Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications

This work introduces the Separable Neural Architecture (SNA), a function representational class combining neural approximation with tensor decomposition. The SNA decouples localized coordinate functions (atoms) from global interactions governed by a sparse, low-rank interaction object. This architecture possesses a compact and smooth inductive bias well-suited for solving partial differential equations (PDEs). When viewed as a Galerkin trial space under the variational SNA (VSNA) framework, the formulation satisfies classical variational guarantees under Lax-Milgram: well-posedness, quasi-optimality, convergence, and stability. In high-dimensional spatiotemporal--parametric PDEs, the VSNA mitigates the curse of dimensionality by scaling algebraically rather than exponentially. Exploiting an entirely factorized, tensor-native alternating least squares (ALS) optimization framework reduces this cost to linear in dimension. The VSNA is validated across elliptic, hyperbolic, and parabolic systems, demonstrating close alignment with predicted algebraic and spectral scaling rates. We showcase the SNA as a "solve once, query anywhere" physical world model via two engineering case studies: a 7D parametric manufacturing simulation and an experimental thermal-to-property inversion pipeline for Inconel 718. The VSNA executes a 1,000,000-query Monte Carlo sweep in 102s on a standard laptop CPU, yielding a 150,000x speedup over a full-grid finite element baseline hosted on an NVIDIA A100 GPU. It further enables real-time generative inverse-mode reconstructions under 100ms. These results demonstrate that the SNA serves as a compact mathematical substrate for continuous parameter manifolds to enable real-time inversion, optimization loops, and rapid uncertainty propagation.

Separable neural architectures as a primitive for unified predictive and generative intelligence

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.

LiCQA : A Lightweight Complex Question Answering System

Over the last twenty years, significant progress has been made in designing and implementing Question Answering (QA) systems. However, addressing complex questions, the answers to which are spread across multiple documents, remains a challenging problem. Recent QA systems that are designed to handle complex questions work either on the basis of knowledge graphs, or utilise contem- porary neural models that are expensive to train, in terms of both computational resources and the volume of training data required. In this paper, we present LiCQA, an unsupervised question answer- ing model that works primarily on the basis of corpus evidence. We empirically compare the effectiveness and efficiency of LiCQA with two recently presented QA systems, which are based on different underlying principles. The results of our experiments show that LiCQA significantly outperforms these two state-of-the-art systems on benchmark data with noteworthy reduction in latency.

Agile Reinforcement Learning through Separable Neural Architecture

Deep reinforcement learning (RL) is increasingly deployed in resource-constrained environments, yet the go-to function approximators - multilayer perceptrons (MLPs) - are often parameter-inefficient due to an imperfect inductive bias for the smooth structure of many value functions. This mismatch can also hinder sample efficiency and slow policy learning in this capacity-limited regime. Although model compression techniques exist, they operate post-hoc and do not improve learning efficiency. Recent spline-based separable architectures - such as Kolmogorov-Arnold Networks (KANs) - have been shown to offer parameter efficiency but are widely reported to exhibit significant computational overhead, especially at scale. In seeking to address these limitations, this work introduces SPAN (SPline-based Adaptive Networks), a novel function approximation approach to RL. SPAN adapts the low rank KHRONOS framework by integrating a learnable preprocessing layer with a separable tensor product B-spline basis. SPAN is evaluated across discrete (PPO) and high-dimensional continuous (SAC) control tasks, as well as offline settings (Minari/D4RL). Empirical results demonstrate that SPAN achieves a 30-50% improvement in sample efficiency and 1.3-9 times higher success rates across benchmarks compared to MLP baselines. Furthermore, SPAN demonstrates superior anytime performance and robustness to hyperparameter variations, suggesting it as a viable, high performance alternative for learning intrinsically efficient policies in resource-limited settings.

A Separable Architecture for Continuous Token Representation in Language Models

Transformer scaling law analyses typically treat parameters as interchangeable; an abstraction that accurately predicts loss-compute relationships. Yet, in sub-billion-parameter small language models (SLMs), embedding matrices dominate the parameter budget. This work argues that this allocation is as suboptimal as it is counterintuitive. Leviathan is an architecture with a continuous embedding generator to replace the discrete lookup tables of canonical models. Evaluating on the Pile dataset under isoparametric settings, Leviathan consistently outperforms a standard, LLaMA-style architecture. By means of an empirical power-law fit, Leviathan exhibits a markedly superior effective parameter capacity. Across the regime studied, Leviathan behaves as a dense model with $1.47$ to $2.11 \times$ more parameters.

One Word is Enough: Minimal Adversarial Perturbations for Neural Text Ranking

Neural ranking models (NRMs) achieve strong retrieval effectiveness, yet prior work has shown they are vulnerable to adversarial perturbations. We revisit this robustness question with a minimal, query-aware attack that promotes a target document by inserting or substituting a single, semantically aligned word - the query center. We study heuristic and gradient-guided variants, including a white-box method that identifies influential insertion points. On TREC-DL 2019/2020 with BERT and monoT5 re-rankers, our single-word attacks achieve up to 91% success while modifying fewer than two tokens per document on average, achieving competitive rank and score boosts with far fewer edits under a comparable white-box setup to ensure fair evaluation against PRADA. We also introduce new diagnostic metrics to analyze attack sensitivity beyond aggregate success rates. Our analysis reveals a Goldilocks zone in which mid-ranked documents are most vulnerable. These findings demonstrate practical risks and motivate future defenses for robust neural ranking.

