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Codebook collapse is a common problem in training deep generative models with discrete representation spaces like Vector Quantized Variational Autoencoders (VQ-VAEs). We observe that the same problem arises for the alternatively designed…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…
Post-quantum cryptographic (PQC) algorithms, especially those based on the learning with errors (LWE) problem, have been subjected to several physical attacks in the recent past. Although the attacks broadly belong to two classes - passive…
We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH…
Quantum error mitigation is a crucial technique for suppressing errors especially in noisy intermediate-scale quantum devices, enabling more reliable quantum computation without the overhead of full error correction. Zero-Noise…
Deep Neural Network (DNN) has achieve great success in solving a wide range of machine learning problems. Recently, they have been deployed in datacenters (potentially for business-critical or industrial applications) and safety-critical…
For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…
We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…
Large Reasoning Models (LRMs) have shown exceptional reasoning capabilities, but they also suffer from the issue of overthinking, often generating excessively long and redundant answers. For problems that exceed the model's capabilities,…
Many positional encodings (PEs) are designed to exhibit long-term decay, based on an entrenched and long-standing inductive opinion: tokens farther away from the current position carry less relevant information. We argue that long-term…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
Continuous Relation Extraction (CRE) aims to incrementally learn relation knowledge from a non-stationary stream of data. Since the introduction of new relational tasks can overshadow previously learned information, catastrophic forgetting…
This paper presents algorithms for local inversion of maps and shows how several important computational problems such as cryptanalysis of symmetric encryption algorithms, RSA algorithm and solving the elliptic curve discrete log problem…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the…
When the predicted sequence length exceeds the length seen during training, the transformer's inference accuracy diminishes. Existing relative position encoding methods, such as those based on the ALiBi technique, address the length…
Fully homomorphic encryption (FHE) allows an untrusted party to evaluate arithmetic cir- cuits, i.e., perform additions and multiplications on encrypted data, without having the decryp- tion key. One of the most efficient class of FHE…
Eker{\aa} and H{\aa}stad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Eker{\aa}-H{\aa}stad's algorithm solves the short DLP in groups of unknown order. In this…
Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by…
Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), it is still a challenging task to design an efficient binary-coded DE algorithm. Inspired by the learning mechanism of…