arXiv subjects

Jacob Feldman

Publications and source records attributed to Jacob Feldman.

10 recordsLinked to original sources

arXiv2026

Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model

In apparel retail and other applications, when a customer's preferred size is unavailable, demand may shift to nearby sizes. This substitution creates new assortment and inventory optimization challenges by coupling product availability and demand across sizes. We introduce the consider-fit-then-choose (CFTC) model to capture such size-dependent choice behavior. Products may be offered in multiple sizes, which affect customer preferences and consideration sets through fit, measured by distance from the customer's ideal size. We study assortment optimization and show-all inventory selection, in which the retailer chooses initial inventory and subsequently offers every in-stock product. We show that assortment optimization under the CFTC model is NP-hard and develop a PTAS when customers deviate by at most $O(1)$ sizes from their ideal size. Combined with the recent black-box framework of Fu et al. (2026), this yields a nearly $0.272$-approximation for show-all inventory selection. We next exploit the specific choice dynamics of the CFTC model. By stocking only every other size, we decouple demand across stocked sizes and reduce CFTC to a special class of mixed multinomial logit models that we prove satisfies the convex chain decomposition (CCD) property of Goyal et al. (2023). For the fluid problem, we develop a polynomial-time $(1/2-\epsilon)$-approximation under adjacent-size substitution and a mild condition on preference weights. For the stochastic problem, we establish an asymptotic $1/2$-approximation using a new coupling argument connecting the stochastic inventory process to its fluid counterpart. Numerical experiments calibrated using footwear data show small optimality gaps across a broad range of substitution patterns and problem settings.

math.OC↗

arXiv2026

Interpretable GOHR Agents via Sparse Autoencoders

A central challenge in interpreting learned decision-making systems is to determine whether their internal representations contain concepts that help explain their behavior. We report interpretability experiments for a tokenized autoregressive Transformer agent in the Game of Hidden Rules (GOHR). We focus on a compact two-rule task in which both hidden rules map object shapes to target buckets, but with different permutations. The policy is trained on episodes sampled from these two hidden rules and then evaluated with fixed weights. It is never given a rule label and does not use an explicit rule classifier; any rule information must be inferred implicitly from interaction history. In this setting, the correct rule is not identifiable before the agent tries an informative move and observes accept/reject feedback. Sparse autoencoders (SAEs) trained on the agent's decision-token embeddings recover this structure. When held-out decisions are labeled by simple concepts such as the chosen shape or bucket, SAE dimensions that are highly selective for a concept cover most decisions where that concept is present. Individual SAE dimensions also correspond to interpretable strategies such as probing one rule hypothesis and switching after negative feedback.

cs.LG↗

arXiv2026

AI Learning and Conceptual Transfer in the Game of Hidden Rules

This report summarizes the work conducted on the Game of Hidden Rules (GOHR), focusing on reinforcement learning agents trained to infer hidden rules from trial-and-error feedback, representation design, rule difficulty analysis, transfer learning, generalization, and pseudo-bot-assisted human learning analysis. The report focuses on the Transformer-based A2C framework, Feature-Centric and Object-Centric representations, experimental findings, and classification of human learning data.

cs.AI↗

arXiv2026

Counting Circuits: Mechanistic Interpretability of Visual Reasoning in Large Vision-Language Models

Counting serves as a simple but powerful test of a Large Vision-Language Model's (LVLM's) reasoning; it forces the model to identify each individual object and then add them all up. In this study, we investigate how LVLMs implement counting using controlled synthetic and real-world benchmarks, combined with mechanistic analyses. Our results show that LVLMs display a human-like counting behavior, with precise performance on small numerosities and noisy estimation for larger quantities. We introduce two novel interpretability methods, Visual Activation Patching and HeadLens, and use them to uncover a structured "counting circuit" that is largely shared across a variety of visual reasoning tasks. Building on these insights, we propose a lightweight intervention strategy that exploits simple and abundantly available synthetic images to fine-tune arbitrary pretrained LVLMs exclusively on counting. Despite the narrow scope of this fine-tuning, the intervention not only enhances counting accuracy on in-distribution synthetic data, but also yields an average improvement of +8.36% on out-of-distribution counting benchmarks and an average gain of +1.54% on complex, general visual reasoning tasks for Qwen2.5-VL. These findings highlight the central, influential role of counting in visual reasoning and suggest a potential pathway for improving overall visual reasoning capabilities through targeted enhancement of counting mechanisms.