Fine Grained Evaluation of LLMs-as-Judges

A good deal of recent research has focused on how Large Language Models (LLMs) may be used as `judges' in place of humans to evaluate the quality of the output produced by various text / image processing systems. Within this broader context, a number of studies have investigated the specific question of how effectively LLMs can be used as relevance assessors for the standard ad hoc task in Information Retrieval (IR). We extend these studies by looking at additional questions. Most importantly, we use a Wikipedia based test collection created by the INEX initiative, and prompt LLMs to not only judge whether documents are relevant / non-relevant, but to highlight relevant passages in documents that it regards as useful. The human relevance assessors involved in creating this collection were given analogous instructions, i.e., they were asked to highlight all passages within a document that respond to the information need expressed in a query. This enables us to evaluate the quality of LLMs as judges not only at the document level, but to also quantify how often these `judges' are right for the right reasons. Our findings suggest that LLMs-as-judges work best under human supervision.

A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Field

Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we blend sparse high-fidelity (HF) data with low-fidelity (LF) information to predict aerodynamic fields under varying constraints in computational resources. Unlike traditional approaches, KHRONOS is built upon variational principles, interpolation theory, and tensor decomposition. These elements provide a mathematical basis for heavy pruning compared to dense neural networks. Using the AirfRANS dataset as a high-fidelity benchmark and NeuralFoil to generate low-fidelity counterparts, this work compares the performance of KHRONOS with three contemporary model architectures: a multilayer perceptron (MLP), a graph neural network (GNN), and a physics-informed neural network (PINN). We consider varying levels of high-fidelity data availability (0%, 10%, and 30%) and increasingly complex geometry parameterizations. These are used to predict the surface pressure coefficient distribution over the airfoil. Results indicate that, whilst all models eventually achieve comparable predictive accuracy, KHRONOS excels in resource-constrained conditions. In this domain, KHRONOS consistently requires orders of magnitude fewer trainable parameters and delivers much faster training and inference than contemporary dense neural networks at comparable accuracy. These findings highlight the potential of KHRONOS and similar architectures to balance accuracy and efficiency in multi-fidelity aerodynamic field prediction.

A Unified Generative-Predictive Framework for Deterministic Inverse Design

Inverse design of heterogeneous material microstructures is a fundamentally ill-posed and famously computationally expensive problem. This is exacerbated by the high-dimensional design spaces associated with finely resolved images, multimodal input property streams, and a highly nonlinear forward physics. Whilst modern generative models excel at accurately modeling such complex forward behavior, most of them are not intrinsically structured to support fast, stable \emph{deterministic} inversion with a physics-informed bias. This work introduces Janus, a unified generative-predictive framework to address this problem. Janus couples a deep encoder-decoder architecture with a predictive KHRONOS head, a separable neural architecture. Topologically speaking, Janus learns a latent manifold simultaneously isometric for generative inversion and pruned for physical prediction; the joint objective inducing \emph{disentanglement} of the latent space. Janus is first validated on the MNIST dataset, demonstrating high-fidelity reconstruction, accurate classification and diverse generative inversion of all ten target classes. It is then applied to the inverse design of heterogeneous microstructures labeled with thermal conductivity. It achieves a forward prediction accuracy $R^2=0.98$ (2\% relative error) and sub-5\% pixelwise reconstruction error. Inverse solutions satisfy target properties to within $1\%$ relative error. Inverting a sweep through properties reveal smooth traversal of the latent manifold, and UMAP visualization confirms the emergence of a low-dimensional, disentangled manifold. By unifying prediction and generation within a single latent space, Janus enables real-time, physics-informed inverse microstructure generation at a lower computational cost typically associated with classical optimization-based approaches.

Retriv at BLP-2025 Task 2: Test-Driven Feedback-Guided Framework for Bangla-to-Python Code Generation

Large Language Models (LLMs) have advanced the automated generation of code from natural language prompts. However, low-resource languages (LRLs) like Bangla remain underrepresented due to the limited availability of instruction-to-code datasets and evaluation benchmarks. To address this, the BLP Workshop at IJCNLP-AACL 2025 introduced a shared task on "Code Generation in Bangla". In this work, we propose a method that combines instruction prompting with a test-driven, feedback-guided iterative refinement process using a fine-tuned Qwen2.5-14B model. The model generates code from Bangla instructions, tests it against unit tests, and iteratively refines any failing outputs through three evaluation passes, using test feedback to guide each step. This approach helped our team "Retriv" to secure 2nd place in the shared task with a Pass@1 score of 0.934. The analysis highlights challenges in Bangla instruction understanding and Python code generation, emphasizing the need for targeted methods in LRLs. We made experimental scripts publicly available for the community.