How do latent and inference time computations enable large language models (LLMs) to solve multi-step reasoning? We introduce a framework for tracing and steering algorithmic primitives that underlie model reasoning. Our approach links reasoning traces to internal activation patterns and evaluates algorithmic primitives by injecting them into residual streams and measuring their effect on reasoning steps and task performance. We consider four benchmarks: Traveling Salesperson Problem (TSP), 3SAT, AIME, and graph navigation. We operationalize primitives by clustering neural activations and labeling their matched reasoning traces. We then apply function vector methods to derive primitive vectors as reusable compositional building blocks of reasoning. Primitive vectors can be combined through addition, subtraction, and scalar operations, revealing a geometric logic in activation space. Cross-task and cross-model evaluations (Phi-4, Phi-4-Reasoning, Llama-3-8B) show both shared and task-specific primitives. Notably, comparing Phi-4 with its reasoning-finetuned variant highlights compositional generalization after finetuning: Phi-4-Reasoning exhibits more systematic use of verification and path-generation primitives. Injecting the associated primitive vectors in Phi-4-Base induces behavioral hallmarks associated with Phi-4-Reasoning. Together, these findings demonstrate that reasoning in LLMs may be supported by a compositional geometry of algorithmic primitives, that primitives transfer cross-task and cross-model, and that reasoning finetuning strengthens algorithmic generalization across domains.
Frustration is the negative emotional state that arises from the unexpected omission, reduction, delay, or inaccessibility of an appetitive reinforcer. Building upon a century of discoveries since Edward C. Tolman’s pioneering 1925 work on expectancy, this review explores the multifaceted phenomenon of Frustrative Nonreward (FNR), a specific type of frustration. We synthesize psychological and biological perspectives to illustrate how FNR shapes motivation, aggression, conflict resolution, and partial reinforcement phenomena, as well as broader learning processes. By linking foundational animal studies with cutting-edge human research, we underscore the relevance of FNR to clinical conditions such as substance abuse, anxiety, and mood disorders. This integrative overview aims to deepen our understanding of how frustration dynamics operate across species and contexts, while highlighting its translational applications for future scientific and therapeutic advances.
Brachinite meteorites are typically linked to the olivine-rich A-type asteroids. In this study, however, they appear to exhibit unexpected spectral diversity. Spectroscopic analysis of seven meteorites from the brachinite clan reveals two distinct populations in band parameters, overlapping with both the A-type and S-complex asteroids. This dual association shows that a single meteorite group can originate from multiple asteroid taxonomies. Notably, one S-complex-like specimen, Northwest Africa (NWA) 14,635, displays band parameters similar to those of asteroid (65803) Didymos, the target of the European Space Agency's (ESA) ongoing Hera mission. These results underscore the value of spectroscopic characterization of poorly understood meteorite groups and identifying potential analogs that are highly relevant for current and future mission planning.
Let C subset of [0,1] be a Cantor set. In the classical C +/- C problems, modifying the "size" of C has a magnified effect on C +/- C. However, any gain in C necessarily results in a loss in Cc, and vice versa. This interplay between C and its complement Cc raises interesting questions about the delicate balance between the two, particularly in how it influences the "size" of Cc-C. One of our main results indicates that the Lebesgue measure of Cc-C has a greatest lower bound of 32.
This article introduces a computational method, called "Recapture of Diffusive Agents Particle Swarm Optimization" (RDA-PSO), designed to estimate the dispersal parameter of diffusive insects in mark-release-recapture (MRR) field experiments. In addition to describing the method, its properties are discussed, with particular focus on robustness in estimating the observed diffusion coefficient in the presence of uncertainty. It is shown that RDA-PSO provides a simple and reliable approach to quantify insect dispersal that can handle low recapture rates and uneven capture site distributions without the need for area corrections. Tests on synthetic data, for which the actual diffusion coefficient is known, show the method outperforms three techniques based on the solution of the diffusion equation, which are also introduced in this work. Examples of application to real field data for the yellow fever mosquito are provided.
