Dawar Jyoti Deka

Nilesh Sarkar, Dawar Jyoti Deka

Sparse autoencoders (SAEs) decompose transformer residual streams into interpretable feature dictionaries, yet the relationship between SAE width and causal influence on model output has not been systematically characterised. We introduce causal dimensionality kappa(L, M, T), defined as the effective rank of the expected Jacobian outer product at layer L, and show it can be estimated via the SAE width sweep paired with attribution patching. Across seven SAE widths from 16,384 to 1,048,576 features on Gemma-2-2B layer 12, representational capacity grows 15.6x while causal capacity grows only 4.35x: a robust separation we term the representational-causal wedge. A saturating fit yields kappa-hat approximately 1,990 with kappa-hat / d_model = 0.86 and participation-ratio lower bound kappa_PR approximately 280. Crucially, kappa is invariant to model scaling: Gemma-2-9B and Gemma-2-2B yield identical N_causal = 328 at the same SAE width despite a 3.46x parameter increase (the count is forced to 2% of SAE width by calibration; the substantive empirical claim is shape invariance of the AtP score distribution under matched seq=512 conditions). Across eight network depths kappa is constant while the absolute attribution threshold drops 20x from layer 1 to layer 23. Five controls (architecture invariance, threshold robustness, geometric privilege, synthetic ground-truth recovery, and a four-cell encoder/decoder ablation) pin down what kappa measures and what it does not. Our findings establish kappa as a measurable, model-intrinsic property of transformer layers: sub-linearly recoverable by SAE width, invariant to model scaling, and structured across network depth.

Dawar Jyoti Deka, Amit Sethi, Syed Mohammad Ali

Vision-language models enable open-vocabulary object grounding through natural language queries, under the implicit assumption that semantically equivalent descriptions yield consistent outputs. We examine this assumption using a controlled pipeline combining DETR for object proposals with CLIP for language-conditioned selection on 263 COCO val2017 images. We find that overlapping prompts such as "a person," "a human," and "a pedestrian" frequently select different instances, with mean instability of 2.11 distinct selections across six prompts. PCA analysis shows this variability is structured and directional, not random. Prompt ensembling does not improve quality and often shifts selections toward generic regions. We further show that text embedding proximity explains only 34% of grounding disagreement (r = -0.58), confirming that instability arises from the argmax selection mechanism rather than text-level distances alone.

Dawar Jyoti Deka

Interactive video segmentation models such as SAM2 have demonstrated strong generalization across diverse visual domains. However, under weak user supervision, for example, when sparse point prompts are provided on a single frame, their predictions often suffer from temporal instability, including flickering boundaries, object dropout, and inconsistent object extents across frames. These issues limit their reliability in downstream video understanding and control applications. In this paper, we propose an inference-time temporal probability smoothing method that improves the temporal stability of SAM2-based video segmentation without retraining or architectural modification. Our approach operates directly on per-frame segmentation probability maps and leverages optical-flow-based motion warping together with pixel-wise uncertainty estimates derived from segmentation entropy, and forward-backwards flow consistency. These signals are used to adaptively blend current-frame predictions with motion-aligned historical estimates, yielding temporally coherent segmentation outputs under weak prompts. We evaluate the proposed method on four diverse video sequences using a comprehensive set of frame-wise and temporal stability metrics, including motion-compensated IoU, boundary consistency, object persistence, and area volatility. Experimental results demonstrate consistent improvements in temporal stability over vanilla SAM2 inference while preserving spatial accuracy. The proposed framework is lightweight, model-agnostic, and well-suited for real-time, interactive video segmentation.

Dawar Jyoti Deka, Nilesh Sarkar

Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width $d_S$ can encode at most $d_S \cdot g(α)$ features, where $g(α) = 1/((1-α)\ln\frac{1}{1-α})$ is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure $F \approx 28{,}700$ features at $α\approx 0.992$ (critical width $d_S^* \approx 1{,}065$). Distillation into five student widths confirms the predicted monotonic floor ordering. The observed floor decomposes into a geometric component and a width-independent architectural baseline ($R^2 = 0.993$). Linear probing shows coarse concepts survive even 88% feature loss, revealing the floor arises from aggregate loss of fine-grained features in the importance distribution's long tail. Our results connect representation geometry to distillation limits and provide a practical tool for predicting distillation performance from SAE measurements alone.