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This paper contributes to the set-theoretic side of understanding Keisler's order. We consider properties of ultrafilters which affect saturation of unstable theories: the lower cofinality $\lcf(\aleph_0, \de)$ of $\aleph_0$ modulo $\de$,…
Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…
Reasoning systems increasingly separate intermediate computation into private and public channels, creating evaluation cases that look similar in transcripts: independent co-derivation, direct access to private content, and indirect…
Pretrained molecular encoders have become indispensable in computational chemistry for tasks such as property prediction and molecular generation. However, the standard practice of relying solely on final-layer embeddings for downstream…
Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria, require specifying a model to select optimal designs. They are not model free and the optimal designs selected by them are not robust to model uncertainty. Recently,…
We identify a previously unknown calibration property of large language models: providing one confirmed intermediate fact toward a multi-step reasoning chain increases the model's confident-wrong-answer rate before full evidence eliminates…
Counterfactual examples are widely employed to enhance the performance and robustness of large language models (LLMs) through counterfactual data augmentation (CDA). However, the selection of the judge model used to evaluate label flipping,…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K…
Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures…
We study inference on the optimal welfare in a policy learning problem and propose reporting a lower confidence band (LCB). A natural approach to constructing an LCB is to invert a one-sided t-test based on an efficient estimator for the…
In fact, the broadcast nature of every transmitter makes it possible for other transceivers in the channel to overhear the broadcasted signal. The proposed idea in cooperative communication is to use these intermediate transceivers as relay…
Despite the success of large language models (LLMs) in natural language generation, much evidence shows that LLMs may produce incorrect or nonsensical text. This limitation highlights the importance of discerning when to trust LLMs,…
If $X$ is a topological space and $\kappa$ is a cardinal then $\mathsf{BA}_\kappa (X)$ is the statement that for each pair $A, B \subseteq X$ of $\kappa$-dense subsets there is an autohomeomorphism $h:X \to X$ mapping $A$ to $B$. In…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
A new class of semi-implicit numerical schemes for linear advection equation on Cartesian grids is derived that is inspired by so-called $\kappa$-schemes used with fully explicit discretizations for this type of problems. Opposite to fully…