Classical supervised learning evaluates models primarily via predictive risk on hold-out data. Such evaluations quantify how well a function behaves on a distribution, but they do not address whether the internal decomposition of a model is uniquely determined by the data and evaluation design. In this paper, we introduce \emph{Modular Jets} for regression and classification pipelines. Given a task manifold (input space), a modular decomposition, and access to module-level representations, we estimate empirical jets, which are local linear response maps that describe how each module reacts to small structured perturbations of the input. We propose an empirical notion of \emph{mirage} regimes, where multiple distinct modular decompositions induce indistinguishable jets and thus remain observationally equivalent, and contrast this with an \emph{identifiable} regime, where the observed jets single out a decomposition up to natural symmetries. In the setting of two-module linear regression pipelines we prove a jet-identifiability theorem. Under mild rank assumptions and access to module-level jets, the internal factorisation is uniquely determined, whereas risk-only evaluation admits a large family of mirage decompositions that implement the same input-to-output map. We then present an algorithm (MoJet) for empirical jet estimation and mirage diagnostics, and illustrate the framework using linear and deep regression as well as pipeline classification.

Clustering is a central problem in unsupervised learning.

We introduce Perception Learning (PeL), a paradigm that optimizes an agent's sensory interface $f_ϕ:\mathcal{X}\to\mathcal{Z}$ using task-agnostic signals, decoupled from downstream decision learning $g_θ:\mathcal{Z}\to\mathcal{Y}$. PeL directly targets label-free perceptual properties, such as stability to nuisances, informativeness without collapse, and controlled geometry, assessed via objective representation-invariant metrics. We formalize the separation of perception and decision, define perceptual properties independent of objectives or reparameterizations, and prove that PeL updates preserving sufficient invariants are orthogonal to Bayes task-risk gradients. Additionally, we provide a suite of task-agnostic evaluation metrics to certify perceptual quality.

Clustering is a central problem in unsupervised learning.

We propose Convexity-Driven Projection (CDP), a boundary-free linear method for dimensionality reduction of point clouds that targets preserving detour-induced local non-convexity. CDP builds a $k$-NN graph, identifies admissible pairs whose Euclidean-to-shortest-path ratios are below a threshold, and aggregates their normalized directions to form a positive semidefinite non-convexity structure matrix. The projection uses the top-$k$ eigenvectors of the structure matrix. We give two verifiable guarantees. A pairwise a-posteriori certificate that bounds the post-projection distortion for each admissible pair, and an average-case spectral bound that links expected captured direction energy to the spectrum of the structure matrix, yielding quantile statements for typical distortion. Our evaluation protocol reports fixed- and reselected-pairs detour errors and certificate quantiles, enabling practitioners to check guarantees on their data.

Existing studies on fairness are largely Western-focused, making them inadequate for culturally diverse countries such as India. To address this gap, we introduce INDIC-BIAS, a comprehensive India-centric benchmark designed to evaluate fairness of LLMs across 85 identity groups encompassing diverse castes, religions, regions, and tribes. We first consult domain experts to curate over 1,800 socio-cultural topics spanning behaviors and situations, where biases and stereotypes are likely to emerge. Grounded in these topics, we generate and manually validate 20,000 real-world scenario templates to probe LLMs for fairness. We structure these templates into three evaluation tasks: plausibility, judgment, and generation. Our evaluation of 14 popular LLMs on these tasks reveals strong negative biases against marginalized identities, with models frequently reinforcing common stereotypes. Additionally, we find that models struggle to mitigate bias even when explicitly asked to rationalize their decision. Our evaluation provides evidence of both allocative and representational harms that current LLMs could cause towards Indian identities, calling for a more cautious usage in practical applications. We release INDIC-BIAS as an open-source benchmark to advance research on benchmarking and mitigating biases and stereotypes in the Indian context.

We are interested in the construction of software that can act as scientific assistants to domain specialists. It is expected that such assistants will be needed to accelerate the identification of ways to address complex problems requiring urgent solutions. In this paper, our focus is not on a specific scientific problem, but on the software-engineering of such 'science accelerators'. Recent developments in 'No Code' techniques would seem to suggest that scientist can simply hypothesise solutions simply by conversing with a large language model (LLM). However, for complex scientific problems, this seems unlikely given the current state of LLM technology. What does appear feasible is that a software engineer can use LLMs to rapidly construct programs for use by a domain-specialist, including the specialist's requirements expressed in natural language. We propose the design of an interactive form of 'structured' inductive programming in which a software-engineer and an LLM collaboratively construct an 'assistant' for a scientific data analysis. The paper describes a simple implementation called iStrucInd that adapts a '2-way Intelligibility' protocol to implement the interaction between the software engineer and the LLM. We test the tool on two different non-trivial scientific data analysis tasks. Specifically, we compare the system constructed by iStrucInd against systems constructed manually and by Low Code/No Code methods along dimensions of: (a) program performance; (b) program quality; and (c) programming effort. The results show iStrucInd allows a software engineer to develop better programs faster suggesting interactive structured induction can play a useful role in the rapid construction of scientific assistants.

In multi-turn dialogues, large language models (LLM) face a critical challenge of ensuring coherence while adapting to user-specific information. This study introduces the persona knowledge gap, the discrepancy between a model's internal understanding and the knowledge required for coherent, personalized conversations. While prior research has recognized these gaps, computational methods for their identification and resolution remain underexplored. We propose Conversation Preference Elicitation and Recommendation (CPER), a novel framework that dynamically detects and resolves persona knowledge gaps using intrinsic uncertainty quantification and feedback-driven refinement. CPER consists of three key modules: a Contextual Understanding Module for preference extraction, a Dynamic Feedback Module for measuring uncertainty and refining persona alignment, and a Persona-Driven Response Generation module for adapting responses based on accumulated user context. We evaluate CPER on two real-world datasets: CCPE-M for preferential movie recommendations and ESConv for mental health support. Using A/B testing, human evaluators preferred CPER's responses 42% more often than baseline models in CCPE-M and 27% more often in ESConv. A qualitative human evaluation confirms that CPER's responses are preferred for maintaining contextual relevance and coherence, particularly in longer (12+ turn) conversations.