arXiv subjects

Manu Ghulyani

Publications and source records attributed to Manu Ghulyani.

6 recordsLinked to original sources

arXiv2026

PACMS: Submodular Context Selection as a Pluggable Engine for LLM Agents

Conversational and tool-using LLM agents operate over a context window that fills from several directions simultaneously. As a session proceeds, the agent accumulates user and assistant turns, entries drawn from a persistent memory store, and often largest of all, the verbatim outputs of tool calls such as file reads, search results, and API responses. Once the cumulative context exceeds the model's token budget, the framework must decide what to keep. The prevailing mechanism is recency truncation, sometimes paired with periodic summarization. This is topic-blind: a fact established early in a session is discarded simply because it is old, even when the current user query is about exactly that fact; conversely, verbose but irrelevant recent material is retained. Agents that must recall information across many turns, the defining case for memory, are precisely where recency truncation fails. Existing alternatives sit outside the agent's assembly step. Retrieval augmented generation fetches external documents into the prompt but does not arbitrate the agent's \emph{already-present} pooled context. Context-compression methods reduce token count by rewriting or pruning text, but operate query-blind and lossily. Neither treats memory entries, conversation turns, and tool outputs as a single candidate pool to be selected from by relevance at the moment the prompt is assembled.

cs.IR↗

arXiv2023

Non-convex regularization based on shrinkage penalty function

Total Variation regularization (TV) is a seminal approach for image recovery. TV involves the norm of the image's gradient, aggregated over all pixel locations. Therefore, TV leads to piece-wise constant solutions, resulting in what is known as the "staircase effect." To mitigate this effect, the Hessian Schatten norm regularization (HSN) employs second-order derivatives, represented by the pth norm of eigenvalues in the image hessian, summed across all pixels. HSN demonstrates superior structure-preserving properties compared to TV. However, HSN solutions tend to be overly smoothed. To address this, we introduce a non-convex shrinkage penalty applied to the Hessian's eigenvalues, deviating from the convex lp norm. It is important to note that the shrinkage penalty is not defined directly in closed form, but specified indirectly through its proximal operation. This makes constructing a provably convergent algorithm difficult as the singular values are also defined through a non-linear operation. However, we were able to derive a provably convergent algorithm using proximal operations. We prove the convergence by establishing that the proposed regularization adheres to restricted proximal regularity. The images recovered by this regularization were sharper than the convex counterparts.

math.OC↗

arXiv2023

Compact Representation of n-th order TGV

Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of oscillations in reconstructions when directly generalizing TV-1 to higher orders (3 or more). Addressing this, Bredies et. al introduced a notable approach for generalizing total variation, known as Total Generalized Variation (TGV). This technique introduces a regularization that generates estimates embodying piece-wise polynomial behavior of varying degrees across distinct regions of an image.Importantly, to our current understanding, no sufficiently general algorithm exists for solving TGV regularization for orders beyond 2. This is likely because of two problems: firstly, the problem is complex as TGV regularization is defined as a minimization problem with non-trivial constraints, and secondly, TGV is represented in terms of tensor-fields which is difficult to implement. In this work we tackle the first challenge by giving two simple and implementable representations of n th order TGV

eess.IV↗

arXiv2021

Structurally Adaptive Multi-Derivative Regularization for Image Recovery from Sparse Fourier Samples

The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction, magnetic resonance imaging, and so on. Originally, the primary role of the regularization was to stabilize the computational inversion of the imaging forward model against noise. However, a recent framework pioneered by Donoho and others, known as compressive sensing, brought the role of regularization beyond the stabilization of inversion. It established a possibility that regularization can recover full images from highly undersampled measurements. However, it was observed that the quality of reconstruction yielded by compressive sensing methods falls abruptly when the under-sampling and/or measurement noise goes beyond a certain threshold. Recently developed learning-based methods are believed to outperform the compressive sensing methods without a steep drop in the reconstruction quality under such imaging conditions. However, the need for training data limits their applicability. In this paper, we develop a regularization method that outperforms compressive sensing methods as well as selected learning-based methods, without any need for training data. The regularization is constructed as a spatially varying weighted sum of first- and canonical second-order derivatives, with the weights determined to be adaptive to the image structure; the weights are determined such that the attenuation of sharp image features -- which is inevitable with the use of any regularization -- is significantly reduced. We demonstrate the effectiveness of the proposed method by performing reconstruction on sparse Fourier samples simulated from a variety of MRI images.

eess.IV↗

arXiv2021

Generalized Hessian-Schatten Norm Regularization for Image Reconstruction

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging process. In the past decades, total variation regularization, especially second-order total variation (TV-2) regularization played a dominant role in the literature. Two forms of generalizations, namely Hessian-Schatten norm (HSN) regularization, and total generalized variation (TGV) regularization, have been recently proposed and have become significant developments in the area of regularization for imaging inverse problems owing to their performance. Here, we develop a novel regularization for image recovery that combines the strengths of these well-known forms. We achieve this by restricting the maximization space in the dual form of HSN in the same way that TGV is obtained from TV-2. We name the new regularization as the generalized Hessian-Schatten norm regularization (GHSN), and we develop a novel optimization method for image reconstruction using the new form of regularization based on the well-known framework called alternating direction method of multipliers (ADMM). We demonstrate the strength of the GHSN using some reconstruction examples.

eess.IV↗

arXiv2019

Fast roughness minimizing image restoration under mixed Poisson-Gaussian noise

Image acquisition in many biomedical imaging modalities is corrupted by Poisson noise followed by additive Gaussian noise. While total variation and related regularization methods for solving biomedical inverse problems are known to yield high quality reconstructions, such methods mostly use log-likelihood of either Gaussian or Poisson noise models, and rarely use mixed Poisson-Gaussian (PG) noise model. There is a recent work which deals with exact PG likelihood and totalariation regularization. This method is developed using the log-likelihood of PG model along with total variation regularization adapts the primal-dual splitting algorithm, whose step size is restricted to be bounded by the inverse of the Lipschitz constant of PG log-likelihood. This leads to limitations in the convergence speed. On the other hand, ADMM methods do not have such step size restrictions; however, ADDM has never been applied for this problem, for the possible reason that PG log-likelihood is quite complex. In this paper, we develop an ADMM based optimization for total variation minimizing image restoration under PG log-likelihood. We achieve this by first developing a novel iterative method for computing the proximal solution of PG log-likelihood, deriving the termination conditions for this iterative method, and then integrating into a provable convergent ADMM scheme. The effectiveness of the proposed methods is demonstrated using restoration examples.

eess.IV↗