a mixture of UMMs.
The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima. In a network of d−1 hidden layers with nk neurons in layers $k = 1, \ldots, …
Model shows how capital accumulation can lead to poverty traps and well-being states.
problem Capital accumulation and its effects on poverty and well-being.
method Stochastic Solow growth model with sigmoidal saving fraction and bimodal steady state distribution.
result Existence of poverty trap with fluctuation-driven transitions between poverty and well-being states.
Method reduces model bias in water temperature prediction using physics-guided GNNs.
problem Model bias in traditional physics-based models across different income and education levels.
method Physics-guided GNNs with refined neighbor selection and weights.
result Preserves equitable performance across different sensitive groups in the Delaware River Basin.
CausalRivers benchmarks causal discovery methods on real-world river discharge data.
problem Lack of in-the-wild evaluation of causal discovery methods on complex, real-world data.
method Introduces CausalRivers, a large-scale dataset of river discharge data for benchmarking.
result Demonstrates the utility of CausalRivers in evaluating causal discovery methods.
Dataset for rainfall modeling in central Europe from 1981-2011.
problem Improving rainfall streamflow modeling beyond simple catchments.
method Spatially resolved meteorological and ancillary data compilation.
result Dataset for neural network-driven hydrological modeling.