Prasanth K K

Prasanth K K

Low-Rank Adaptation (LoRA) has emerged as a widely adopted approach for adapting large language models, yet the internal representational changes induced by LoRA fine-tuning remain insufficiently understood. In this work, we investigate the geometry of LoRA-induced representations using Sparse Autoencoders (SAEs). We introduce a delta activation framework that isolates the adapter-specific contribution to the residual stream. Using Gemma-2-9B with LoRA ranks 4, 8, 16, and 32, we train adapter-specific SAEs across multiple transformer layers and compare their learned feature spaces with pretrained SAE dictionaries. We evaluate representational alignment using cosine similarity between decoder directions, principal-angle analysis of feature subspaces, and Centered Kernel Alignment (CKA) between activation representations. Across layers and ranks, we consistently observe comparatively weak geometric alignment between LoRA-induced feature dictionaries and pretrained SAE features. Adapter-specific SAEs also reconstruct delta activations more effectively than pretrained SAEs, suggesting that LoRA updates occupy partially distinct representational structure within the residual stream. Additionally, feature density increases with rank and depth, while geometric divergence remains relatively stable across ranks. These findings provide empirical evidence that LoRA fine-tuning can induce feature structures that are not fully captured by pretrained interpretability dictionaries, with implications for mechanistic interpretability, adaptation analysis, and safety auditing of fine-tuned language models.

Prasanth K K, Shubham Sharma

Standard Recurrent Neural Networks, including LSTMs, struggle to model long-range dependencies, particularly in sequences containing noisy or misleading information. We propose a new architectural principle, Output-Conditioned Gating, which enables a model to perform self-reflection by modulating its internal memory gates based on its own past inferences. This creates a stabilizing feedback loop that enhances memory retention. Our final model, the EchoLSTM, integrates this principle with an attention mechanism. We evaluate the EchoLSTM on a series of challenging benchmarks. On a custom-designed Distractor Signal Task, the EchoLSTM achieves 69.0% accuracy, decisively outperforming a standard LSTM baseline by 33 percentage points. Furthermore, on the standard ListOps benchmark, the EchoLSTM achieves performance competitive with a modern Transformer model, 69.8% vs. 71.8%, while being over 5 times more parameter-efficient. A final Trigger Sensitivity Test provides qualitative evidence that our model's self-reflective mechanism leads to a fundamentally more robust memory system.

Prasanth K K, Shubham Sharma

Many real world categories are multimodal, with single classes occupying disjoint regions in feature space. Classical linear models (logistic regression, linear SVM) use a single global hyperplane and perform poorly on such data, while high-capacity methods (kernel SVMs, deep nets) fit multimodal structure but at the expense of interpretability, heavier tuning, and higher computational cost. We propose the Geometric Mixture Classifier (GMC), a discriminative model that represents each class as a mixture of hyperplanes. Within each class, GMC combines plane scores via a temperature-controlled soft-OR (log-sum-exp), smoothly approximating the max; across classes, standard softmax yields probabilistic posteriors. GMC optionally uses Random Fourier Features (RFF) for nonlinear mappings while keeping inference linear in the number of planes and features. Our practical training recipe: geometry-aware k-means initialization, silhouette-based plane budgeting, alpha annealing, usage-aware L2 regularization, label smoothing, and early stopping, makes GMC plug-and-play. Across synthetic multimodal datasets (moons, circles, blobs, spirals) and tabular/image benchmarks (iris, wine, WDBC, digits), GMC consistently outperforms linear baselines and k-NN, is competitive with RBF-SVM, Random Forests, and small MLPs, and provides geometric introspection via per-plane and class responsibility visualizations. Inference scales linearly in planes and features, making GMC CPU-friendly, with single-digit microsecond latency per example, often faster than RBF-SVM and compact MLPs. Post-hoc temperature scaling reduces ECE from about 0.06 to 0.02. GMC thus strikes a favorable balance of accuracy, interpretability, and efficiency: it is more expressive than linear models and lighter, more transparent, and faster than kernel or deep models.