Representation Geometry

Masked language modelling (MLM) has been the dominant pre-training objective for text encoders since BERT, yet it encourages representations that are strongly anchored to surface-form token identity rather than deeper semantic structure. Inspired by the success of Joint Embedding Predictive Architectures (JEPA) (LeCun, 2022) in vision and audio, we propose a hybrid pre-training objective that combines a JEPA-style latent-space prediction loss with a standard MLM objective over a single shared encoder. A learnable scalar parameter continuously balances the two objectives during training. We pre-train both a hybrid model and a pure-MLM baseline on English Wikipedia using identical architectures and compute budgets (NVIDIA H100). Extensive representation analysis across five GLUE benchmarks (SST-2, MRPC, MNLI, CoLA, STS-B) using four pooling strategies reveals that the hybrid encoder produces significantly more uniform embeddings (uniformity less than -0.16 vs -0.05 for MLM), exhibits richer spectral geometry under max pooling, encodes less surface-level lexical information, and achieves a better semantic-to-lexical balance. Despite similar linear-probe downstream accuracy, the geometric differences are consistent and significant, suggesting that the JEPA predictive objective reshapes the latent space in ways that standard accuracy metrics alone cannot capture.

Merging multiple Low-Rank Adaptation (LoRA) modules is promising for constructing general-purpose systems, yet challenging because LoRA update directions span different subspaces and contribute unevenly. When merged naively, such mismatches can weaken the directions most critical to certain task losses while overemphasizing relatively less important ones, ultimately reducing the model's ability to represent all tasks faithfully. We revisit this problem through two perspectives: subspace coverage, which captures how broadly LoRA directions cover diverse representational directions, and anisotropy, which reflects the imbalance of influence across those directions. We propose TARA-Merging (Task-Rank Anisotropy Alignment), which aligns merging weights using a preference-weighted cross-entropy pseudo-loss while preserving task-relevant LoRA subspaces. This ensures broad subspace coverage and mitigates anisotropy via direction-wise reweighting. Across eight vision and six NLI benchmarks, TARA-Merging consistently outperforms vanilla and LoRA-aware baselines, demonstrating strong robustness and generalization, and highlighting the importance of addressing both subspace coverage and anisotropy in LoRA merging.

Understanding the internal representations of large language models (LLMs) is a central challenge in interpretability research. Existing feature interpretability methods often rely on strong structural assumptions--such as linearity or sparsity--that may not hold in practice. In this work, we introduce InverseScope, an assumption-light and scalable framework for interpreting neural activations via input inversion. Given a target activation, InverseScope characterizes its encoded information by generating natural-language inputs that produce nearby activations, grounding abstract internal states in concrete language. To overcome the prohibitive cost of sampling in high-dimensional activation spaces, we propose a novel control-layer conditioning architecture that substantially improves sample efficiency compared to prior token-prepending approaches. We demonstrate that InverseScope reveals rich geometric structure in LLM representation spaces, including sentence-level linear analogies. The framework scales to state-of-the-art open-source models of up to 14B parameters and generalizes to out-of-distribution inputs, enabling systematic analysis of activation neighborhoods.