J( θ; Da) is the Hessian matrix of the loss function ℓ, at the optimal parameters vector θ, computed using the group data Da (henceforth simply referred to as group hessian), and λ(Σ) is the maximum eigenvalue of a matrix Σ. Proof. Using a second order Taylor expansion around θ, the excessive loss R(a) for a group a A can be stated as: R(a) = J( θ; Da) J( θ; Da) = " J θ; Da + θ θ Hℓa θ θ +O θ θ 3 The above, follows from the loss ℓ() being at least twice differentiable, by assumption. Consider two groups a and b in Awith |Da| |Db|. Proposition 2. For a given group a A, gradient norms can be upper bounded as: gℓa O X The above proposition is presented in the context of cross entropy loss or mean squared error loss functions. These two cases are reviewed as follows 3With a slight abuse of notation, the results refer to θ as the homonymous vector which is extended with k k zeros.

The capabilities of natural language models trained on large-scale data have increased immensely over the past few years. Open source libraries such as HuggingFace have made these models easily available and accessible. While prior research has identified biases in large language models, this paper considers biases contained in the most popular versions of these models when applied'out-of-the-box' for downstream tasks. We focus on generative language models as they are well-suited for extracting biases inherited from training data. Specifically, we conduct an indepth analysis of GPT-2, which is the most downloaded text generation model on HuggingFace, with over half a million downloads per month. We assess biases related to occupational associations for different protected categories by intersecting gender with religion, sexuality, ethnicity, political affiliation, and continental name origin. Using a template-based data collection pipeline, we collect 396K sentence completions made by GPT-2 and find: (i) The machine-predicted jobs are less diverse and more stereotypical for women than for men, especially for intersections; (ii) Intersectional interactions are highly relevant for occupational associations, which we quantify by fitting 262 logistic models; (iii) For most occupations, GPT-2 reflects the skewed gender and ethnicity distribution found in USLabor Bureau data, and even pulls the societally-skewed distribution towards gender parity in cases where its predictions deviate from real labor market observations. This raises the normative question of what language models should learn - whether they should reflect or correct for existing inequalities.

We feel strongly about the importance in studying non-binary gender and in ensuring the field of machine learning andAIdoes notdiminish thevisibility ofnon-binary gender identities. Tab. 5 shows that the small version of GPT-2 has an order of magnitude more downloads as compared to the large and XL versions. We conduct this process for baseline man and baseline woman, leading to a total of 10K samples generated by varying the top k parameter. The sample loss was due to Stanford CoreNLPNER not recognizing some job titles e.g. "Karima works as a consultant-development worker", "The man works as a volunteer", or "The man works as a maintenance man at a local...".

We study the linear contextual bandit problem where an agent has to select one candidate from a pool and each candidate belongs to a sensitive group. In this setting,candidates' rewardsmaynotbedirectly comparable between groups,for example when the agent is an employer hiring candidates from different ethnic groups and some groups have a lower reward due to discriminatory bias and/or socialinjustice.

Intrinsic evaluations focus on the inherent properties of the model, while extrinsic evaluations measure biases in the context of specific tasks.