Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm.

In this section we give proofs for all the results in Sec. 2, which explores the phenomenon of feature suppression in contrastive learning using the InfoNCE loss. We invite the reader to consult Sec. Recall, for a measure on a space U and a measurable map h: U! V let h# denote the pushforward h# (V)= (h We now recall the definition of feature suppression and distinction. Consider an encoder f: X! S However here our goal is to establish that it is possible for InfoNCE optimal encoders both to suppress features in the sense of Def. 1, but also to separate concepts out in a desirable manner. For this purpose we found this strong notion of distinguishing to suffice. Since g is injective, we know there exists a left inverse h: X!Zsuch that h g(z) =z for all z 2Z.

The generalization of representations learned via contrastive learning depends crucially on what features of the data are extracted. However, we observe that the contrastive loss does not always sufficiently guide which features are extracted, a behavior that can negatively impact the performance on downstream tasks via "shortcuts", i.e., by inadvertently suppressing important predictive features. We find that feature extraction is influenced by the difficulty of the so-called instance discrimination task (i.e., the task of discriminating pairs of similar points from pairs of dissimilar ones). Although harder pairs improve the representation of some features, the improvement comes at the cost of suppressing previously well represented features. In response, we propose implicit feature modification (IFM), a method for altering positive and negative samples in order to guide contrastive models towards capturing a wider variety of predictive features. Empirically, we observe that IFM reduces feature suppression, and as a result improves performance on vision and medical imaging tasks. The code is available at: https://github.

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm.

In this section we give proofs for all the results in Sec. 2, which explores the phenomenon of feature suppression in contrastive learning using the InfoNCE loss. We invite the reader to consult Sec. Recall, for a measure on a space U and a measurable map h: U! V let h# denote the pushforward h# (V)= (h We now recall the definition of feature suppression and distinction. Consider an encoder f: X! S However here our goal is to establish that it is possible for InfoNCE optimal encoders both to suppress features in the sense of Def. 1, but also to separate concepts out in a desirable manner. For this purpose we found this strong notion of distinguishing to suffice. Since g is injective, we know there exists a left inverse h: X!Zsuch that h g(z) =z for all z 2Z.

The generalization of representations learned via contrastive learning depends crucially on what features of the data are extracted. However, we observe that the contrastive loss does not always sufficiently guide which features are extracted, a behavior that can negatively impact the performance on downstream tasks via "shortcuts", i.e., by inadvertently suppressing important predictive features. We find that feature extraction is influenced by the difficulty of the so-called instance discrimination task (i.e., the task of discriminating pairs of similar points from pairs of dissimilar ones). Although harder pairs improve the representation of some features, the improvement comes at the cost of suppressing previously well represented features. In response, we propose implicit feature modification (IFM), a method for altering positive and negative samples in order to guide contrastive models towards capturing a wider variety of predictive features. Empirically, we observe that IFM reduces feature suppression, and as a result improves performance on vision and medical imaging tasks. The code is available at: https://github.