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Nikhil Singh

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Published work

6 published item(s)

preprint2026arXiv

Position: Safety and Fairness in Agentic AI Depend on Interaction Topology, Not on Model Scale or Alignment

As large language models are increasingly deployed as interacting agents in high-stakes decisions, the AI safety community assumes that safety properties of individual models will compose into safe multi-agent behavior. This position paper argues that this assumption is fundamentally mistaken. In agentic AI, safety is determined by interaction topology, not model weights. When agents deliberate sequentially or aggregate via parallel voting with a judge, the structure of information flow and decision coupling dominates outcomes. Evidence across model families and scales reveals three persistent topology-driven pathologies: ordering instability, where system behavior depends primarily on agent sequence; information cascades, where early judgments propagate regardless of correctness; and functional collapse, where systems satisfy fairness metrics while abandoning meaningful risk discrimination. Contrary to intuition, scaling to more capable models strengthens these effects by increasing consensus formation and reducing the challenge of initial decisions. These failure modes are invisible to model-centric evaluation and alignment procedures. We argue that agentic AI must be treated as a dynamical system rather than a collection of aligned components. Interaction topology must become a primary target of safety evaluation and regulation, with systems required to demonstrate robustness across architectural variations before deployment.

preprint2022arXiv

A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.

preprint2022arXiv

niksss at HinglishEval: Language-agnostic BERT-based Contextual Embeddings with Catboost for Quality Evaluation of the Low-Resource Synthetically Generated Code-Mixed Hinglish Text

This paper describes the system description for the HinglishEval challenge at INLG 2022. The goal of this task was to investigate the factors influencing the quality of the code-mixed text generation system. The task was divided into two subtasks, quality rating prediction and annotators disagreement prediction of the synthetic Hinglish dataset. We attempted to solve these tasks using sentence-level embeddings, which are obtained from mean pooling the contextualized word embeddings for all input tokens in our text. We experimented with various classifiers on top of the embeddings produced for respective tasks. Our best-performing system ranked 1st on subtask B and 3rd on subtask A.

preprint2022arXiv

Normalized Field Product method for Topology Optimization

The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity free solutions to exist within the design space. The density formulation proposed herein is independent of user specified parameters, other then the length scale. Sensitivity analysis for the formulation obtained by combining the proposed density evaluation with the SIMP material model reveal that for compliance minimization and small deformation compliant mechanism problems, objective gradients vanish at pure 0-1 topologies. The methodology is implemented to solve well known examples in literature for different mesh refinements presenting mesh independent and close to binary solutions without the use of heuristics or continuation methods.

preprint2022arXiv

Topology Optimization with Tetra-kai-decahedra and Spheroidal Masks

A novel meshing scheme, based on regular tetra-kai-decahedron, also referred to as truncated octahedron, cells is presented for use in spatial topology optimization. A tetra-kai-decahedron mesh ensures face connectivity between elements thereby eliminating singular solutions from the solution space. Various other benefits of implementing the said mesh are also highlighted, and the corresponding finite element is introduced. Material mask overlay strategy or MMOS, a feature based method for topology optimization is extended for use in 3-dimensions (MMOS-3D) via the aforementioned finite element and spheroidal negative masks. Formulation for density computation and sensitivity analysis for gradient based optimization is developed. Examples on traditional structural topology optimization problems are presented with detailed discussion on efficacy of the proposed approach.

preprint2015arXiv

Parametric Regression on the Grassmannian

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in Euclidean spaces and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a time-warped variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.