Related papers: A Stronger Soft-Covering Lemma and Applications
We show that in supersymmetric theories, knowing the soft theorem for a single particle in a supermultiplet allows one to immediately determine soft theorems for the remainder of the supermultiplet. While soft theorems in supersymmetric…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is…
Knowledge extraction is used to convert neural networks into symbolic descriptions with the objective of producing more comprehensible learning models. The central challenge is to find an explanation which is more comprehensible than the…
Recent large language models (LLMs) perform strongly on mathematical benchmarks yet often misapply lemmas, importing conclusions without validating assumptions. We formalize lemma$-$judging as a structured prediction task: given a statement…
Strong student models can learn from weaker teachers: when trained on the predictions of a weaker model, a strong pretrained student can learn to correct the weak model's errors and generalize to examples where the teacher is not confident,…
The use of deep learning-based techniques for approximating secure encoding functions has attracted considerable interest in wireless communications due to impressive results obtained for general coding and decoding tasks for wireless…
Earlier work on machine learning for automated reasoning mostly relied on simple, syntactic features combined with sophisticated learning techniques. Using ideas adopted in the software verification community, we propose the investigation…
From human tissue to fruits, many soft materials are coated by a thin layer of a stiffer material. While the primary role of such a coating is often to protect the softer material, the thin, stiff coating also has an important effect on the…
The software is changing rapidly with the invention of advanced technologies and methodologies. The ability to rapidly and successfully upgrade software in response to changing business requirements is more vital than ever. For the…
In problems of lossy source/noisy channel coding with side information, the theoretical bounds are achieved using "good" source/channel codes that can be partitioned into "good" channel/source codes. A scheme that achieves optimality in…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Metaphors play a significant role in our everyday communication, yet detecting them presents a challenge. Traditional methods often struggle with improper application of language rules and a tendency to overlook data sparsity. To address…
Lightweight cryptography is a novel diversion from conventional cryptography that targets internet-of-things (IoT) platform due to resource constraints. In comparison, it offers smaller cryptographic primitives such as shorter key sizes,…
Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
Knowledge distillation has been widely adopted in a variety of tasks and has achieved remarkable successes. Since its inception, many researchers have been intrigued by the dark knowledge hidden in the outputs of the teacher model.…