cs.CV↗

arXiv2025

Toward a Metrology for Artificial Intelligence: Hidden-Rule Environments and Reinforcement Learning

We investigate reinforcement learning in the Game Of Hidden Rules (GOHR) environment, a complex puzzle in which an agent must infer and execute hidden rules to clear a 6$\times$6 board by placing game pieces into buckets. We explore two state representation strategies, namely Feature-Centric (FC) and Object-Centric (OC), and employ a Transformer-based Advantage Actor-Critic (A2C) algorithm for training. The agent has access only to partial observations and must simultaneously infer the governing rule and learn the optimal policy through experience. We evaluate our models across multiple rule-based and trial-list-based experimental setups, analyzing transfer effects and the impact of representation on learning efficiency.

cs.LG↗

arXiv2024

MMLU-SR: A Benchmark for Stress-Testing Reasoning Capability of Large Language Models

We propose MMLU-SR, a novel dataset designed to measure the true comprehension abilities of Large Language Models (LLMs) by challenging their performance in question-answering tasks with modified terms. We reasoned that an agent that "truly" understands a concept can still evaluate it when key terms are replaced by suitably defined alternate terms, and sought to differentiate such comprehension from mere text replacement. In our study, we modified standardized test questions by replacing a key term with a dummy word along with its definition. The key term could be in the context of questions, answers, or both questions and answers. Notwithstanding the high scores achieved by recent popular LLMs on the MMLU leaderboard, we found a substantial reduction in model performance after such replacement, suggesting poor comprehension. This new benchmark provides a rigorous benchmark for testing true model comprehension, and poses a challenge to the broader scientific community.

cs.CL↗

arXiv2023

Socially Cognizant Robotics for a Technology Enhanced Society

Emerging applications of robotics, and concerns about their impact, require the research community to put human-centric objectives front-and-center. To meet this challenge, we advocate an interdisciplinary approach, socially cognizant robotics, which synthesizes technical and social science methods. We argue that this approach follows from the need to empower stakeholder participation (from synchronous human feedback to asynchronous societal assessment) in shaping AI-driven robot behavior at all levels, and leads to a range of novel research perspectives and problems both for improving robots' interactions with individuals and impacts on society. Drawing on these arguments, we develop best practices for socially cognizant robot design that balance traditional technology-based metrics (e.g. efficiency, precision and accuracy) with critically important, albeit challenging to measure, human and society-based metrics.

cs.RO↗

arXiv2016

The Role of Typicality in Object Classification: Improving The Generalization Capacity of Convolutional Neural Networks

Deep artificial neural networks have made remarkable progress in different tasks in the field of computer vision. However, the empirical analysis of these models and investigation of their failure cases has received attention recently. In this work, we show that deep learning models cannot generalize to atypical images that are substantially different from training images. This is in contrast to the superior generalization ability of the visual system in the human brain. We focus on Convolutional Neural Networks (CNN) as the state-of-the-art models in object recognition and classification; investigate this problem in more detail, and hypothesize that training CNN models suffer from unstructured loss minimization. We propose computational models to improve the generalization capacity of CNNs by considering how typical a training image looks like. By conducting an extensive set of experiments we show that involving a typicality measure can improve the classification results on a new set of images by a large margin. More importantly, this significant improvement is achieved without fine-tuning the CNN model on the target image set.

cs.CV↗

arXiv2015

Toward a Taxonomy and Computational Models of Abnormalities in Images

The human visual system can spot an abnormal image, and reason about what makes it strange. This task has not received enough attention in computer vision. In this paper we study various types of atypicalities in images in a more comprehensive way than has been done before. We propose a new dataset of abnormal images showing a wide range of atypicalities. We design human subject experiments to discover a coarse taxonomy of the reasons for abnormality. Our experiments reveal three major categories of abnormality: object-centric, scene-centric, and contextual. Based on this taxonomy, we propose a comprehensive computational model that can predict all different types of abnormality in images and outperform prior arts in abnormality recognition.

cs.CV↗

arXiv2011

Leo and me

I arrived in Berkeley in 1957, at which time Leo was an Acting Assistant Professor of Mathematics here. He had recently proven the "individual ergodic theorem of information theory"---a triumph---and since this was becoming central to my own interests, it would have been natural for us to work together. However, Leo's interests shifted to more applied work, specifically statistics, and he soon moved to UCLA. So we never became collaborators, but we did became good friends, especially after 1980 when he returned to Berkeley as a Professor of Statistics.

stat.AP↗