February 2026

Second-order optimizers can significantly accelerate large-scale training, yet their naive federated variants are often unstable or even diverge on non-IID data. We show that a key culprit is emph{preconditioner drift}: client-side second-order training induces heterogeneous emph{curvature-defined geometries} (i.e., preconditioner coordinate systems), and server-side model averaging updates computed under incompatible metrics, corrupting the global descent direction. To address this geometric mismatch, we propose texttt{FedPAC}, a emph{preconditioner alignment and correction} framework for reliable federated second-order optimization. texttt{FedPAC} explicitly decouples parameter […]

Ver mais

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit spectral bias, whereby low-frequency components of the solution are learned significantly faster than high-frequency modes. While spectral bias is often treated as an intrinsic representational limitation of neural architectures, its interaction with optimization dynamics and physics-based loss formulations remains poorly understood. In this work, we provide a systematic investigation […]

Ver mais

On-the-fly Directed Controller Synthesis (OTF-DCS) mitigates state-space explosion by incrementally exploring the system and relies critically on an exploration policy to guide search efficiently. Recent reinforcement learning (RL) approaches learn such policies and achieve promising zero-shot generalization from small training instances to larger unseen ones. However, a fundamental limitation is anisotropic generalization, where an RL policy exhibits strong performance only in a specific region of the domain-parameter space while remaining fragile elsewhere due to training stochasticity and trajectory-dependent […]

Ver mais

How I think about Codex Gabriel Chua (Developer Experience Engineer for APAC at OpenAI) provides his take on the confusing terminology behind the term “Codex”, which can refer to a bunch of of different things within the OpenAI ecosystem: In plain terms, Codex is OpenAI’s software engineering agent, available through multiple interfaces, and an agent is a model plus instructions and tools, wrapped in a runtime that can execute tasks on your behalf. […] At a high level, […]

Ver mais

Tabular foundation models aim to make machine learning accessible for enterprise data without task-specific training. This paper presents the first independent evaluation of SAP’s Retrieval Pretrained Transformer (RPT-1) from a practitioner perspective. RPT-1 is a compact 64.6 MB model pretrained on 1.34 TB of structured data across 3.1 million tables. We benchmark it against tuned gradient-boosted decision trees (XGBoost, LightGBM, CatBoost) on three SAP business scenarios: demand forecasting across SD/MM/PP modules, predictive data integrity in BC/MM/QM, and financial […]

Ver mais

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for Large Language Model (LLM) reasoning, yet current methods face key challenges in resource allocation and policy optimization dynamics: (i) uniform rollout allocation ignores gradient variance heterogeneity across problems, and (ii) the softmax policy structure causes gradient attenuation for high-confidence correct actions, while excessive gradient updates may destabilize training. Therefore, we propose DynaMO, a theoretically-grounded dual-pronged optimization framework. At the sequence level, we prove that uniform allocation is suboptimal […]

Ver mais

Federated learning (FL) is a privacy-preserving machine learning paradigm that enables multiple parties to collaboratively train models on privately owned data without sharing raw information. While standard FL typically addresses either horizontal or vertical data partitions, many real-world scenarios exhibit a complex hybrid distribution. This paper proposes Hybrid Federated Learning (HybridFL) to address data split both horizontally across disjoint users and vertically across complementary feature sets. We evaluate HybridFL in a financial crime detection context, where a transaction […]

Ver mais

I reformulated the Bellman Expectation Equation using vector dot products instead of the usual summation sigma summation notation. g = γ⃗ · r⃗ o⃗ = r⃗ + γv⃗’ q = p⃗ · o⃗ v = π⃗ · q⃗ Together they express the full Bellman Expectation Equation: discounted return (g), one-step Bellman backup (o for outcome), Q-value as expected outcome (q) given dynamics (p), and state value (v) as expected value under policy π. This makes the computational structure […]

Ver mais