# created ```dataview LIST WITHOUT ID file.link FROM -"windsurf" WHERE file.cday = date(this.file.name) AND !startswith(file.folder, "windsurf") SORT file.cday ASC ``` # modified ```dataview LIST WITHOUT ID file.link FROM -"windsurf" WHERE file.mday = date(this.file.name) AND !startswith(file.folder, "windsurf") SORT file.mday ASC ``` --- # [[diary and thoughts]] #thought #diary --- # Understanding Trajectory in [[Semiotic Physics]]: A Detailed Explanation #llmtext #paper/environmentalaestheticsofai - this is an llm comment from this chat [raycast://extensions/raycast/raycast-ai/ai-chat?context=%7B%22id%22:%2236410118-A5D4-4789-B732-E08B61231F1F%22%7D] - about this text A Note on '[[Semiotic Physics]]' Let me break down exactly what the article means by "trajectory" with explicit detail and concrete examples. ### The Article's Definition The article provides a precise definition: "the term trajectory to mean the sequence of tokens—prompt plus generated-output-so-far—after each iteration of the autoregressive loop." This definition is deceptively simple but profoundly important. Let me unpack each component: ### What Happens in the Autoregressive Loop The article explains [[the process]]: "we have it roll out a continuous passage of text by predicting a token, appending that token to [[the prompt]], predicting another token, appending that, and so on." **Here's what this means concretely** (my elaboration with an example): Let's say we start with [[the prompt]]: "The scientist discovered" 1. **Iteration 1**: - Input to GPT: "The scientist discovered" - GPT outputs probability distribution over all tokens - Sample from distribution, get: "a" - Trajectory is now: "The scientist discovered a" 2. **Iteration 2**: - Input to GPT: "The scientist discovered a" - GPT outputs new probability distribution - Sample from distribution, get: "strange" - Trajectory is now: "The scientist discovered a strange" 3. **Iteration 3**: - Input to GPT: "The scientist discovered a strange" - GPT outputs new probability distribution - Sample from distribution, get: "pattern" - Trajectory is now: "The scientist discovered a strange pattern" And so on... ### The Trajectory as a Growing Object **Crucially** (drawing from the article): "the growing sequence of prompt+output text, repeatedly fed back into the loop, preserves information and therefore constitutes state, like the tape of a Turing machine." This means the trajectory isn't just the final output - it's the entire sequence at each moment in time. **My clarification**: Think of it as a movie rather than a photograph. The trajectory includes: - The starting prompt - The state after adding the first token - The state after adding the second token - And every intermediate state until completion ### Why "Trajectory" and Not Just "Output"? The article emphasizes [[this distinction]] by quoting janus: "when we talk about 'GPT's' capabilities, impacts, or alignment, we're usually actually concerned about the behaviors of an algorithm which calls GPT in an autoregressive loop repeatedly writing to some prompt-state..." **My elaboration**: The word "trajectory" captures several critical aspects: 1. **Path through semantic space**: Just as a physical trajectory traces a path through 3D space, a linguistic trajectory traces a path through the space of possible meanings 2. **Historical dependence**: Each point on the trajectory depends on all [[previous points]], not just the immediate predecessor 3. **Dynamic evolution**: The trajectory unfolds in time, with each token addition representing a discrete time step ### The Multiverse Aspect of Trajectories The article states: "every token in the generated trajectory is a branch point in the sense that other possible paths would be followed given different rolls of the sampling dice." **Let me make this concrete** (my example): Starting from "The scientist discovered a strange pattern", the [[next token]] could be: - "in" (leading to: "...pattern in the data") - "that" (leading to: "...pattern that defied explanation") - "of" (leading to: "...pattern of behavior") - "." (ending the sentence) Each choice creates a different trajectory branch. The article quotes janus: "text generated by GPT is analogous to an Everett branch in an implicit multiverse." ### Trajectory as the Unit of [[Analysis The]] article emphasizes: "In [[semiotic physics]], as is common in both popular and technical discourse, by default we talk about GPT as a generator of (linguistic) trajectories, not context-free individual tokens." **What this means practically** (my interpretation): - We don't study "the probability of 'cat' following 'the'" - We study how entire passages unfold: "The cat prowled through the moonlit garden, its eyes gleaming..." - We examine how semantic coherence is maintained across the full trajectory ### The State-Space View of Trajectories Though not explicitly detailed in this article, the trajectory concept implies movement through a state space. **My elaboration**: Each trajectory can be thought of as: 1. **A sequence of positions**: [token₁, token₂, token₃, ...] 2. **A path through embedding space**: Each token has a high-dimensional embedding, so the trajectory traces a path through this space 3. **A branching structure**: At each position, multiple continuations were possible ### [[Why This Matters]] for [[Semiotic Physics]] The article explains that researchers can "try to infer a common law that generated them all" by studying trajectories. **The trajectory concept is essential because** (my synthesis): - It's [[the level]] at which semantic phenomena emerge - It's what we actually observe and care about - It preserves the full context needed to understand GPT's behavior - It allows us to study dynamics, not just statistics ### A Complete Example Trajectory **Let me illustrate with a full example** (my construction): Initial prompt: "In the beginning" The trajectory evolution: 1. "In the beginning" → 2. "In the beginning was" → 3. "In the beginning was the" → 4. "In the beginning was the Word" → 5. "In the beginning was the Word," → 6. "In the beginning was the Word, and" → 7. "In the beginning was the Word, and the" → 8. "In the beginning was the Word, and the Word" → 9. "In the beginning was the Word, and the Word was" → 10. "In the beginning was the Word, and the Word was with" Each arrow represents one iteration of the autoregressive loop. The full trajectory at step 10 is the entire string: "In the beginning was the Word, and the Word was with". **The [[key insight]]**: This trajectory maintains semantic coherence (it's recognizable as the opening of the Gospel of John) despite being built token by token through probabilistic sampling. The "physics" of the system governs how such coherence emerges and is maintained. This is what semiotic physics studies: not individual token predictions, but the principles governing how meaningful trajectories unfold through semantic space, maintaining coherence while exploring the vast multiverse of possible continuations.