Ankur Mani

Moulik Choraria, Ibtihal Ferwana, Ankur Mani et al.

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments. The success of IRM requires an important assumption: the underlying causal mechanisms/features remain invariant across environments. When not satisfied, we show that IRM can over-constrain the predictor and to remedy this, we propose a relaxation via $\textit{partial invariance}$. In this work, we theoretically highlight the sub-optimality of IRM and then demonstrate how learning from a partition of training domains can help improve invariant models. Several experiments, conducted both in linear settings as well as with deep neural networks on tasks over both language and image data, allow us to verify our conclusions.

Moulik Choraria, Argyrios Gerogiannis, Vidhata Jayaraman et al.

Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the role of external context in recall. In this work, we propose a two-stage associative memory architecture, wherein a context-gate subcircuit reshapes the retrieval energy landscape before and during recall. We show theoretically that context gating increases inter-memory separation while inducing sparsity, translating into exponential improvements in retrieval. Crucially, we prove that the system admits a unique self-consistent fixed point, revealing that the resulting retrieval state is driven by both a direct contextual bias and a second-order retrieval-gate feedback loop. We then bridge this theory to transformers; specifically, we evaluate a first-order approximation on Llama-3, confirming that in-context learning acts as context-gated retrieval. Native dynamics mirror our theory: context localizes a memory subspace, enabling the zero-shot query to cleanly discriminate. Ultimately, this framework provides a mechanistic link between associative memory theory and LLM phenomenology.

Moulik Choraria, Ibtihal Ferwana, Ankur Mani et al.

The Invariant Risk Minimization (IRM) framework aims to learn invariant features from a set of environments for solving the out-of-distribution (OOD) generalization problem. The underlying assumption is that the causal components of the data generating distributions remain constant across the environments or alternately, the data "overlaps" across environments to find meaningful invariant features. Consequently, when the "overlap" assumption does not hold, the set of truly invariant features may not be sufficient for optimal prediction performance. Such cases arise naturally in networked settings and hierarchical data-generating models, wherein the IRM performance becomes suboptimal. To mitigate this failure case, we argue for a partial invariance framework. The key idea is to introduce flexibility into the IRM framework by partitioning the environments based on hierarchical differences, while enforcing invariance locally within the partitions. We motivate this framework in classification settings with causal distribution shifts across environments. Our results show the capability of the partial invariant risk minimization to alleviate the trade-off between fairness and risk in certain settings.